Advances in
ATOMIC, MOLECULAR, AND OPTICAL PHYSICS VO L UME 50
Editors BENJAMIN BEDERSON New York University New York, New York HERBERT WALTHER University of Munich and Max-Planck-Institut ffir Quantenoptik Garching bei Mtinchen Germany
Editorial Board P.R. BERMAN
University of Michigan Ann Arbor, Michigan C. JOACHAIN Universit6 Libre de Bruxelles Brussels, Belgium M. GAVRILA F.O.M. Instituut voor Atoom- en Molecuulfysica Amsterdam, The Netherlands M. INOKUTI Argonne National Laboratory Argonne, Illinois CHUN C. LIN University of Wisconsin Madison, Wisconsin
Founding Editor SIR DAVID BATES
Supplements 1. Atoms in Intense Laser Fields, Mihai Gavrila, Ed. 2. Cavity Quantum Electrodynamics, Paul R. Berman, Ed. 3. Cross Section Data, Mitio Inokuti, Ed.
AD VANCES IN
ATOMIC, MOLECULAR
AND OPT CA/ PHYSICS Edited by
Benjamin Bederson DEPARTMENT OF PHYSICS NEW YORK UNIVERSITY NEW YORK, NEW YORK
Herbert Walther UNIVERSITY OF MUNICH AND MAX-PLANCK-INSTITUT FI21R Q U A N T E N O P T I K MUNICH, G E R M A N Y
Volume 50 2005
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Contents CONTRIBUTORS .................................................................................
vii
Assessment of the Ozone Isotope Effect K. Mauersberger, D. Krankowsky, C. Janssen and R. Schinke I. II. III. IV. g. VI. VII. VIII. IX. X.
I n t r o d u c t i o n ......................................................................... P h o t o c h e m i s t r y of the O x y g e n - O z o n e System .................... O z o n e Isotopes P r o d u c e d in N a t u r a l O x y g e n ..................... O z o n e F o r m a t i o n in Isotopically Enriched O x y g e n Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . R a t e Coefficients o f Isotope-Specific O z o n e F o r m a t i o n Processes .............................................................................. Theoretical Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The O z o n e I s o t o p e Effect in the E a r t h ' s A t m o s p h e r e ......... S u m m a r y a n d O u t l o o k ........................................................ A c k n o w l e d g m e n t s ................................................................ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
4 8 10
17 26
4o 49 51 52
Atom Optics, Guided Atoms, and Atom Interferometry J. Arlt, G. Birkl, E. Rasel and W. Ertmer I. I n t r o d u c t i o n ......................................................................... II. A t o m Optical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. A t o m s in Optical Micro-Structures: I n t e g r a t e d A t o m Optics a n d Q u a n t u m I n f o r m a t i o n Processing ..................... IV. C o h e r e n t A t o m Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The State-of-the-Art in A t o m I n t e r f e r o m e t r y . . . . . . . . . . . . . . . . . . . . . . VI. C o n c l u d i n g R e m a r k s ............................................................ VII. A c k n o w l e d g m e n t s ................................................................ VIII. References ............................................................................
55 56
58 66 73
82 83 83
Atom-Wall Interaction D. Bloch and M. Ducloy I. I n t r o d u c t i o n ......................................................................... II. L o n g R a n g e A t o m - S u r f a c e Interaction: Principles a n d N e a r - F i e l d Limit ...........................................................
92 94
Contents
vi
III. E x p e r i m e n t a l A p p r o a c h e s for the P r o b i n g o f A t o m - S u r f a c e I n t e r a c t i o n ............................................................................. IV. S R S p e c t r o s c o p y as a D i a g n o s t i c s T o o l o f the A t o m - S u r f a c e I n t e r a c t i o n ..................................................... V. N e w D e v e l o p m e n t s a n d P r o s p e c t s ........................................ VI. C o n c l u s i o n ............................................................................ VII. A c k n o w l e d g m e n t s ................................................................. IX. R e f e r e n c e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
107 125
136 146 147 147
Atoms Made Entirely of Antimatter: Two Methods Produce Slow Antihydrogen G. Gabrielse I. II. III. IV. V. VI. VII. VIII. IX. X. XI. XII.
I n t r o d u c t i o n a n d O v e r v i e w ................................................... M o t i v a t i o n s ........................................................................... I n g r e d i e n t s o f Slow A n t i h y d r o g e n ........................................ P r o d u c t i o n M e t h o d I: D u r i n g e + C o o l i n g o f ~ in a N e s t e d P e n n i n g T r a p ............................................................ B e y o n d C o u n t i n g H A t o m s .................................................. T h r e e B o d y H F o r m a t i o n , a n d R e l a t e d E x p e r i m e n t s .......... P r o d u c t i o n M e t h o d II" L a s e r - C o n t r o l l e d H P r o d u c t i o n ...... C o m p a r i n g the H P r o d u c t i o n M e t h o d s ................................ F u t u r e ................................................................................... C o n c l u s i o n s ........................................................................... A c k n o w l e d g m e n t s ................................................................. R e f e r e n c e s .............................................................................
156
162 168 175 185 195 198 200 200 208 210 210
Ultrafast Excitation, Ionization, and Fragmentation of C6o L V. Hertel, T. Laarmann and C.P. Schulz I. II. III. IV. V.
I n t r o d u c t i o n .......................................................................... P r e l i m i n a r i e s .......................................................................... I o n i z a t i o n , C h a r g e States, a n d F r a g m e n t a t i o n ..................... A b o v e T h r e s h o l d I o n i z a t i o n ................................................. Multielectron Excitation, Energy Redistribution, and C o u p l i n g to N u c l e a r M o t i o n ................................................ VI. C o n c l u s i o n a n d O u t l o o k ....................................................... VII. A c k n o w l e d g m e n t s ................................................................. V I I I . R e f e r e n c e s .............................................................................
219
223 240 255 260 277 279 279
INDEX ..............................................................................................
287
CONTENTS OF VOLUMES IN THIS SERIAL .........................................
299
Contributors
J. ARLT (55), Institut fiir Quantenoptik, Universit~it Hannover, Welfengarten 1, D-30167 Hannover, Germany G. BIRKL (55), Institut ffir Quantenoptik, Universit/it Hannover, Welfengarten 1, D-30167 Hannover, Germany D. BLOCH (91), Laboratoire de Physique des Lasers, UMR 7538 du CNRS, Universit4 Paris l03, 99 Av JB Cl4ment, F-93430 Villetaneuse, France M. DUCLOY (91), Laboratoire de Physique des Lasers, UMR 7538 du CNRS, Universit6 Parisl03, 99 Av JB C16ment, F-93430 Villetaneuse, France W. ERTMER (55), Institut ffir Quantenoptik, Universit~it Hannover, Welfengarten 1, D-30167 Hannover, Germany G. GABRIELSE(155), Harvard University, Cambridge, MA 02138, USA I.V. HERTEL (219), Max-Born-Institut, Max-Born-Str. 2a, D-12489 Berlin, Germany, and Free University of Berlin, Dept. of Physics, Berlin, Germany C. JANSSEN (1), Max-Planck-Institut ffir Kernphysik, Bereich Atmosph~irenphysik, D-69029 Heidelberg, Germany D. KRANKOWSKY(1), Max-Planck-Institut fiir Kernphysik, Bereich AtmosphS.renphysik, D-69029 Heidelberg, Germany T. LAARMANN(219), Max-Born-Institut, Max-Born-Str. 2a, D-12489 Berlin, Germany K. MAUERSBERGER (1), Max-Planck-Institut f~r Kernphysik, Bereich
AtmosphS.renphysik, D-69029 Heidelberg, Germany E. RASEL (55), Institut fiir Quantenoptik, Universit~it Hannover, Welfengarten 1, D-30167 Hannover, Germany
vii
viii
Contributors
R. SCHINKE(1), Max-Planck-Institut ftir Str6mungsforschung, D-37073 G6ttingen, Germany C.P. SCHULZ(219), Max-Born-Institut, Max-Born-Str. 2a, D- 12489 Berlin, Germany
ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 50
A S S E S S M E N T OF T H E O Z O N E ISOTOPE EFFECT K. M A U E R S B E R G E R l, D. K R A N K O W S K Y 1, C. J A N S S E N 1 and R. S C H I N K E 2 1Max-Planck-Institut ffir Kernphysik, Bereich Atmosph6renphysik, 69029 Heidelberg, Germany; 2Max-Planck-Institut ffir Str6"mungsforschung, 37073 Gdttingen, Germany I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. P h o t o c h e m i s t r y of the O x y g e n - O z o n e System . . . . . . . . . . . . . . . . . . . . . . . . III. Ozone Isotopes Produced in N a t u r a l Oxygen . . . . . . . . . . . . . . . . . . . . . . . . . A. Experiments: Ozone Production, Pressure, and T e m p e r a t u r e Effects Observed in 490 3 and 5o0 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV.
V.
VI.
VII.
VIII. IX. X.
B. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ozone F o r m a t i o n in Isotopically Enriched Oxygen Mixtures . . . . . . . . . . . . . . A. Experiments: Selection of Gas Mixtures, Ozone Production, and Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rate Coefficients of Isotope-Specific Ozone F o r m a t i o n Processes . . . . . . . . . . . A. Concepts and Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Results of Relative Rate Coefficient Measurements . . . . . . . . . . . . . . . . . . C. Rate Coefficient Dependence on Temperature, Pressure, and Third Body . . Theoretical Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Classical Trajectory, R R K M , and Other Model Calculations . . . . . . . . . . B. Accurate Potential Energy Surface for Ozone . . . . . . . . . . . . . . . . . . . . . . C. Exchange Reactions and Their T e m p e r a t u r e and Isotope Dependences . . . D. Lifetimes of Ozone Complexes F o r m e d in O and 02 Collisions . . . . . . . . . The Ozone Isotope Effect in the E a r t h ' s A t m o s p h e r e . . . . . . . . . . . . . . . . . . . A. Troposphere: Experiment and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Stratosphere: Experiment and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Ozone Isotope Transfer to Stratospheric CO2 . . . . . . . . . . . . . . . . . . . . . S u m m a r y and O u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............ References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1 4 8 8 9 10 10 15 17 17 20 22 26 27 29 32 36 40 41 42 46 49 51 52
I. Introduction Over 20 years of research have been necessary to unravel one of the most unusual isotope effects in molecular physics. After the first atmospheric measurement in 1981 [1] of heavy ozone 5o0 3 in which ~80 is substituted for 160 and first laboratory experiments in 1983 [2], a unique isotope effect in
Copyright 9 2005 Elsevier Inc. All rights reserved 1049-250X DOI: 10.1016/S1049-250X(04)50001-0
2
K. Mauersberger et al.
[I
ozone was reported in 1985 by Heidenreich and Thiemens [3]. A small but equal enrichment in 490 3 and 5~ was found relative to expected values derived from the isotope distribution of the O2 gas. While ozone was generated in early experiments at low temperatures, subsequent investigations at room temperatures in two laboratories resulted in enrichments as high as 11% and 13 %, respectively [4,5]. This was in contrast to an analysis of the ozone isotope formation process, which predicted a small depletion for 5~ [6]. The enrichments, instead of small depletions, their magnitude of over 10% and the almost equally high values of 490 3 and 5~ demonstrated that a new and anomalous isotope fractionation had been found. This surprising effect was not explainable with standard mass-dependent processes, which dominate isotope research in geochemistry. By 1990, ozone produced in isotopically-enriched oxygen mixtures had expanded the range of the ozone molecules studied and included even the heaviest isotope 5403 with three 180 atoms. These results and others from later investigations [7,8] revealed that most of the isotopologues carried well-defined and sometimes very large enrichments, except the two, i.e., the triple-170 and -180 molecules, which were depleted by a lesser percent [8]. The pressure and temperature dependence of the ozone isotope anomaly was carefully investigated in laboratory experiments [5,9]. Stratospheric measurements, however, showed enrichments that scattered considerably [10]. Attempts to model the ozone isotope anomaly during this period failed to develop a fundamental explanation [11,12]. At first, processes related to the 03 molecular symmetry were thought to play a major role [13], but in 1997, a paper by Anderson et al. [14] opened the door for a new and unexpected explanation of the ozone isotope effect: Four isotope-specific formation rate coefficients of ozone were measured and it was found that molecular symmetry appears to have no significance in the enrichment process. The number of known rate coefficients was increased by Mauersberger et al. [15] and Janssen et al. [16] to a total of 15, revealing a surprising difference of 60% between the slowest and the fastest rates measured. Complex temperature-dependent kinetics was found in the association reaction of atomic and molecular oxygen [17]. Until now, mass dependence has always been the trademark of isotope research. The results of the oxygen-ozone system, however, showed for the first time that the fractionation observed for the isotopologues must be governed by other rules. This review presents the state-of-the-art description of the ozone isotope effect from a molecular perspective with some results from atmospheric investigations. It will be necessary to first introduce a number of aspects of the oxygen-ozone system because O and O2 contribute in specific ways to the final enrichments observed in the ozone isotopologue formation.
ASSESSMENT OF THE OZONE ISOTOPE E F F E C T
3
Special consideration will be given to the oxygen isotope exchange reaction, which plays an intrinsic role in the ozone formation and which has been known for many years to introduce a mass-dependent isotope effect [6]. More details about ozone in our atmosphere and the associated photochemistry can be found in a review by Wayne [18]. After the introduction of the oxygen system, essential laboratory experiments for ozone production and measurements will precede results and discussions of ozone isotopes produced in natural oxygen and in specific oxygen mixtures to unfold the complexity of the effect. It has been found that the high variability initially observed in ozone isotope enrichments was later reduced by a better control of parameters such as pressure and temperature, and the amount of ozone produced. In addition, the final isotopic analysis was considerably improved. For this reason, some experimental details are presented, which inform the reader how the data that we consider representative and accurate were obtained, while early atmospheric and laboratory experiments and results that showed large variations and uncertainties will only be briefly discussed or not mentioned at all in this chapter. The presentation of the laboratory experiments is followed by a detailed review of present-day theoretical concepts and models. After the discovery of the crucial role of ozone formation rates a number of kinetic models have been completed or are under development. Finally, recent atmospheric measurements will be presented to show that isotope values determined in a laboratory environment match those found in the atmosphere when relevant temperature and pressure are considered. A new challenge in molecular physics arises when isotope transfer processes from ozone to other atmospheric trace gases, particularly CO2, are investigated [19]. When all the facts are stated and the conclusions are drawn, a very unusual and complex isotope effect will emerge that can be traced from isotope-specific single channels in ozone formation rates to enrichments and depletions measured in the numerous isotopologues. A few explanations related to expressions and definitions used in this chapter are added here. The expression "mass-independent" has been repeatedly employed to characterize the ozone isotope effect in 490 3 and 5~ and in results observed for other trace gases that may be affected by reactions with ozone. Mass independence is a descriptive label that carries little scientific information except that the process in question is not standard mass-dependent, while mass dependence in chemical and physical processes is well-defined: Molecules that have ~80 substituted are about twice as much fractionated as those with 170 [2]. As this review will show, the multitude of ozone isotopologues and rate coefficient ratios require a clear and precise description related to physical parameters. For an overall
4
K. Mauersberger et al.
[II
characterization the term "anomalous" will occasionally be applied, while "mass-independent" will be avoided. The expressions "ozone isotopes" and "isotopologues" are often interchangeably quoted. They characterize the different atomic combinations found in molecules between mass 48 and 54 of which 4903 (160160170) and 500 3 (160160180) are the two prominent heavy isotopologues in the atmosphere. Throughout the chapter, we will label a mass or a mass peak just by its number and not with the dimensions of units (u) or atomic mass units (amu). Enrichments or depletions are calculated with the expression E ( % ) = [(Mo3/4803)meas/(Mo3/4803)calc -- 1] X 100% with mass M = 49 through 54. For ozone molecules of mass 50, 51 and 52, two different molecular combinations are possible (e.g., 170170170 or 160170180 of mass 51) and thus, the molecule has to be clearly specified. Using combinatoric, the calculated ratios are determined from the oxygen isotope distribution of the gas in which ozone is produced. Sometimes, E (%) is replaced with the &value such as a170 (in % or %o) to characterize enrichments in 4903 and likewise with a180 in case of 5~ Here, the expressions "isotope ratios" and "enrichments or depletions" will be used besides the standard expression "isotope fractionation." Finally, in all experiments reported in this chapter the amount of ozone generated was considerably lesser than the amount of O2 present in the system. This of course, is always the case in the atmosphere. For laboratory experiments, the small amount of ozone means that the isotope composition of the bath gas changes very little during ozone production.
II. Photochemistry of the Oxygen-Ozone System Already in 1930, Chapman proposed a photochemical model for pure oxygen reactions [20] to explain the presence of ozone in the atmosphere. Ignoring isotope-specific processes for the moment, the five Chapmanreactions that describe the interconnection between the three forms of oxygen are: 0 2 -~- h v
O+O+M 02 + 0 +
M
0 3 -f- h v
03 -'l-O
O+ O
(1)
> 02+M
(2)
> 0 3 --1-M
(3)
0 + 02
(4)
>
>
> 202.
(5)
II]
A S S E S S M E N T OF T H E O Z O N E ISOTOPE E F F E C T
5
Reaction (2) is too slow to take place in the stratosphere but is significant at altitudes above 100 km. The two important reactions for ozone formation are (1), where solar photons of at least 5.2 eV dissociate molecular oxygen in the middle and upper stratosphere, and reaction (3), which is the important process of ozone formation in a three-body reaction. Other processes leading to ozone have been searched for, but it is (3) that is of significance in troposphere and stratosphere. The final loss-process of "odd" oxygen is reaction (5). Particularly in (4) during ozone photolysis excited atoms and molecules can be produced such as O(1D) or O2(1A). It should be noted that many more reactions are active in the atmosphere to destroy ozone, often proceeding in catalytic cycles. The ozone formation rate equation has the well-known general form at low pressures: d[O3]/dt = k[O][O2][M],
(6)
where k is the formation rate coefficient, and the other three factors are the densities of atomic and molecular oxygen and of any molecule M including 02 that wil! stabilize the ozone from an excited collision complex. A typical value for k is 6 x 10 -34 cm6s-l[14], which signifies that the ozone formation is a rather slow gas kinetic process at normal atmospheric pressures. Turning now to the three stable isotopes of oxygen, 160, 170, and 180, of which the first one is much more abundant in air than the other two, a large variety of ozone molecules (or isotopologues) can be constructed. Because [160] >> [170], [180] only three are observable in atmospheric oxygen: 160160160 of mass 48 and the singly-substituted molecules 160160170 of mass 49 and 160160180 of mass 50. Depending on where the heavy atom resides, the molecules are either symmetric (Czv symmetry) with 170 or 180 at the apex or asymmetric (Cs symmetry) when the heavy atom is located at one end of the open isosceles triangle. The example of 5o03 shown below provides some detailed information on how the ozone isotopologues may be formed through various reaction channels:
180 + 160160 + M
160 + 160180 ~-- M
> 180160160 --]-M
(7)
) 160180160 --1-M
(8)
~ 160160180 -+- M
(9)
)' 160180160 + M.
(10)
6
K. Mauersberger et al.
[II
Already in 1991, Larsen et al. [21] reported evidence that insertion is not a likely process in ozone formation and thus reaction (8) will probably not make a significant contribution to the ozone molecules in the atmosphere. Similarly, for all isotopologues such isotope-specific channels can be identified. In case of the combination 160170180 of mass 51 a total of nine are possible, while for 170170170 and 180180180 there is only one. Inspired by the early results of unusual ozone isotope measurements [1], Kaye and Strobel investigated the ozone formation process for the atmospheric heavy isotope 5o03 [6]. The main focus of their paper was the role of the well-known isotope exchange reaction between atomic and molecular oxygen in their electronic ground state. Two of many possible exchange processes are shown below:
180 + 160160 ~ 180160 + 160
(11)
170 ..[_.160160 ~_ 170160 + 160.
(12)
These fast reactions determine the equilibrium abundance of atomic oxygen in an O2 gas [14]. The exchange cycles will be repeated numerous times before, in a three-body reaction, an ozone molecule will be produced. Because of the different zero-point energies (ZPE) of the participating O2 molecules the rate coefficients of the different channels are higher for exothermic processes, which in (11) and (12) proceed from left to right, and are lower for endothermic processes, which are from right to left (for (11), AZPE = 22 cm-1). Thus, the distribution of the three oxygen atoms in a gas mixture is governed by an exchange that will lower [170] and [180] compared to what would be expected from the abundance of isotopes in molecular oxygen. Kaye and Strobel [6] estimated, using the rate coefficients of the exchange reactions and the equilibrium constant, that a depletion of about 3% in 5o03 would result and, as Morton et al. [5] later showed, half as much in 4903. This fractionation is well-understood; it is a conventional massdependent isotope effect and it will increase in magnitude as the temperature of the gas in which atomic oxygen is produced decreases. While all exchange reactions are faster at low temperatures, the forward reactions will become more pronounced with decreasing temperatures [22], and therefore the density of [170] and [180] will rapidly decrease and correspondingly the fractionation of heavy oxygen increases as shown in Fig. 1. As a consequence the difference between the expected and the actual atomic isotope ratios will become larger. To somewhat emphasize this more: According to Anderson et al. [14] at 298 K the 180 density is about 7% lower than statistically expected and since only one reaction channel (180+180180+M) contributes to mass 54 there should be an isotope
II]
A S S E S S M E N T OF T H E O Z O N E ISOTOPE E F F E C T
-4
g-, .0
._o m c
/ "
,
,
J
-12
~
u.. -16 -20
// /
/ 100
200
300
400
Temperature (K)
F~6. 1. Temperature dependence of [170] and [180] densities in oxygen mixtures shown as fractionation with respect to the isotopic composition of molecular oxygen. Atomic oxygen is in its ground electronic state (3p).
fractionation of approximately - 7 % in 540 3 compared to 4803, assuming that the rate coefficient of formation is the same for both molecules. In contrast, experiments showed otherwise: 5403 was lower, by only - 4 . 5 % . This result demonstrates that in ozone formation another isotope effect must be present besides the one caused by the oxygen isotope exchange reaction. Not included in this chapter is a potential isotope effect in ozone due to thermal gas-phase decomposition such as: 03 + M
~ 02 -+-0-Jr- M,
(13)
which is the reverse reaction of (3). Very few isotope measurements have been made to investigate this particular ozone loss process [23,24]. They are difficult to perform due to secondary reactions including competing heterogeneous wall losses. As Chapman already pointed out [20], the process of thermal decomposition plays no role in the atmosphere where photolysis and direct chemical reactions dominate the ozone photochemistry. The initial results [23,24], however, suggest additional investigations. It has been repeatedly speculated that ozone photolysis may introduce an additional isotope effect [25]. Ozone is preferentially dissociated in the atmosphere in two wavelength r a n g e s - visible and UV. Morton et al. [5] showed with an uncertainty of 0.6% that the Chappuis band dissociation is isotopically neutral. Whether an isotope effect is introduced in the UV
8
K. Mauersberger et al,
[III
dissociation in the Hartley bands cannot be decided due to a lack of convincing results from very few experiments. Regardless, whether present or not, high-altitude atmospheric ozone isotope measurements show that the magnitude of this additional effect can only be small.
III. Ozone Isotopes Produced in Natural Oxygen A. EXPERIMENTS: OZONE PRODUCTION, PRESSURE, AND TEMPERATURE EFFECTS OBSERVED IN 490 3 AND 500 3
In the early years of ozone isotope research, natural oxygen (also called atmospheric oxygen) was the choice of gas in which ozone was produced to study in laboratory experiments the isotope fractionation. In atmospheric oxygen 160, 170, and 180 have an abundance of 0.99763, 3.7 x 10-4, and 2.00 x 10-3, respectively. Because of this distribution only 4 9 0 3 and 5o0 3, besides the major molecule 4803 are of significance. The expected ratios of the two heavy isotopes a r e [4803]/[4903] -- 899 and [4803]/[5o03] = 163. For the production of ozone a number of experimental methods have been employed which include, among others, electric discharge [2,5], microwave discharge [26], and illumination with UV light [4]. The O atoms in the gas will undergo extensive isotope exchange reactions before an ozone molecule is finally formed. After some time has elapsed, the production of ozone is stopped and the gas is directed through a liquid nitrogen trap in which ozone is condensed. Residual O2 is removed by pumping and a pure ozone sample is obtained, which will often be visible as a dark blue solid or liquid on a cold glass surface. It is of importance that for cryogenic collection of ozone sufficient amounts of gas must be produced to avoid isotope fractionation during condensation on a cold surface. It was soon recognized [2] because of the high abundance of 160 compared to 180 and 170 that the ozone isotope signature will be maintained after ozone has been recombined into O2. While direct ozone analysis with mass spectrometers requires a special gas inlet system (see Sect. IV), O2, however, can be directly admitted to the ion source of a mass spectrometer. This fact has greatly facilitated the early ozone isotope research. Any of the dissociation methods will also generate excited and possibly charged atoms and molecules, which were suggested to be responsible for or which contribute to the isotope effect. Morton et al. [5] described a method by which only ground state atoms and molecules are present to produce ozone. This technique called "photolysis-recycling" starts with a small amount of ozone that is placed into a glass bulb, which may have a volume of 2 to 3 1 and is silver-coated on the outside. Subsequently, the bulb is filled
III]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
9
with 02 gas to the final pressure considered for a particular investigation. Visible light from a 240 W tungsten filament lamp is directed into the glass sphere through a small opening in the reflective coating. Within the Chappuis bands, which cover the visible light range, ozone will be photolyzed and the resulting oxygen atoms w i l l - after extensive isotope exchange- react with the 02 in the bath gas to produce new ozone. The coating on the outside will increase the light path inside considerably. When the recycling of ozone approaches 100% (after approximately 45 to 60 min) the light is turned off and ozone is recovered from the mixture in a cold trap and analyzed for its isotope abundance with a standard mass spectrometer. The total gas pressure, the temperature and the collection efficiency of the ozone are carefully monitored. The photolysis-recycling process in ozone formation has proven to be the most reliable method to control the 02 composition as well as the pressure and temperature of the gas. It must be recognized, however, that the recycled ozone has not only been "re-formed" but has also been repeatedly photolyzed. In a UV dissociation process of 02 the final product ozone can be kept sufficiently low in density to avoid additional ozone photolysis. B. RESULTS AND DISCUSSION Initial ozone isotope studies showed a high variability in the enrichments of 490 3 and 5003 with depletions measured as well [26]. Observations in the stratosphere added to the uncertainty with respect to the actual magnitude of the effect [27,28]. Starting in 1988, however, and continuing into 1990 a series of papers [4,5,9] was published that showed convergence to a consistent set of laboratory data describing the pressure and temperature dependence of the isotope enrichments in 490 3 and 5~ It must be noted here that the expression "ozone isotope effect" is a very general, unspecific characterization of the two heavy isotopologues. For pure oxygen or for air pressures below 100 mbar and at room temperature and slightly above, the enrichments finally measured were 11 and 13% [8], respectively. There are two contributions to those enrichments: The oxygen isotope exchange reactions will lower [170] and [180] densities in the 02 gas and as a consequence the abundance of the two heavy ozone isotopologues will be lower by 1.2% and 2.4%, respectively [5], than statistically expected (see Sect. II). Therefore under the experimental conditions stated before, a specific isotope effect in the formation process must exist that has a magnitude of 12.2% for 490 3 and 15.4% for 5003. Both values, however, are only a characterization of the overall effect since different reaction channels will contribute to the isotopologues as shown for 5~ in equations (7) through (10).
10
K. Mauersberger et al.
[IV
The temperature dependence of the isotope fractionation strongly influences the magnitude of the enrichments in 490 3 and S~ Morton et al. [5] measured the change between 170 K and 370 K analyzing ozone generated in pure natural oxygen in a photolysis-recycling process. The average measured enrichments of both isotopologues are shown in Fig. 2(a) with calculated contributions from the isotope exchange reactions plotted in the lower part (b). A third part (c) is added to Fig. 2, which shows the magnitude of the ozone-specific isotope effect for 490 3 and S~ 3, displaying a strong change of the two isotopologues as the temperature of the gas changed in which 03 was produced. Figure 3 shows another phenomenon of the total ozone fractionation: As the pressure of the gas increases - here at room t e m p e r a t u r e - the enrichments start to decrease around 100 mbar, whereas the pressure dependence of the ozone recombination reaction deviates from the low pressure, third-order behavior only around 8 bar [29,30]. Ozone was also generated at pressures well below 10 mbar [26]. The magnitude of the enrichments decreases and a depletion is measured at very low pressures. A more recent result shown in Fig. 4 [31] reveals a massdependent fractionation with ~170 approximately half as low as S~80. From a similar experiment Morton et al. [5] concluded that the ozone isotope effect is a gas-phase process and that as the mean free path in the gas increases, O atoms reach increasingly the walls of the reaction volume. Ozone now is formed in a heterogeneous process, which does not fractionate the heavy isotopes. The depletions are a result of the diffusion process of O atoms and of the isotope exchange reactions. As stated above, the exchange processes are almost thousand times faster than ozone formation and thus will still be present in the low-pressure experiment. A comparison between the results of Figs. 3 and 4 emphasizes this fact again: in Fig. 3, enrichments remain high to pressures below 10 mbar when ozone was produced in a glass volume of a few liters, while in Fig. 4 a rapid decrease is already observed at 20 mbar, when ozone was generated in a small discharge tube, strongly supporting the concept of heterogeneous production of 03 on the walls of the apparatus.
IV. Ozone Formation in Isotopically Enriched Oxygen Mixtures A. EXPERIMENTS: SELECTIONOF GAS MIXTURES, OZONE PRODUCTION, AND MEASUREMENTS In the last section, pressure and temperature were introduced as the parameters that control the enrichments in 490 3 and S~ 3, which were
IV]
II
A S S E S S M E N T OF THE O Z O N E ISOTOPE E F F E C T 0
I
'
I
'
I
'
I
'
I
'
I
'
I
I
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I
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15
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C
E
o
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tc" C
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I
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15 v C (1.)
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t" C
10
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I
1O0
,
I
150
~
I
200
~
I
250
Temperature
,
300
350
I
400
(K)
FIG. 2. Temperature dependence of heavy ozone enhancement in natural oxygen [5]. (a) measured change in enhancements; (b) calculated contributions from isotope exchange reactions; (c) Ozone-specific enhancement change after substracting contributions of isotope exchange reactions from measured enhancements. (Adapted from J. Morton et al., 1990, J. Geophys. Res. 95, 901, Fig. 3, reproduced by permission of American Geophysical Union.)
derived from ozone produced in natural oxygen or in air. The isotopic analysis can easily be made with standard mass spectrometers when ozone in a sample is left to recombine into O2. Information on the ozone isotope anomaly can be substantially increased when additional isotopologues are
12 I
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.
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.
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i ii!ii i i iiiii i i ii!ii - ' -.- .! -. +. .- '. - ' i ..................... i, - i -. - i .- - i. ! i .' i . ..................... . . . . . . . . !iii-i-ii
2
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10
i i iiiii
..................... .i i.i.i.i.i .i . .... "..... ' ..... ".... ;:: ; ' ,::; ; ;:: ; :::::: : : .......... ~ ~ i~ . . . . . . . .i . :::: . .:: ::i:: . . . . .
-iii'i!i
w
::' ii::::~ . . . .
'syk t,o,s
o
m
o
-~--~--~-~-~i ................ ~.... i--i--~--i-~-ii .......... i .......... i..i..;,i.,~,'.; ..................... i--~---,'--Fi-h'---
::i::iii . . . . . .
12
:: :: i ii::i
9
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i i iiiii
16
:: ::::::::::::
-i--i~--!-N .......... T. ......... i']--i~--i-ii .......... : .......... i..i..i..i.i.5,003 s o l i d s y m b o ! s . ! . i i . . _ . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E
o
lllI
i i iiii
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12
O
[IV
K. Mauersberger et al.
E E m
o
(--
' ...... '.... :.:~. .,.:;.;.:.:; '; -: : :
6
. . . . . . .
,,,=
i. :: :: :: ::~,
i i iiiii 9 .................... !--i--i-~,-i-i!--- 4
.
2
1000
3
i i iiiil 456 10000
2
(mbar)
FIG. 3. Pressure dependence of ozone isotope enhancement in natural oxygen. Square symbols Ref. [5], downside triangles Ref. [4], and upside triangles Ref. [9]. (Adapted from J. Guenther et al., 1999, Chem. Phys. Lett. 306, 209, Fig. 1, with permission from Elsevier.)
''"I
15
'
9
10 O
v
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''
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tO t-
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-5
I
m
,,,,I
I
67
2
I
3
I
4
I I Illl
2
5 67
1
10
Pressure
3
4 5 6 7 100
(mbar)
FIG. 4. Pressure dependence of ozone isotope fractionation with ozone produced in a small flow-tube discharge experiment.
IV]
ASSESSMENT OF T H E O Z O N E ISOTOPE E F F E C T
13
included and analyzed. Their production requires a careful selection of the isotope distribution in oxygen mixtures, a proper gas admittance, and a mass spectrometer system. Described here are the selection of gases, the ozone production, and the analysis system to determine intensities of mass peaks from 48 to 54. Specific gas mixtures contained either excess 180 or were considerably enriched in 170 and their composition was carefully determined. Table I shows two mixtures [8,32], which permitted the formation of specific molecular combinations and minimized others with the same mass. Initially, the gas was carefully checked to be well-scrambled and, if necessary, electric discharge was employed to complete isotope mixing through isotope exchange reactions. Applying combinatoric, the statistically expected ozone isotope distribution was calculated for all molecules. As shown in the table, mixtures heavily enriched in 170 provide molecular combinations such as 160170170 of mass 50 or 170170170 of mass 51. On the other hand, oxygen gas with excess 180 but also containing some 160 and 170 will allow the measurement of 160160180 and 160170180 to separate those from the same mass containing 170. Corrections for small mass interference have been applied when necessary.
Table I Two examples of approximate ozone isotopic distributions produced in enriched gas mixtures [8,32] to determine selected isotopologues from mass 48 to 54. Isotopically enriched 02 mixtures
03 Mass no.
160(48%) 170(10~
160(23%) 170(73%) 180(4%)
160160160 160160170 160160180(95O//o) 160170170(5O/o) 160170180(99%) 170170170(1%) 160180180(95o/o) 170170180(5o//0)
160160160 160160170 160170170(98%) 160160180(20/o) 170170170(90%) 160170180(10o,/o) 170170180(92O./o) 160180180(8O//o)
53
170180180
170180t80
54
180180180
48 49 50 51 52
14
K. Mauersberger et al.
[IV
The ozone production is usually made by employing the photolysisrecycling technique [5] described in the previous section to ensure that the reactants are in the electronic ground state. A small ozone sample, often made by a discharge from the same mixture that is later used as bath gas, is placed into a glass sphere, which is filled thereafter with the specific 02 gas. Visible light photolyzes the ozone and after the isotope exchange reaction has cycled the atoms through the oxygen gas, new ozone molecules are produced. Similar but considerably more exchange processes besides those shown in (11) and (12) will be at work. It should be noted that 03 is always a minor constituent in the bath gas and thus during the recycling process the enriched mixtures, did almost not change their composition. Pressures are kept in the low-pressure region ( _< 100 mbar) and temperatures are carefully controlled and after many recycling times, typically requiring 45 to 60 minutes, the ozone sample is collected in a liquid nitrogen cooled trap. It is purified by removing excess residual 02 gas through pumping and finally admitted into a chamber that is attached to a gas analysis system. The special 02 gas mixture is recovered in a liquid helium cooled trap that followed the ozone collector. Care is taken so that the partial pressure of 03 during transfer to the trap is always high enough to be condensed without fractionation. For the direct analysis of ozone isotopologues a unique system was developed that permitted precision measurements of all ozone molecules in gas mixtures. Shown in Fig. 5 is a sketch of the mass spectrometer beam system (MSBS) [33], which has served for over two decades as a crucial instrument for trace gas analysis and isotope studies [34]. Its major parts are a small entrance orifice O1 into a vacuum system that contains two liquid helium bath pumps providing very high pumping speeds and permitting the formation of a molecular beam. The separation between the two chambers provides differential pumping, reducing the ambient pressure around the ion source in the second chamber by factors of about 101~ The gas density in the beam, however, will be over a factor of 100 above the background in the second chamber. The beam is directed collision-flee through the ion source of the mass spectrometer in which the ozone molecules cross the ionizing electron beam. A flag in front of the ion source can either block the beam for precision background measurements or is retracted for gas analysis. The mass spectrometer used throughout the ozone isotope measurements is a magnetic instrument [35]. The pressure in front of the entrance orifice ranges during the ozone experiments from a few tenths of a millibar to a few hundreds. An important feature of the analysis system is the absolute calibration of gases and gas mixtures at well-known pressures and with specific compositions. The calibration gas is placed into the volume in front of
IV]
ASSESSMENT OF THE O Z O N E ISOTOPE E F F E C T
15
FIG. 5. Mass spectrometer beam system(MSBS) for analysis of reactive and adsorptive gases (e.g., ozone).
orifice O 1 and the signals measured by the mass spectrometer can be directly related to the pressure or density of the gas. For the ozone studies, pure 4803 and pure 5403 as well as 320 2 and 3602 are frequently used when calibrating the 03 and the O2 scale. During calibrations and subsequent analyses the sample- and calibration-gas pressures in front of O1 are identical. The pressure range is selected in such a way that the response of the counting multiplier detectors are linear. It is possible to determine the isotope ratios for 32 to 36 (O2) and 48 to 54 (03) with an uncertainty of less than 1%.
B. RESULTSAND DISCUSSION A number of various oxygen isotope mixtures were used to investigate the multitude of ozone isotopologues. Figure 6 is a summary of values that were determined in two separate investigations [8,32]. The figure demonstrates that there is no simple mass dependence or any regularity related to either the molecular combination or the increasing mass of the isotopologues. The best characterization is perhaps that this isotope effect is "anomalous,"
16
[IV
K. M a u e r s b e r g e r et al.
20 -i
67~3
15 v
677 ~ 767
667 676
0
~= 10 cO
688 I 868
~668 686
787
0 x_
!
50 0 m
o
--()
788 878
666
I!
777 m S
888
-
48
49
50
51 52 Ozone mass (u)
53
54
FIG. 6. Measured enrichments or depletions of all possible ozone isotopologues. The labels 6, 7, and 8 represent 160, 170, and 180, respectively. Ozone was produced in well-scrambled enriched oxygenmixtures at about 90 mbar and at room temperature. (From K. Mauerberger et al., 1993, Geophys. Res. Lett. 20, 1031, Fig. 1, reproduced by permission of American Geophysical Union.)
which has been repeatedly quoted in publications but sometimes with the understanding that 6170 (of 4903) and 3180 (of 5o03) are almost or exactly equal. While this may be the case for the two isotopologues produced in natural oxygen at very low temperatures (Fig. 2), the multitude of the entire set of ozone isotopes does not show such a behavior and 490 3 and 5~ are of no special significance as Fig. 6 shows. Although heavily enriched O2 gas mixtures were used for 03 formation, the measured enrichments of 490 3 and 5~ remain almost the same as they were when produced in natural oxygen. The isotope effect does not depend on the composition of the original gas in which ozone is produced. Whenever an ozone molecule is formed in a well-scrambled gas mixture, the enrichment is - within the present measurement uncertainty- always the same for that isotopologue. Another interesting observation in Fig. 6 is the variability of the measured ratios. While the molecular combinations 160170180, which are exclusively asymmetric molecules, have a very high enrichment of about 18%, two isotopes actually show a depletion, with 180180180 twice as much as 170170170. This is a typical mass-dependent
v]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
17
relationship of the two symmetric molecules. Most of the others are composed of 1/3 symmetric and 2/3 asymmetric molecules (e.g., 160180160 VS. 180160160 and 160160180), and thus an average enrichment of about 12% can actually be estimated from the graph. These results led to the conclusion [13] that the ozone isotope effect has its roots in molecular symmetry. As the next chapter will show, this assumption was misleading. It should be noted that in the gas mixtures where photolysis and recycling takes place the isotope exchange reaction will contribute extensively to the departure from statistical values. Because it lowers the isotopologue abundance the net effect of enhancement or depletion will always be a combination of contributions from isotope exchange and of a specific ozone isotope effect as discussed in the last section. To demonstrate this for one example, ozone of mass 54 is formed by the single reaction 180+ 180180+ M. As explained in Sect. II the isotope exchange reaction will lower the 180 distribution in the gas about 7% compared to statistical values. Therefore the measured depletion of 4.5% is actually considerably lesser than that would be expected from just an isotope exchange.
V. Rate Coefficients of Isotope-Specific Ozone Formation Processes A. CONCEPTSAND EXPERIMENTS Ozone isotope research progressed from two heavy isotopologues in natural oxygen to a detailed study of all possible molecular combinations. Their isotopic fractionation are shown in Fig. 6. It must be recognized that those enrichments or depletions represent final products with contributions from isotope exchange reactions and particularly from different specific ozone formation channels. An example has been provided in Sect. II of all possible channels leading to 5o0 3 (Eqs. (7) through (10)). The rate coefficients for those reactions would provide another important information about processes that may control the observed ozone fractionations. This was recognized by Sehested et al. [36,37] although the rate coefficients they determined raised more questions then they were able to answer. Described in the following are two experiments of which the first led to the discovery of the origin of a kinetic isotope effect in ozone formation, manifested in its rate coefficients. Therefore this section of the chapter is the most significant part concerning the molecular aspect of ozone formation. The first of the two rate coefficient experiments was conducted by Anderson et al. [14] and designed according to the following concept: A gas mixture of N2:3202:3602 with ratios of 80:10:10 is placed into a small
18
[V
K. Mauersberger et al.
reaction cell attached to the orifice O1 shown in Fig. 5. The mixture is illuminated with UV-light from a deuterium lamp. The 3202 contains only molecules of 160 atoms, while 3602 is of nearly pure 180. The total pressure in the cell is 250 mbar, and initially no heteronuclear species 160180 are present. When the light is switched on, 160 and 180 atoms form and undergo with the oxygen molecules rapid isotope exchange reactions, resulting in a fast rise of 160180. At the same time, however, ozone is produced in a three-body reaction of 160 and 180 with the homonuclear oxygen molecules, and, if the measurement sequence is short, the heteronuclear 160180 plays only a minor role in the ozone production. The MSBS (Fig. 5) described in the previous section monitors the initial composition of the gas in the cell and the products that form during photolysis by directing a small molecular beam through the ion source. After the UV-lamp is switched off, the analysis continues as the pressure in the cell decreases. Four specific ozone formation channels can be investigated:
160 -t- 160160 -[- M
> 160160160 --1-M
k48
(14)
180 --1--160160 -'1-M
> 180160160 -[--M
kso
(15)
160 -~- 180180 -~- M , > 160180180 -~- M
k52
(16)
180 + 180180 + M ....> 180180180 + M
k54.
(17)
Anderson et al. explored the rate of 160180 formation to determine the atom number densities in the cell and to place the four rate coefficients on an absolute scale [14]. This aspect, however, will not be elaborated any further. Here, we will instead consider, as Mauersberger et al. [15] later did, only relative rates of single channel ozone reactions. Ratios are formed using the rate coefficient k48 to relate all others to the reference process 160 nt- 160160 % M with k48 = 6 x 10-34 cm6s -1 [14] or relative, with k]8 = 1.0. Shown here is an example for the 160-180 system involving reactions (14) and (16) to obtain the relative rate coefficient k~2 from the corresponding rate equations
k5---~2- [3202] d[5203]/dt k 4 8 - [3602] • d[4803]/dt "
(18)
With this procedure, the atomic oxygen concentration is eliminated and the ratio can be directly calculated from the increase in intensities of 4803
v]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
19
and 520 3 and the molecular oxygen concentrations in the cell. Derivatives can be replaced by differences in finite photolysis intervals for linear time evolution of the ozone molecules. The number of formation rates expanded considerably when highly enriched 170170 gas became available. The studies were extended using the Anderson experiment with the following combinations: 320 2 and 340 2 as well as 340 2 and 3602, all mixed with pure N2 to a pressure of about 250 mbar. Although the reference was always the standard rate of the 480 3 formation, the other rate coefficient for 540 3 (Eq. (17)) served as a transfer reference to k48. Anderson et al. actually derived k48 from the measured depletion of 540 3 depicted in Fig. 6. After additional studies by Mauersberger et al. [15], all rates with homonuclear oxygen molecules were known, but some crucial coefficients were still missing that involved the ozone formation with heteronuclear molecular oxygen. Janssen et al. [16] developed a tunable diode laser (TDL) experiment in combination with mass spectrometer analysis to measure the missing relative rates for the 160-180 system. This analysis was another important contribution to the discovery of the origin of the ozone isotope effect. Absorption spectroscopy of both rovibrational or purely rotational molecular transitions allows symmetry-specific detection of ozone molecules. In particular the branching ratio of the 160 + 160180 reaction, leading to the two different product channels shown in Eqs. (9) and (10), can thus be determined. Furthermore, the tentative assumption [21] that the ozone formation reaction is exclusively end-on can be verified by quantitative analysis of symmetric molecules resulting from a reaction like 180 + 160160. To accomplish this, three different types of ozone samples were admitted for spectroscopic analysis to a multi-path absorption cell that combined a small volume (0.3 1) with a long light path (18 m). Pressures in the cell were kept below 1 mbar to avoid pressure broadening, thus minimizing overlap of neighboring absorption lines. Analysis was performed by sweeping the light of a lead salt laser diode operating around 10 ~tm over several selected ozone lines. As in the mass spectrometer experiment, sample preparation was again a crucial step in obtaining the desired information about the ozone isotopes. The degree of atom insertion in the reactions Eqs. (15) and (16) with homonuclear oxygen molecules could be determined from an ozone sample that had been generated by UV photo-dissociation of a [3202]/[3602] = 1 mixture that also contained N2 like in the experiment by Anderson et al. [14]. Due to the anticipated low abundance of symmetric product molecules, 160180160 and 180160180, known intensities [38,39], with an accuracy of about 10% could directly be used for ozone isotopomer quantification. For determining the branching ratio in the 160+ 160180 and 180+ 160180
20
[V
K. Mauersberger et al.
reactions with sufficient accuracy, a special calibration method was necessary. It included a direct comparison of the absorption features of ozone, which was generated both at high and at low pressures (Fig. 4), to significantly reduce the uncertainty in the absorption lines. Details are presented by Janssen et al. [16]. B. RESULTS OF RELATIVE RATE COEFFICIENT MEASUREMENTS As soon as the four rate coefficients of Anderson et al. [14] were known, it became evident that the concept of molecular symmetry as an exclusive explanation of the anomaly was not tenable. Shown in the upper part of table II, the reaction 180 + ~80180 is with a relative rate of 1.03 comparable to the standard of 160+ 160160. The second and third, however, are 60% different although asymmetric molecules are formed. More relative rates were added [15] which are listed in the middle part. Although the ozone molecules are all asymmetric, the difference in the rates proves the fact that
Table II Results of relative rate coefficients. Process
Ozone mass
Relative rate
Reference
coefficient 160 at- 160160 ~ 160160160
48
1.0
[14]
180 + 160160 ~ 180160160
50
0.92
[14,16]
160 + 180180 ~ 160180180
52
1.50
[14,16]
180 + 180180 ~ 180180180
54
1.03
[141
170 --I-160160 ~ 170160160
49
1.03
[15]
170 + 180180 ~ 170180180
53
1.31
[15]
180+ 170170.__+ 180170170
52
1.03
[15]
160 + 170170 ~ 160170170
50
1.23
[15]
170 + 170170 ~ 170170170
51
1.02
[15]
160 + 160180 .._.+160180160
50
1.45
[16]
160 + 180160 ~ 160160180
50
1.08
[16]
180 q.- 160160 ~ 160180160
50
0.01
[16]
180 + 160180 ~ 180160180
52
1.04
[16]
180+ 180160 ~ 180180160
52
0.92
[16]
160 + 180180 ~ 180160180
52
0.03
[161
v]
ASSESSMENT OF T H E O Z O N E ISOTOPE E F F E C T
21
symmetry cannot be the driving factor in the search for a fundamental explanation of the ozone isotope anomaly. The table concludes with the results by Janssen et al. [16] who completed the set of rate coefficients for the 160-~80 system. Their data show that the association reaction is indeed an end-on process and insertion for the reaction 160 + 180180 is only a minor event. In the table, four reactions are shown with heteronuclear oxygen ~60180; three rate coefficients are between 0.92 and 1.08, while one has a high relative rate of 1.45. With 15 rate coefficients on hand, it is possible to calculate a number of isotopologue enrichments using the exchange reactions and the values of the rate coefficients in table II. The rate k~4 = 1.03 for the formation of ~80+~80~80 strongly supports the fractionation o f - 4 . 5 % measured repeatedly [8, 32] when ozone was produced in a well-scrambled enriched oxygen mixture. As outlined in Sect. II, isotope exchange reactions will lower the lSo density by 7.5% (Fig. 1) and thus with a rate coefficient of 1.03 a fractionation o f - 4 . 5 % would be expected as measured (Fig. 6). Janssen et al. [17] showed in detail for the 5o0 3 isotopologue that exchange processes and the three rate coefficients lead to an enrichment of E ( 5 o 0 3 ) - 12.9%, while 13.0% has been measured. Finally, Janssen [31] derived a reliable enrichment ratio of asymmetric molecules 160160180 (A) over symmetric 160180160 (S). This ratio is of significance in atmospheric ozone photolysis and for the production of O(1D). At a temperature of 360 K, the fractionation ratio is A/S = 1.74 4-0.09. The separate contributions of 160160180/160160160 and 16018016/0160160160 are 16.8 + 0.3% and 9.6 + 0.4%, respectively, for a total enrichment of 5o03 at 360 K of 14.4%. Ten years earlier Anderson et al. [40] had measured for the first time a less accurate ratio of A/S = 1.7 + 0.4. Initially, it was difficult to find some common physical relationships that would correlate with the large variability in the rate coefficients, since the mass of the ozone molecules offered no correlation as one would expect for a standard isotope fractionation. A clue was found in the isotope exchange reactions: During these processes an excited collisional complex is formed that can either dissociate back to the educts or, in an exchange reaction, will form a different atom and molecule (e.g., Eqs. (11) and (12)). While dissociation and exchange will take place, a third process, a collision with a bath gas molecule leading to ozone formation can occur. Janssen et al. [17] found that the difference in the zero-point energies (ZPE) of the O2 molecules before and after exchange correlates in an approximately linear fashion with the relative rate coefficients of the asymmetric ozone molecules. The symmetric ones, however, are about 20% lower than the linear fit line would predict as shown in Fig. 7. The graph suggests that endothermic exchange reactions carry high rate coefficients and thus the collisional
22
iv
K. Mauersberger et al.
1.s
..............................................
.,..., c 1.4 "6
I
I
i ...................
[
i '
i : !
9
,
-
o o 9
1.2
o
._> 1.1 m
~
I ................
1.3 .................................................. .............................................
-.L-
................
...............................................
1.0 _-_~. 0.9
i ......
f
I 1 ~
---! ........ .......... . ................... i ..............................................
-20
I
I
-10
0 A(ZPE)
10
20
(cm -1)
FIG. 7. Relative rate coefficients from table II vs ZPE differences in oxygen molecules participating in the isotope exchange reactions that would lead, if third-body collision occurs, to a specific ozone molecule. (From C. Janssen et al., 2001, P C C P 3, 4178, Fig. 1, reproduced by permission of the PCCP Owner Societies.)
complex must have a longer lifetime to favor stabilization. In contrast, exothermic reactions have lower rate coefficients as a result of shorter complex lifetimes. In a theoretical analysis Hathorn and Marcus [41] pointed this fact out in connection with other molecular parameters that may correlate with rate coefficients. Experimental data favor the difference in zero-point energies AZPE which has been recently confirmed by Gao and Marcus [42]. In the next section this will be further elaborated.
C. RATE COEFFICIENT DEPENDENCE ON TEMPERATURE, PRESSURE, AND THIRD BODY
Morton et al. [5] published the first clear evidence of a pronounced temperature dependence of 4903 and 5o0 3 enrichments (Fig. 2). The discovery of the high variability in the rate coefficients requires additional studies as to which rate will change with temperature or if all are affected that contribute to an isotopologue. Janssen et al. [43] used the Anderson experiment [14] to determine over a large temperature range the change of rate coefficients of the 160-~80 system. It must be recognized that the formation process of ozone, represented by 160 + 160160 + M, is highly temperature-dependent, increasing with decreasing temperatures [30].
v]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
23
Therefore, in all of the following studies, the ozone 480 3 formation will serve again as a reference and, whenever the temperature dependence or independence of relative rate coefficients is reported, it is measured against k48 that increases as T decreases. In a second, separate experiment the temperature dependence of the four isotopologues 4803, 5003, 5203, and 540 3 was studied in a well-scrambled enriched oxygen mixture in which 160 and ~80 were equally abundant. The photolysis-recycling technique was employed for ozone production. A cooling system provided stable temperatures between 130 and 320 K during the recycling process. Ozone recovery and analysis were performed as previously described (Sects. III and IV). A calibrated MSB system measured the intensities of the four ozone molecules. The first part of the experiment produced the temperature dependence of the two rate coefficients 160 ._.{_18O18 O and ~80 + 16O160, which have values at room temperature (table II) of 1.50 and 0.92. Shown in Fig. 8 are the changes of the two rates over a large temperature range. The higher rate remains almost constant while the lower rate for 180+ 160160 changes considerably as the temperature of the ozone production decreases. Results of the second part of this experiment, involving the three isotopologues 5003, 5203, and 5403, are shown in Fig. 9. As expected, 5003 has the same temperature dependence as measured for that isotope in natural oxygen [5]. An impressive change, however, shows the 540 3 isotope, which increases rapidly in depletion and has at 150 K a fractionation o f - 1 5 % . This
_, , , , I , , , , I I , , , I , , , ,_
1.4C "~-.o_
t,,i,-,
1.2
o
O
r
-
-
0
k(160+180180)
/ k(160+160160)
9 k(180+160160) / k(180+180180)
-
-
1.0-
rr 0.8-
-.............,,.iLl,,~'
- , , , , I , , , , I , , , , 25O 3O0
I,,,,350
Temperature of bath gas (K)
FIG. 8. Temperature dependence of measured rate coefficient ratios k50/k48 and k52/k54 according to Eqs. (14) to (17). (From C. Janssen et al., 2003, Chem Phys. Lett. 367, 34, Fig. 1, with permission of Elsevier.)
24
[V
K. Mauersberger et al. |
H_ r O r
,
,
|
|
,
,
,
,
|
|
|
0 -10 t
c] H" 0 N --20 ] - O ]~,~ [ II
100
,
,
~ /
~
O 5003Janssen et al. (2003) Janssen et al. (2003) -
3
O 5403Janssen et al. (2003)
,
,
l
200
- - - atomic Q/0 ,
,
,
,
I
.
.
.
.
300
I
400
Temperature of oxygen bath (K) FIG. 9. Temperature dependence of ozone isotopologue fractionation. Open symbols represent measured fractionation data, filled symbols are data from Morton et al. [5]. The dashed line shows the hypothetical fractionation of 540 3 due to 180 abundance only. (From C. Janssen et al., 2003, Chem Phys. Lett. 367, 34, Fig. 2, with permission of Elsevier.)
behavior can be explained entirely with the change in the 180/160 atom density in the gas. The 5403 has only one reaction channel, and thus the depletion in [180] will translate directly into its fractionation while the rate coefficient ratio k54/k48 will remain constant. Turning now to 5o03, three channels contribute to that isotopologue, but the temperature dependence of only one, ~ao + 160160, has been measured. As shown in Fig. 8, the rate continuously decreases and when considering this change, the 5~ fractionation can be completely explained. Although the temperature dependence of the other two rate coefficients involving 160180 is not known, the magnitude of the change in ~So+ 160160 suggests that those rates will remain constant and thus will have the same temperature dependence as k4a. Similarly for 5203, the high rate coefficient for 160+ laOlaO is almost constant with changing temperature. The decrease observed in the isotopologue enrichment must occur in either of the two other reactions involving 160~So, and thus Janssen et al. [43] suggested that it will be in the reaction 180+180160--~ 180180160 with a rate coefficient at room temperature of 0.92 and not in the reaction leading to the symmetric molecule. It has been concluded in the previous part of this section that the high rate coefficients are associated with endothermic exchange processes (Fig. 7). We now suggest, with the limited evidence available, that the exothermic exchange reactions in contrast to the endothermic or neutral show a pronounced temperature dependence that will lower the relative rate coefficients as the temperature of the gas decreases. This, in turn, will
v]
A S S E S S M E N T OF T H E O Z O N E I S O T O P E E F F E C T
25
explain the temperature dependence of the isotopologues 5~ and 520 3 produced in a 160-180 system. The Anderson experiment with the reaction cell has been used to investigate some other parameters that may influence the magnitude of the rate coefficients. Gfinther e t al. [44] used a 3202-360 2 mixture, first in N2 and later in noble gases, CH4, and CO2, to study the dependence of the highest and lowest rate coefficients as a function of pressure and bath gas. It was found that the different gases do not alter the two relative rate coefficients, therefore the stabilizing collision does not influence the isotope effect in ozone. The different gases do, however, change the overall rate of ozone production, a fact, which is well-known [30]. Figure 10 shows the results obtained when the pressure was changed over a wide range [45]. It was found that the high rate decreases, which in turn would mean that the isotopologue 5~ will carry a lower enrichment as the pressure is raised well above 100mbar. The increasing pressure will increase the collision frequency, and the lifetime advantage of the collision complex, which is expressed in the high rate coefficient, will slowly be lost. As discussed in
1.8
1.7 1.6
"~ 1.5 ~ 1.4 ._~ -~ 9 1.a 0
1.0
~
0.9 0.8 2
3 456
2
10 2
3 456
10 3 Pressure [mbar]
2
3 456
10 4
FIG. 10. Change in rate of coefficients when the pressure of the 160--180 system is varied between 50 and 4400 mbar. The partial pressures of the O2 gases are kept constant at 53 mbar each, while N2 made up the total pressure. (From J. Guenther et al., 1999, Chem Phys. Lett. 306, 209, Fig. 3, with permission of Elsevier.)
26
K. Mauersberger et al.
[VI
Sect. VII, atmospheric ozone isotope measurements confirm the pressure dependence when measurements between the troposphere and stratosphere are compared.
VI. Theoretical Perspectives Soon after the enrichments of the heavy isotopologues in the atmosphere were discovered, first models were developed to explain this anomalous effect [11,12,46]. They were developed before the relative rate coefficients for the formation of ozone became available. New measurements, however, in both the atmosphere and the laboratory showed the deficiencies of these early explanations and, therefore, they will not be reviewed here. In this section we will focus on attempts to explain the isotope dependence of the formation rate coefficient, which is at the heart of the ozone isotope problem. According to the Lindemann-Hinshelwood mechanism the formation of ozone is assumed to occur in two consecutive steps: O + 02 O~ + M
> O~
(19)
~ 03 -t- M.
(20)
Equation (19) describes the formation of a highly excited ozone complex, O~, after collisions of oxygen atoms with oxygen molecules and Eq. (20) represents the stabilziation of this complex in collisions with bath gas atoms or molecules M. In this picture, the low-pressure ozone formation rate depends mainly on the lifetime of the excited complex, r, and therefore, the dependence of r on the isotopic constitution is the crucial quantity which controls the formation rates. Equations (19) and (20) describe a complex process involving many aspects of molecular dynamics. A rigorous treatment has to start from a three-dimensional potential energy surface (PES) for the ground electronic state of O3(11A'). The PES has to be both accurate and global. It must describe the three equivalent 03 potential wells and the three O(3p) + E 2 ~ asymptotic channels. The dynamics of the three oxygen
02 (3 N
I
atoms on this PES - the formation of O~, the intramolecular energy redistribution and the fragmentation of the complex - can be studied either fully quantum mechanically, by means of classical trajectories, or by some combination of quantum and classical mechanics. The treatment of the stabilization process requires a six-dimensional (if M is an atom) PES, which describes the interaction between O~ and M. The collisions of highly excited O~ with M have to be treated most likely by classical trajectories.
VI]
ASSESSMENT OF THE OZONE ISOTOPE E F F E C T
27
If symmetry effects are important, exact or at least approximate quantum mechanical calculations, which have the symmetry built in, are mandatory. A rigorous theoretical investigation along these lines has yet to be performed. We first review several more recent attempts to model the isotope dependence of the ozone formation rate coefficients. Subsequently, we describe in some detail further progress toward more rigorous treatments. This is a status report; a conclusive explanation of the ozone isotope effect in terms of dynamical calculations is awaited.
A. CLASSICAL TRAJECTORY, R R K M , AND OTHER MODEL CALCULATIONS
An extensive classical trajectory study of the ozone formation process, with argon as M, and its isotope dependence has been performed by Gross and Billing [47] - before the relative rate coefficients discussed in the preceding section were known. The ozone PES used in this investigation was a modification of the ab initio PES calculated by Yamashita et al. (YMLL) [48]. An ad-hoc modification was necessary because of the unrealistically high barrier on the YMLL-PES along the reaction coordinate. The calculated 03 formation rates showed only a marginal dependence on the isotope composition. It is important to note that these trajectory calculations did not take into account the difference of the zero-point energies, AZPE, of the two fragmentation channels of 03 which are of substantial importance as we show later. In one of the early theoretical papers, Robert and Camy-Peyret [49] calculated rate coefficients based on an angular isotope effect in scattering processes distinguishing between identical and non-identical particles. By adjusting four parameters they were able to reproduce some of the laboratory results. Miklavc and Peyerimhoff [50] developed a model, in which the very first impact of O on O2 is the dominant step. They calculated the probability P0 ~ ~ for making a transition from vibrational state v - 0 to 1 in O2, using several approximations. They related this probability to the formation rate coefficient: The larger the initial energy transfer, the stronger the energy redistribution, the longer the lifetime of O~ and, therefore, the larger is the formation rate coefficient. After modifying some of the essential potential parameters, which enter their model, and defining effective masses Miklavc and Peyerimhoff could reproduce some of the the measured ratios of formation rates; the lower ratios, however, are consistently underestimated. There are several points of criticism to be made. First, the step from P0~ ~ to the relative rate coefficents is large. Second, the O-O bond strengths in the free oxygen molecule and in ozone are not comparable, i.e.,
28
K. Mauersberger et al.
[VI
using the frequency of the free oxygen molecule in the expression of Po--,1 is unreasonable. Third, the dissociation of the excited ozone complex and the influence of AZPE on the complex lifetime are not considered at all. Charlo and Clary [51] evaluated the isotope dependence of the energy transfer in collisions of O~ with Ar atoms using approximate quantum mechanical scattering calculations. In order to keep the treatment tractable, the bending degree of freedom of 03 was fixed; this limitation is not realistic, because the low-frequency bending motion contributes the most to the density of states in a triatomic molecule. The comparison of the calculated rate ratios with the measured ones is at present unsatisfactory and does not show a consistent trend. For example, the relative rate for the formation of ozone in collisions 180+ 3202 is about the same as in 160+ 360 2 collisions, in disagreement with the experimental observation. Marcus and coworkers, using statistical methods, have performed an extensive treatment of the isotope effect in ozone [41,42,52-54]. On the basis of the R R K M theory they calculated the exchange reaction rate coefficient, relative formation rate coefficients for the 15 known rates, and predicted others. The pressure dependent absolute formation rate coefficient and enrichment factors were also derived. The R R K M theory assumes that the mixing between all the internal degrees of freedom is so strong that the energy is completely randomized. The numerical task is to find the transition state (TS), to determine the number of channels perpendicular to the reaction coordinate which are accessible for a particular energy E and rotational state J, N(E, J), and to calculate the density of states, p(E, J). Since the R R K M theory is a quantum mechanical model, the difference of zero-point energies of the two fragmentation channels is included. AZPE enters the model through partitioning factors of the form Ya,b = Na,b(Na + Nb), where a and b specify the two product channels to which O~ can dissociate [41,52] (see Fig. 12 in [42]). To model the stabilization process the master equation approach was employed. By adjusting several parameters the experimental data were well reproduced. There are, however, several aspects of this theory which deserve a close assessment. While the assumption of complete energy randomization is commonly assumed to be well-founded for large molecules with many degrees of freedom, triatomic molecules near the dissociation threshold may be noticeably non-statistical [55]. Because the dissociation energy of ozone is very small, the average spacing between neighboring states is of the order of 10 cm -1 for total angular momentum J = 0; the mixing between states normally increases with decreasing energy spacing. Around the threshold a number of quantum states are assignable or, at least, their wave functions do not show the kind of nodal patterns typical for statistical molecules. This
VI]
ASSESSMENT OF THE OZONE ISOTOPE E F F E C T
29
indicates that the statistical assumption is not completely fulfilled for ozone. The pure symmetric stretch mode and the bending mode continue to high energies above the threshold with assignable, only weakly perturbed wave functions [56]. Various PESs, necessary for determining the TS, were used by Marcus and coworkers. In the model from the first two papers [41,42], PESs with a rather loose TS were employed and adjusted to reproduce the experimental exchange rate coefficient [57] and its temperature dependence [58]. Later, the YMLL-PES as modified by Gross and Billing [47] was applied by Gao et al. [54]. This PES has a tight TS and therefore is completely different from the two model PESs. Nevertheless, the results for the various potentials agree reasonably well with each other and thus it appears t h a t - within the R R K M m o d e l - the isotope dependent formation rate coefficients are largely independent of the PES. The necessary requirement is that the partioning factors Ya,b are similar. The two main parameters in the R R K M treatment, in addition to those used to adjust the PESs, are AE and 71. The first one is the average energy step for downward energy transfer in deactivation collisions of O~ with the buffer gas M. It enters in the master equation for the description of the stabilization process and was set as high as 210 cm -~. With the second parameter at 1.18, the densities of states of the symmetric molecules ABA are lowered and thus their relative formation rates are reduced. The two parameters have been adjusted to fit the measured relative formation rates for the two extreme cases: 0.92 for the reaction ~80 + 320 2 and 1.53 for the reaction ~60 + 360 2. The net effect of ~ > 1 is to match the experimental observation that the formation rates for the symmetric molecules are about 20% below the linear fit curve shown in Fig. 7. Despite the success of the R R K M approach, the next step in the model development will be the treatment of the isotope effect considering the intramolecular dynamics without statistical assumptions. Discussed next are the critical factors in such a process. Presented also are early results by Babikov, Schinke, and their coworkers.
B. ACCURATE POTENTIAL ENERGY SURFACE FOR OZONE
An accurate and global PES for the electronic ground state of ozone was only recently calculated by Siebert et al. [56,59]. It has a complex structure with a total of seven potential wells. First, there are the three identical wells with Czv symmetry representing the normal ozone molecule. The number of three results from the permutation of the three oxygen atoms. These three potential wells are separated by high barriers, so that each well can be
30
K. Mauersberger et al.
~"
[VI
6.0
180
5.5
160
5.0
140
4.5
120 100 "~
4.0
9
80
3.5
60
3.0
40
2.5 2.0 I
2
I
2.5
I
3
I
3.5
I
4
2
I
2.5
r.~
o
I
3.5
Rl[ao]
I
4
I
4.s
|
5
4.5
60
Rl[[ao]
FIG. 11. Two-dimensional representations of the ground-state PES of ozone. R1 and R2 are the two bond distances of the end atoms to the center atom and ~ is the bond angle. In (a) the bond angle is ~ = 116.8~ and in (b) the bond distance R2 is 2.409a0.
considered separately, except for energies close to the dissociation threshold and above it. Each well is connected to two shallow van der Waals (vdW)like wells. The vdW-like wells and the deeper 03 wells are separated by tiny barriers. The seventh minimum has D3h symmetry and represents cyclic ozone [60]. It is separated from the other wells by a high rim, which is the result of an avoided crossing between the lowest two states with 1A' symmetry, and therefore does not play any role in the low-energy kinetics. Figure 11 shows two-dimensional representations of the PES as contour plots. Figure 1 l(a) shows that no significant barrier hinders the formation of O~ in collisions of O and O2 or the exchange of one atom. Figure 11 (b), on the other hand, demonstrates that the TS around ~ ~ 120 ~ and R2 ~ 3.8a0 is tight; the bending frequency at the TS is 267 cm -~ [56]. Because of the high barrier for angles between 60 ~ and 90 ~ direct insertion, i.e., 160 -i- 36 0 2 ---+18 0 1 6 0 1 8 0
is
not possible at
low collision
energies. However,
the following mechanism is possible [61]: 160 ..1_36 0 2
> 16018018 0
> 16018 0 . . . 180
) 180160180
> 18016 0 . . . 18 O
(21)
VI]
ASSESSMENT
OF THE
OZONE
ISOTOPE
EFFECT
31
where dots indicate loosely bound complexes. The third step is a rotation of the diatom within the vdW complex. This mechanism seems to exist as the small formation rate of 0.029 for the process in Eq. (21) shows. The ground-state PES of ozone has a peculiar edge-like shape as O and O2 separate. Figure 12 shows the potential energy along the minimum energy path. The sudden change of the slope around 3.8a0 may be interpreted as the result of strong interaction with a higher excited electronic state [62]. A possible candidate for this mixing is the third singlet state with 1A' symmetry, the state which is responsible for the Hartley absorption band [63]. 1.2
I
I
I
s ....
1.0
I
". ....
I
- . . . . . .
7~
~o ....~
9...............
0.8
> .~. t.u
I
I
I
I
I
I
VTZ
.......
J-
voz vsz cBs
---
i-
0.6
I
.-.
i-
....
_
i i "\-
o oo
i i:,,~-
!i;i i, ",<'..~
0.4
-0.05
0.2
I i
3
i
I
I
I
I
4
5
6
7
8
9
R1 [ao] 0.0
3
4
5
6
7
8
9
R1 [ao] FIG. 12. Cuts along the minimum energy path of the O + 0 2 potential energy surface for different atomic basis sets: cc-pVTZ, cc-pVQZ, and cc-pV5Z; CBS represents the complete basis set limit. All curves are normalized to E = 0 at the respective global minimum. The inset shows the long-range behavior. Here, the normalization is such that E = 0 corresponds to the value at R1 = 9a0. (From P. Fleurat-Lessart et al., 2003, J. Chem. Phys. 118, 610, Fig. 1, with the permission of the American Institute of Physics.)
32
K. Mauersberger et al.
[VI
The barrier, which marks the TS, strongly influences the kinetics of ozone and therefore it is important to know its height precisely. Calculating the potential energy along the minimum energy path for different atomic basis sets [62,64] shows that the dissociation energy is increased; the result for the complete basis set (CBS) extrapolation is in excellent agreement with the experimental value. Furthermore, the dissociation barrier is clearly pushed below the asymptotic energy of the products (Fig. 12) and therefore it is more reasonable to speak of a "reef" rather than a barrier. Previous electronic structure studies [48,65] predicted considerably higher barriers. Although the electronic PES has only a tiny barrier, the adiabatic potential curves, which also take into account the kinetic energy and which are at the heart of the statistical calculations of Marcus and coworkers, have pronounced barriers as a result of the strong angle dependence of the TS region [62]. Combining the PES of Siebert et al. [56] and the CBS results for the minimum energy path, a hybrid PES was constructed [66]. The new PES has the correct dissociation energy, describes the TS region according to accurate electronic structure calculations for ozone, and it reproduces well the many experimentally known vibrational transition energies [62]. The good agreement with experimentally determined vibrational energies does not probe, however, the accuracy of the PES in the TS region: The bound states, for which experimental data are available, do not extend sufficiently far into the dissociation channels. In the absence of state and energy resolved cross sections the rate coefficent for exchange reactions, k(T), its temperature dependence, and its dependence on the isotopes involved are the only quantities for assessing the accuracy of this part of the PES.
C. EXCHANGE REACTIONS AND THEIR TEMPERATURE AND ISOTOPE DEPENDENCES
The atom exchange reaction in its general form O + 0 2 ~ 0 2 nt- O is one of the key reactions in the ozone kinetics. The first reliable value for the 300 K rate coefficient was determined by Anderson et al. [57]. Classical trajectory studies of this reaction - using various types of PESs - have a long history [47,67-69]. Since the exchange rate coefficient depends on the shape of the PES in the TS region [62], it is not difficult to adjust this part of the PES in such a way that good agreement with the experimental value is obtained, as was done in some of the earlier theoretical investigations as well as in the R R K M treatment.
vi]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
33
C.1. Temperature dependence The exchange reaction was revisited with the new PES using classical trajectories [62]. Quantum mechanical calculations, which inherently include effects such as tunneling, interferences and scattering resonances, are desirable. Because of the relatively deep potential well and the three heavy atoms, such calculations, however, are complicated and very time consuming. At first, exchange reaction cross sections, ~j(Ee), have been calculated as functions of the collision energy Ee and the initial rotational state j of the reactant diatom. The main feature of the cross sections is the strong dependence on j: For collision energies in the region important for calculating the room-temperature rate coefficient, ~j(Ee) rapidly decreases with j. As a consequence of the narrow TS of the PES it becomes more difficult for O and O2 to form a complex when O2 is rotating faster [62]. The strong j dependence influences the temperature behavior of k(T) calculated by Boltzmann averaging of the cross sections over Ee and j. An electronic degeneracy factor f(T) [47] was introduced in order to approximately account for the fact that a total of 27 nondegenerate PESs correlate with the reactants O(3p) + 0 2 (3. ~ g ) but only one of them is reactive [70]. The calculated k(T) is almost independent of T, despite the energy dependence of the individual ~j which hints toward an increase of k with temperature. With increasing T, however, higher and higher rotational states contribute to the rate coefficient and since their cross sections decrease with j, the net effect is an almost T independent rate coefficient. The experimental exchange rate coefficient shows a slightly negative temperature dependence [22,58], which most likely also has its origin in the strong j dependence of the cross sections. The agreement with the measured exchange reaction rate coefficient is not satisfactory with the calculated rate being too small by a factor of 4-5 at low temperatures [62] and by a factor of 2-3 at room temperature. Some effect apparently is not included in the calculations, an effect which increases the rates and which is more important at low temperatures and thus, low energies. There are several possible explanations for this shortcoming. First, the PES, especially its shape in the TS region could be flawed. All recent highlevel electronic structure calculations agree in that there is a small barrier below the O + 02 asymptote [56,64,70]. The precise height of this barrier is, of course, difficult to determine. Calculations in which the barrier is artificially erased yields reasonable agreement with the measured rate coefficient [62]. The extent of this modification, however, is outside the assumed uncertainty of the ab initio calculations. Second, the neglect of x
34
K. Mauersberger et al.
[VI
quantum mechanical effects such as tunneling may be responsible for the underestimation. On the other hand, the first converged quantum calculation of the reaction cross section for j = 0, using the original PES of Siebert et al. [56], yielded satisfactory agreement with the corresponding trajectory calculation [71]. As a third possibility, remains the influence of nonadiabatic transitions among the 27 electronic states, which all correlate with the ground state products [70]. In principle it is possible that transitions among these states may increase the reactivity. First calculations in which only the spin-orbit coupling is included do not give the desired increase of the reactivity [72]. C.2. Isotope dependence The efficiency of the exchange reaction depends on the isotopes involved. Anderson et al. [14] were the first to realize that the rate coefficients for the reactions 180 _~_3202
> 180160 +16 0
(22)
160 + 3602
), 160180 +18 O
(23)
are not identical and derived a value of a b o u t 1.24 for the ratio at room temperature. These two reactions are independent and not just forward and backward reactions as reactions (11) or (12) in Sect. II. The isotope dependence of the exchange reaction may have a similar origin as the isotope dependence of the ozone formation reaction and therefore it is worthwhile to study it, both experimentally and theoretically. Because the stabilization process is not involved, the calculation of ~ is much simpler than the calculation of ratios of the formation rate coefficients. Moreover, it allows to test methods to incorporate AZPE into the classical treatment. Reaction (22) is exothermic with AZPE = 22 cm -1 whereas reaction (23) is endothermic with 23 cm -1 and therefore it is expected that the first reaction is faster than the second one. The exo- and endothermicities are only about 5% of the average kinetic energy (2k~T) at room temperature and therefore a difference of 20-30% in the corresponding rate coefficient is surprising. The ratio 7~ has been recently measured in the range of 230-350 K [22] and a significant negative temperature dependence (Fig. 13) has been observed: 7~ = 1.27 exp [(50 9 4 0 ) ( K / T - 1/300)]. As the average collision energy decreases the endothermicity becomes more pronounced with the result that 7~ increases with decreasing temperature. In the same
7~-~kls+1616/k16+1818
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
VII 1.6
I
I
35
I
1.5 PST rr
if}
1.4
11) 133 tcO
1.3
x
o o L,--
exp.
1.2
r.,..
1.1
~
1.0 200
-"
~
~
~
RRKM
i
t
J
250
300
350
400
T[K]
FIG. 13. The ratio of the exchange reaction rates, 7E, as a function of temperature. Comparison of the experimental ratio (filled squares and the line labeled exp.) and the results obtained with two classical trajectory methods labeled (1) and (2). In (1) AZPE is incorporated into the PES by adding a correction term while the ZPE of O2 is not accounted for. In (2) the PES is not modified and the reactant diatom is started with its correct ZPE. Only trajectories l e a d i n g - after they are finished- to vibrational energies of O2 larger than the corresponding ZPE are counted, thus AZPE is also accounted for. The two dashed lines represent the statistical ratios with the transition state defined by the barriers of the adiabatic potential curves (RRKM) or defined at infinite O + O2 separations (PST).
investigation [62] it is shown that trajectory methods, in which AZPE is
phenomenologically incorporated, are able to satisfactorily reproduce the measured ratio of exchange rates, especially its T dependence (Fig. 13). On the other hand, methods which do not include AZPE yield a rate coefficient ratio that is independent of temperature. We also note, that the results of two types of statistical models, RRKM and phase-space theory (PST), are in poor agreement with the experiment.
36
K. Mauersberger et al.
[VI
Ratios similar to 7Z have been calculated [62] also for the corresponding pairs involving 160/170 and 170/laO; in these cases the differences of zeropoint energies are approximately 4-11 cm -1 and 4-10 cm -1, respectively. Intuitively, the enhancement 7~-1 decreases by about a factor of two and the temperature dependence becomes noticeably weaker. The essence of this combined experimental and theoretical study is that AZPE is indeed an important factor for the isotope exchange reaction at low and intermediate temperatures.
D. LIFETIMES OF OZONE COMPLEXES FORMED IN O AND 0 2 COLLISIONS
D.1. Classical calculations including Z P E differences
At low pressure the lifetime r of the O~ complex is the dominant quantity which determines the formation rate constant. Therefore, in order to unravel the ozone isotope effect it is useful to first investigate the dependence of the lifetime on the isotope constitution. This has been done by Schinke et al. [73] using the trajectory method (1) described in Fig. 13. Calculations have been performed for a range of collision energies and initial rotational states of 02, j. For each complex-forming trajectory r is defined as the time between the entering of one of the deep ozone wells and the leaving of this well. The average lifetime is taken as the average of r over all complex forming trajectories. Figure 14 depicts r as function of Ee for the three complexes 4803, 1803202 and 1603602 formed in collisions 160+3202, 180+3202 and 160-I-3602, respectively. For all energies the lifetime for the complex 1603602 is the longest and the lifetime for 1803202 is the smallest. The differences are substantial at very low energies, but rapidly decline with increasing Ec: As energy increases the tiny zero-point energy difference loses its importance. The results in the inset prove that it is AZPE which leads to the isotope dependence of r. In this study, AZPE is artificially introduced, despite the fact that the three atoms are identical. The results indicate a linear relationship between r and AZPE; the slope decreases with Ee. As pointed out in Sect. V, complexes formed in exothermic reactions have longer lifetimes than complexes created via endothermic reactions. The calculated relative lifetimes (with respect to 4803) show the same qualitative trend as the measured formation rate coefficients. However, in order to make a quantitative comparison between experiment and theory, the lifetimes have to be used in some approximate kinetic model for the recombination of ozone including thermal averaging over energy and rotational state. Work in this direction is in progress.
VII
37
A S S E S S M E N T OF THE O Z O N E ISOTOPE EFFECT 500
i
1
.
(a)
.
!
.
.
i
.
240 220
400
-
2OO
0
180 160
300
140
E
0
-~9 200
D ~
120
~~176 -:~o -1'o
0 >
0 0 9 []
100
Oj ~ 4803
9
/
~
[]
;
A ZPE
1'o
2'o
ao
1603602
gJ
~aoaeoe 0
0
I
I
100
I
I
200
I
I
300
I
400
Ec[cm-1] FIG. 14. (a) The average trajectory lifetime r as a function o f the collision energy Ec for the complexes 4803, 1603602 and 1803202. The initial rotational state of 0 2 is j = 0. (b) r as function of AZPE for 4803; Ec = 70 c m - 1 and j = 0.
Another important effect which emerged from this study [73] is a strong dependence of ~ on the total angular momentum J: For all three isotope combinations r increases exponentially with j2. This underlines that calculations for J - - 0 are of limited significance. For Ee = 70 cm -1 and j = 0, for example, the average rotational angular momentum is about 14 and the maximum is about 27.
D.2. Quantum mechanical calculations of resonance lifetimes In quantum mechanics trapping of trajectories corresponds to the existence of long-lived resonance states [55,74], Resonances are quasi-bound states in the continuum of the molecule, above the first dissociation threshold. They are the continuation of the true bound states into the continuum.
38
[VI
K. Mauersberger et al.
If the resonances do not significantly overlap, the dissociative lifetime associated with a particular resonance is given by h / r , where r is the width of the resonance in the energy domain. A molecular system with a potential well always exhibits resonances, especially in the threshold region. As the energy above the threshold increases, the average lifetime on the average decreases. Depending on the intramolecular coupling between the degrees of freedom there may be a large extent of state specificity, that is, the lifetime varies largely - by orders of m a g n i t u d e - from resonance to resonance [55]. Because trapping of the molecular complex formed in a bimolecular collision is intimately related to resonances, resonances are essential elements of kinetics: Without resonances there is no trapping and consequently no stabilization, except in the high-pressure regime. Babikov et al. [66] calculated the resonance spectrum of several nonrotating (J = 0) isotopologues of ozone at low energies using the hybrid PES described in Sect. VI.B Fig. 15 shows the q u a n t u m mechanical lifetime spectrum for 1603602. The most striking observation is the existence of several very long-lived resonances with lifetimes in the range of several
600 1603602
500 400
300 ,___._,
200
100
-100
0
I
i 20
~ 40
, 60
, 80
, 100
, 120
, 140
E [ c m -1]
FIG. 15. Resonance spectrum of the quantum mechanical calculations of Babikov et al. [66] for the complex 1603602 as a function of the total energy. Some of the lifetimes below 22cm-1, the second threshold, are many thousands of picoseconds long.
VI]
ASSESSMENT OF THE OZONE ISOTOPE E F F E C T
39
nanoseconds between the lower, 180180-4- 160, and the higher, 180-t- 180160, threshold. Above the higher threshold the series of resonances continues, but with substantially shorter lifetimes. For comparison, the spectrum for 4803 does not show the very long-lived quasi-bound states. Thus, the energy region between the lowest and the highest threshold for an asymmetric isotopomer, which corresponds to AZPE, is of special importance. Based on the results presented in Fig. 15, Babikov et al. proposed the following picture in order to qualitatively explain the isotope dependence of the formation rate coefficients [75]. When 160 + 160180 collide and form an 180320 2 complex the long-lived resonances between the two thresholds are experienced. As a consequence, the lifetime of the complex, when averaged over all resonances, is large and so is the probability for ozone formation. On the other hand, when 180 and 3202 approach each other with energies above the higher threshold the long-lived resonances are not experienced with the result that the average lifetime is smaller. Thus, the probability for forming ozone is smaller, in qualitative agreement with the experiment. In their most recent publication, Babikov et al. [76] used a simple kinetic model and the state-dependent resonance lifetimes to calculate two ratios of formation rates. The results point in the right direction; much more work, however, is needed, especially for the calculation of high J values, to make the comparison quantitative. In another quantum mechanical study Grebenshchikov et al. [77] investigated all the bound states of several ozone isotopologues for J - 0 up to the lowest threshold. The main finding of this investigation is that most of the bound states in an energy window of about 150 cm -1 below threshold are localized in the shallow vdW-like minimum at large O . . - O 2 bond distances (Fig. 12). Extrapolation of p(E) from energies well below the bottom of the shallow well to the threshold yields about 0.1 cm -1, while the true calculated value is about seven times larger. The drastic increase is due to the occurrence of states localized in the shallow well. Because of the large anharmonicity of both the angular and the dissociation coordinates and because all three atoms are heavy, the well supports many states. In view of the study of Grebenshchikov et al. [77] it is not implausible to assume that many of the very narrow resonances between the first and the second threshold found by Babikov et al. have mainly vdW-like character. The states with longest lifetimes would correspond to states which are bound with respect to the channel with the higher asymptote. Coupling between this channel, the main ozone well, and the channel with the lower threshold turns the bound states into resonances. An interesting question concerns the influence of the largely enhanced density of states near the threshold on statistical calculations.
40
K. Mauersberger et al.
[VII
Both the classical and the quantum mechanical dynamics calculations are highly involved and numerically challenging. At the present time it is not clear whether they will finally lead to a consistent explanation of the ozone isotope effect. Nevertheless, the progress made in the past two years has also raised new questions, which seem to be essential for understanding the recombination of ozone and its isotope dependence. Several will be addressed in Sect. VIII.
VII. The Ozone Isotope Effect in the Earth's Atmosphere In the last part of this chapter we present atmospheric ozone isotope ratios followed by a particularly impressive example of an isotope transfer reaction. For 490 2 and 5~ a direct comparison between laboratory and atmospheric isotope data can be made when pressures and temperatures are considered. Differences between the two data sets would signify that additional processes in the atmosphere are influencing the enrichments of the two isotopologues, i.e., processes which are not present in the more controlled and gas-kinetically simpler laboratory environment. Thus, isotope ratio measurements could advance our understanding of atmospheric photochemistry. Atmospheric ozone isotope analysis will always be a challenging task since ozone is a trace gas in the stratosphere with mixing ratios in the ppm range, while in the troposphere the mixing ratios are even lower, between 10 and 100 ppb. This section will provide some experimental details as to how the challenge has been met to obtain reliable isotope data in the atmosphere. For meteorological conditions near the ground (approximately 1000 mbar and 300 K) laboratory data show enrichments of (7 4- 1)% for 490 3 and (8 i 1)% for 5~ Pressure and temperature decrease toward the tropopause (between 10 and 15 km); however, no isotope data of ozone have been obtained in this altitude range. The conditions change considerably above 15 km when entering the stratosphere. The pressure drops below 100 mbar and reaches almost 1 mbar near the stratopause in 45 to 50 km. The temperature is low in the lower stratosphere- around 220 K and can even become as low as 180 K in the polar region. Throughout the stratosphere, however, the temperature increases and reaches 270 K near the stratopause. The increasing temperatures will certainly be reflected in the isotope ratios while the pressure changes are within the low-pressure limit where constant enrichments have been found (Fig. 3). For the wide temperature range in the stratosphere, laboratory data suggest enrichments of 6 to 9% for 490 3 and 6 to over 10% for 5o03.
VII]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
41
A. TROPOSPHERE: EXPERIMENT AND RESULTS The difficulty of tropospheric isotope analysis may first be placed in some perspective: To determine the enrichments in 490 3 and 5~ with an accuracy of better than 3% requires the separation of molecules that are present in air with 0.5 ppt or less. Such an analysis can only be made with a special sample collection system in which ozone is extracted from air by condensation at low temperatures over a period of many hours. The first system built for tropospheric 03 collection contained two cryogenic traps [78]. In the first trap at 77 K and with the pressure reduced upstream to 20 mbar, H20, CO2, and other condensables were removed from the air stream. Ozone collection was performed in a second trap at 55 K and at a pressure of about 6 mbar. Both pressure and temperature inside the ozone collection cell are critical to ensure that O2 will not condense while the partial pressure of ozone is well above the saturated vapor pressure of crystalline 03 [34]. After a sufficient amount has been accumulated over many hours (actually together with atmospheric xenon) the flow is stopped, residual gases and Xe are removed from the sample, and ozone allowed to recombine into O2 to be analyzed with a mass spectrometer. Stehr et al. [79] provide a detailed description of the ozone collection and analysis system with the different parts combined into one unit, including the mass spectrometer. In Fig. 16, measured tropospheric enrichments of 490 3 and 5~ are shown in a triple-isotope plot [78]. Over the period July to October 1994, 47 samples were collected at ambient pressures always close to 1000 mbar and temperatures variable from 283 to 307 K. The corresponding variation in isotope enrichments of less than 0.8% cannot be resolved with the collection and analysis technique. The results confirm that the ozone isotope effect is also found in tropospheric ozone. The mean enrichment values are (9.1 4-0.2)% and (7.1 4- 0.3)% for 5~ and 4903, respectively. The magnitude of the enrichments matches the values measured in a considerably different experimental environment, typically comprised of a small glass bulb filled with pure oxygen or air in which 03 is generated. In detail, the agreement for 490 3 is very good while for 5~ the mean tropospheric enrichment is about one percent higher. The difference is not sufficiently large to speculate on additional mass-dependent fractionation. Further information can be obtained from the average mixing ratio of ozone during the time of sample collection. Shown in Fig. 17, upper part, are relative tropospheric ozone densities ranging from below 20 ppb to over 80 ppb. The lower part displays the enrichments measured for 5o0 3. There is no indication that the ozone concentration influences the magnitude of the fractionations in tropospheric ozone isotopes.
[VII
K. Mauersberger et al.
42
I
I
I
I
10
11
10
9 O o~
8
v
O O v
7
v--
I
6
I,
7
I
8 ~180(03) (%
I
9 VS 02)
FIG. 16. Enrichments in 5o0 3 and 490 3 in tropospheric ozone. The 6 values are calculated with respect to the isotope composition of O2 in air. The mean values are (9.1 + 0.2)% and (7.1 4- 0.3)% in 3180(5~ and ~170(4903), respectively, where errors quoted are 2 standard errors of the mean value. (From D. Krankowsky et al., 1995, Geophys. Res. Lett. 22, 1713, Fig. 4, reproduced by permission of American Geophysical Union.)
Two years later, in 1997 other measurements of tropospheric ozone isotope data were published [80] showing variable enrichment values for both isotopologues. The higher values are similar to those in Fig. 16; in addition, however, a pronounced trend toward lower values was found. Three possible problems could have influenced the results: The mean ozone collection efficiency was only 10%, some delays in sample analysis because of transport occured, and the fact that xenon was not removed from the collected ozone and thus was present during mass spectrometric analysis. Additional data are required to check if there is occasionally a change in tropospheric isotope data. B. STRATOSPHERE" EXPERIMENT AND RESULTS
More ozone is present in the stratosphere than near the ground, but there is the added complication of performing the analysis between 15 and 40 km.
VII]
ASSESSMENT OF THE OZONE ISOTOPE E F F E C T
43
FIG. 17. Upper part: tropospheric ozone mixing ratios (in ppbv) during sample collection. Lower part: enrichments in 5~ The shading indicates the range expected from the known pressure and temperature dependence of enrichments. (From D. Krankowsky et al., 1995, Geophys. Res. Lett. 22, 1713, Fig. 3, reproduced by permission of American Geophysical Union.)
Experiments carried out on balloons and satellites or from instruments on the ground have produced a large set of data during the last 20 years. The most accurate method of ozone isotope measurements is the collection of samples onboard a balloon gondola with subsequent analysis in the laboratory. While the remote sensing technique both from the ground or from balloons and satellites has the clear advantage of identifying molecular structures such as 160180160 and 160160180, it has the disadvantage that the uncertainties in the measurements are quite large. This might change in the near future, however, when more advanced equipment is flown on satellites and the analysis technique is more refined. An assessment and an evaluation of stratospheric ozone isotope data has been recently published [81]. It was concluded that almost all of the early mass spectrometer in situ data [1,27] and some of the remote sensing results [28] should be disregarded. Here we present stratospheric data, which we believe are reliable and representative for the lower and middle stratosphere between 20 and 36 km. The data were obtained with an improved dual trap collector system [79,82] cooled with liquid nitrogen that permitted the subsequent collection of four independent ozone samples as well as samples of stratospheric CO2. Briefly, air is directed through a system that contains two cold traps at different temperatures, with the first trap at 80 K, used to
44
[VII
K. Mauersberger et al.
collect CO2, but not ozone. Ozone is condensed in a second trap at 63 K, which is achieved by reducing the temperature to the triple point of liquid nitrogen through pumping. The major atmospheric gases (N2, O2, Ar) will not condense in either of the traps. Laboratory tests show that the fractionation due to the condensation in the traps is less than 1%. After the collection, but still during the balloon flight, a small pump is connected to the sampling chambers to remove for a brief period, atmospheric residual gases. Thereafter, valves close off the purified samples. As soon as the collector is returned to the laboratory, CO2 and ozone are checked for purity and total pressure to determine collection efficiency, and the gases are analyzed with mass spectrometers. Shown in Fig. 18 are the results from nine balloon flights in which the sample collector was flown into an altitude range from 20 to about 36 km. The lower altitude limit of collection is given by the partial vapor pressure of O2, the upper limit is due to the rapidly decreasing ozone density and thus the potential for isotope fractionation during the condensation process. A total of 35 samples were obtained in flights from Kiruna/Sweden and Aire-sur-l'Adour/France covering different seasons. Very low enrichments, between 5 and 6%, were found for both isotopologues in two recent flights from Kiruna/Sweden when samples were collected within the cold polar
|
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.=T=.
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9
,
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i
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i
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~'o(o3) (% vs 02)
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I
4
i
'
'
6
8
i
I
10
9
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i
14
~'8o(o3)(% vs 02)
FIG. 18. a) Enrichment measured in 490 3 during stratospheric balloon flights, b) Enrichment measured for 5003. Dark symbols are data from Aire-sur-l'Adour/France, open symbols are from Kiruna/Sweden. (From K. Mauersberger et al., 2001, Geophys. Res. Lett. 28, 3155, Fig. 1, reproduced by permission of American Geophysical Union.)
VII]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT 155
Temperature (K) 217 298
Temperature (K) inferred from 8180 155 217 298 397
397
!
12
45
|
|
388
-
o o ...%
10
299
8
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Laboratory ,
4
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8
.
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~'o(o~) (% vs o~)
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,
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5'%(o~) (% vs
.
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o~)
FIG. 19. Left: Enrichments measured in the laboratory for the two main isotopologues (Fig. 2 shows both separately). Right: Enrichments measured in the stratosphere (from Fig. 18). (Adapted from D. Krankowsky et al., 2000, Geophys. Res. Lett. 27(17), 2593, Fig. 1, reproduced by permission of American Geophysical Union.)
vortex. Temperatures between 180 and 190 K prevailed and laboratory temperature studies predict low and almost equal values for 3490 3 and 35~ 3 as shown in Fig. 2. Both enrichments increase toward higher altitudes as stratospheric temperatures rise. Figure 19 shows separately the correlation with temperature: Plotted on the left are the isotope enrichment data measured by Morton et al. [5] at five different temperatures. The gradient has a value of 0.63 + 0.18. On the right, all stratospheric data from Fig. 18 are displayed. Their gradient has been determined by a least-square fit, including x- and y-errors, with a slope of 0.68 4- 0.05. Up to an altitude of about 33 km, those enrichments match very closely the temperature-predicted isotope ratios, while above 33 km a small departure is observed toward higher values, particularly in 5o03. It is not clear at the present time if the departures from laboratory results represent additional photochemical isotope changes in ozone in the upper stratosphere due to UV photolysis, or if the collection system has caused this fractionation in the data. The low density of ozone in the upper stratosphere may prevent a complete condensation preferring the heavy isotopes. Overall, it is observed that the ozone formation process throughout the middle stratosphere produces an isotope ratio that is controlled by the temperature during the formation process.
46
K. Mauersberger et al.
[VII
C. OZONE ISOTOPE TRANSFER TO STRATOSPHERIC C O 2
The large isotope enrichments in stratospheric heavy ozone have the potential for a transfer of the anomalous signature manifested in ~170(4903) to other atmospheric trace gases, which are part of the ozone photochemistry. Ozone is rapidly photolyzed with increasing altitude in the middle and upper stratosphere, producing either O atoms in ground state O(3p) or in excited state O(1D). Furthermore, direct chemical reactions with radicals such as C1, NO, and others can also transfer the isotope signature. When O atoms are produced in their ground electronic state, which is the case in the Chappuis band photolysis, isotope exchange reactions will rapidly dilute any enrichment that would have resulted from dissociation of the end atoms of the ozone molecules. O(1D) atoms, however, will not exchange with 02 and can transfer any isotope anomaly to other trace gases. The O(1D) density is very low throughout the stratosphere since the excited O atoms are rapidly quenched into the ground state by atmospheric gases or they react, for example with CH4 to produce the important radical OH. Despite the short supply of O(1D) atoms and their high reactivity, Yung et al. [83] proposed a competing reaction with CO2: 03 't- hv
; 0 2 -l- O(1D)
O( 1D) + CO2 CO~
(24)
) CO~
(25)
) CO2 + O(3p).
(26)
They estimated by applying reasonable reaction rates that the enrichment measured in stratospheric 12C160180 [84] is a result of a reaction between O(1D) atoms, produced in ozone photolysis, and CO2. More data have become available over the years and the enrichment in 12C160170 provided a clue that the transfer indeed resulted from the isotope anomaly in ozone [85]. The scatter in the data, however, was substantial [86] and no detailed molecular model, which must include the unusual enrichment in 170, has yet been developed. The quality of the data has improved considerably with the dual gas collector system onboard a balloon gondola [79]. This has become the best method to obtain isotope information of 03 and CO2 in the stratosphere although precaution must always be taken to check for contamination. In each of the balloon flights such a measure has been applied: When the balloon reached its maximum altitude, two samples were collected in succession during the float while the third and fourth were taken during descent. The impact on CO2 isotopic ratios as a result of this procedure
VII]
ASSESSMENT OF THE OZONE ISOTOPE EFFECT
47
will be discussed later. Two new independent analytical techniques for the determination of 170 were applied during laboratory sample analysis. One method is based on fluorination to extract molecular oxygen from CO2 [87], while the other technique relies on isotopic equilibration of CO2 with solid cerium oxide [88]. The isotope ratios are reported as departures from the large reservoir of tropospheric CO2, with well-known isotope ratios of 21%o for 12C160170 and 41%o for 12C160180 measured against the standard oxygen scale (SMOW). A total of 39 CO2-samples were collected in 11 flights over Kiruna and Aire-sur-l'Adour. Although four collections are possible per flight, equipment or balloon problems prevented a complete sampling in some cases. As more and more data accumulated it was soon recognized that a unique and tight relationship between enrichments of the two heavy oxygen isotopes in CO2 exists. While enrichments as a function of altitude are still the important atmospheric information, here we present and discuss first the triple-isotope plot shown in Fig. 20. A linear relationship exists, which has not been measured before, with a constant ratio of 1.66 4- 0.09 independent of altitude and latitude. The surprising fact is that in CO2 the isotope with 170 is substantially more enriched than 180. It is of importance to notice that the line of the free fit extends through 3170 ~ 20 %o and 6180 -~ 40 %o, the fractionation values (vs. SMOW) of tropospheric CO2. As mentioned before not all 39 samples resulted in reliable atmospheric isotope data. Figure 20 shows only 33 isotope ratios. Six discarded ratios were all collected over Aire-sur-l'Adour. In four flights, the CO2 accumulated in the first trap during balloon-float resulted in isotope ratios that were considerably different from those on or close to the straight line. In addition, the second sample in two of the flights showed similar departures while all others obtained later during float or descent were on or very close to the line. None of the Kiruna samples were affected, where the relative humidity on the ground was always much lower than in Air-sur-l'Adour. As Lfimmerzahl et al. [19] explained, tropospheric water contamination is the probable cause for this alteration. Water released from structures early during the flight and collected together with CO2 exchanged O-isotopes with CO2 and caused a departure from the atmospheric fractionation line shown in Fig. 20. The ozone data, however, collected simultaneously did not show a difference between the first and the second samples. Finally, Fig. 21 shows the enrichment in CO2 as a function of altitude. A steady increase in both heavy isotopologues is observed. A fit through the data extends to isotope ratios of tropospheric CO2 near 14 km. Some values obtained over Kiruna, however, differ. We believe the departure results from a low tropopause in the polar region. Despite this
48
[VII
K. Mauersberger et al.
40
I
'
I
,
I
'
I
,
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,
I
38 36 ~" 34 0 o9 32 o
o~ 0
0 o
0
30 28 26 24 22 20
40
,
42
44
46
I
48
,
I
50
,
52
5~aO of CO 2 (%0 v s SMOW) FIG. 20. Enrichments in stratospheric CO2. Reference is the oxygen isotope distribution of SMOW (Standard Mean Ocean Water). (From P. L~immerzahl et al., 2002, Geophys. Res. Lett. 29(12), Art. No. 1582, Fig. l, reproduced by permission of American Geophysical Union.)
departure from the fit line, the six data points are on the straight line in Fig. 20. Yung et al. [83] treated in their model the transfer of 180 from O2 to CO2 only. Barth and Zahn [89] introduced ad h o c a fractionation factor to explain data by Zipf and Erdman [90] who showed a gradient in their CO2 data much larger than 1.0 and similar to the value shown above (Fig. 20). A gas kinetic model is yet to be developed that would describe the observed effect in CO2 in detail, starting with the photolysis of ozone and closing with the isotope ratio of CO2 throughout the stratosphere.
VIII] 9
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49
ASSESSMENT OF T H E O Z O N E ISOTOPE E F F E C T
26
~ 24 22
20 18 16
14 0
9 '
9 '
9 '
9 '
2
4
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8
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81r0(C02) (%0 vs troposphere)
i
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4
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8180(C02) (%ov s troposphere)
FIG. 21. Altitude variation of the isotopic composition of oxygen in stratospheric CO2. Open circles are data from Kiruna, Sweden; solid circles are data from Aire-sur-l'Adour, France. The lines indicate the trend of the altitude variation in isotopic enrichment. (From P. L~immerzahl et al., 2002, Geophys. Res. Lett. 29(12), Art. No. 1582, Fig. 2, reproduced by permission of American Geophysical Union.)
VIII. Summary and Outlook It has been a long way from the papers of Kaye and Strobel [6] and Navon and Wasserburg [91] to the molecular origin of the ozone isotope effect. For over 15 years, only the final products, particularly for the two atmospheric isotopologues 490 3 and 5~ were known without understanding the physical processes, which are responsible for the enrichments. When in the late 1990s the isotope-specific ozone formation rate coefficients were measured, the roots of the isotope anomaly were uncovered. The surprising variability of the rate coefficients and the influence of the oxygen isotope exchange reactions, together with different reaction channels, led to an understanding of the enrichments and depletions of the various isotopologues. A set of reliable measurements is now available on the magnitude of the enrichments and their dependence on pressure and temperature of the gas in which ozone is formed. This dependence has also been investigated for selected rate coefficients of the 160--180 system, which include the lowest relative rate for the ~80+ 320 2 reaction and the fastest for ~60+ 360 2. The former reaction shows a pronounced temperature dependence (with respect to 160-nt- 160160) while the latter is pressure-dependent. The type of bath gas
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appears to have no effect on both rate coefficients. It is well-known, however, that the absolute production of ozone is bath gas-dependent. Today we know that it is of no importance how the O-atoms are produced in gas mixtures containing molecular oxygen, whether by UV light, electronic discharge, or other methods. What matters is the temperature and the pressure of the gas during ozone production. Walls of the equipment used in laboratory studies can greatly influence the ozone isotope fractionation. Numerous experiments have shown that the isotope effect is caused by a gas-phase process, which is independent in magnitude from the composition of 02 in the bath gas. Heterogeneous ozone production on the other hand does not lead to an anomalous enrichment. There are still open questions in experimental ozone isotope research. For example, it would be desirable to obtain more rate coefficients, particularly for the 160--170 system, o r - even more challenging- for any of the combination 160170180. Of course all known rate coefficients should be independently re-measured and their pressure and temperature dependence studied in more detail. An isotope effect has also been identified in thermal gas-phase ozone decomposition, but competing reactions make it difficult to study details in laboratory experiments [23]. For similar reasons, the effect of UV and visible light dissociation of ozone remains unresolved if isotope fractionation occurs. Ozone enrichments in the stratosphere, which were measured during the early period of isotope studies to be highly variable and often very large, have been recently determined with much higher accuracy. A sufficient number of samples collected between 20 and 36 km and analyzed in the laboratory show that the stratospheric temperature is the determining parameter for the magnitude of enrichments ranging in the middle stratosphere between 6 and 10% for 490 3 and 6 and 12% for 5o03. Some higher values remain unexplained, particularly for the 5o03 enrichments in the troposphere and above 33 km in the stratosphere. Despite those small uncertainties, tropospheric and stratospheric heavy ozone enrichments are in agreement with laboratory results obtained under similar pressure and temperature conditions. Considerable effort will be required to further reduce the uncertainty in atmospheric measurements. If successfully accomplished, it may provide new information on photochemical processes for atmospheric ozone. With the advent of the ozone rate coefficients the number of theoretical models that have attempted to explain the ozone isotope effect has considerably increased. Marcus and co-workers have presented model developments using the RRKM theory that resulted, when proper parameters and normalizations to the lowest and highest relative rate coefficients were used, in a detailed description of all rate coefficients and
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isotopologue enrichments. An even more rigorous description of the ozone isotope effect based on full dynamical calculations requires all means of theoretical chemistry as we outlined in this chapter. Quantum mechanical resonance calculations as performed by Babikov et al. [66, 75] are the ultimate tool for investigating the formation of ozone; but as the most recent publications show, those attempts are a first step in the direction of "firstprinciple" solutions of the ozone isotope effect. Resonance lifetimes for large total angular momenta are required and their determination is a formidable task. What is the impact of the shallow van der Waals-like wells and the long-lived states they support? Do they contribute to the stabilization process or are these states so fragile that the first collision with M destroys them? What is the role of the excited electronic states which correlate with ground state products? The stabilization process, i.e., how the vibrational energy of the excited complex is removed by the bath atom or molecule is largely not understood. Moreover, a consistent dynamical model should also explain the measured temperature and pressure dependent absolute rate coefficients [30]. The step from the potential energy surface to the formation rates is very challenging, and this makes the comparison between dynamical calculations and experiment extremely demanding. It would be greatly helpful to have other quantities available to assess the quality of theory, for example spectroscopic data at energies around the dissociation threshold, energyand state-resolved exchange cross-sections, or energy transfer probabilities in collisions of excited ozone molecules with rare gas atoms. We hope that this presentation and the uncertainties which still exist will stimulate both new experiments and theoretical work.
IX. Acknowledgments We gratefully acknowledge the important contributions by Stuart Anderson, Jfirgen Gfinther, and Andreas Wolf to our ozone isotope research. We like to thank Peter L~immerzahl who used his experience and skills to prepare and direct so many successful balloon flights and Joachim Janicke for conducting the laboratory measurements. Since our equipment is all "home-made," personnel from the MPI-K electronic and machine shop deserve our special thanks. The CNES balloon team headed by the late Pierre Faucon and personnel in Aire-sur-l'Adour and ESRANGE Kiruna, have provided for many years excellent service always accommodating our requirements to obtain the best samples. R. Schinke acknowledges financial support from the D F G within the Sonderforschungsbereich 357. He is most grateful to R. Siebert, S. Yu. Grebenshchikov, and P. Fleurat-Lessard for
52
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invaluable contributions to the dynamical studies. Last but not least, our thanks to Birgit Jacob for her help in composing the paper.
X. R e f e r e n c e s 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 50
A T O M OPTICS, GUIDED A TOMS, A N D A TO M IN TER FER 0 M E T R Y J. A R L T 1, G. B I R K L I ' 2, E. R A S E L l and W. E R T M E R 1 llnstitut ffir Quantenoptik, Universitdt Hannover, Welfengarten 1, 30167 Hannover, Germany; 2lnstitut ffir Angewandte Physik, Technische Universit6t Darmstadt, Schlossgartenstrafle 7, 64289 Darmstadt, Germany I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. A t o m Optical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Optical Dipole Force and P h o t o n Scattering . . . . . . . . . . . . . . . . . . . . . . B. Magnetic M a n i p u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. A t o m s in Optical Micro-Structures: Integrated A t o m Optics and Q u a n t u m I n f o r m a t i o n Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Microoptical Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Integrated A t o m Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Q u a n t u m I n f o r m a t i o n Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. F u t u r e Prospects: Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. Coherent A t o m Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. BEC and Optical Dipole Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. BEC in Highly Elongated Magnetic Potentials . . . . . . . . . . . . . . . . . . . . . C. Bragg Diffraction of BECs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. The State-of-the-Art in A t o m Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . A. A t o m - I n t e r f e r o m e t r i c Tests of Q u a n t u m Mechanics . . . . . . . . . . . . . . . . . B. The F o u n d a t i o n s of Precision A t o m Interferometry . . . . . . . . . . . . . . . . . C. F u t u r e Inertial A t o m i c Q u a n t u m Sensors . . . . . . . . . . . . . . . . . . . . . . . . D. Optical Clocks: R a m s e y - B o r d 6 Interferometry . . . . . . . . . . . . . . . . . . . . . VI. Concluding R e m a r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55 56 57 58 58 59 60 62 64 66 67 69 71 73 73 74 76 79 82 83 83
I. Introduction The investigation of the wave properties of atomic matter is one of the most active fields of research in atomic physics and quantum optics. Over the last 20 years, a tremendous number of experimental and theoretical achievements have been reported and the course of scientific progress is still accelerating to date. The list of research topics includes such prominent developments as atom optics, atom interferometry, Bose-Einstein condensation, and quantum information processing. Novel experimental techniques including laser 55 1049-250X
Copyright 9 2005 Elsevier Inc. All rights reserved DOI: 10.1016/S1049-250X(04)50002-2
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cooling and trapping, magnetic trapping, evaporative cooling, and several other techniques allowing for the control of atomic matter at the quantum level have been implemented. Based on these results several subfields of physics and science in general have been significantly advanced: In addition to atomic, molecular, and optical physics, being obvious examples, statistical physics, many-particle physics, and some aspects of solid state physics have to be named, but implications reach as far as cryptography and computer science. A number of these aspects have been discussed in [1] recently. A comprehensive presentation of the numerous developments in one paper is a challenging yet hopeless task. Fortunately, there exist a number of excellent reviews and books covering most of the relevant topics, such as laser cooling and trapping [2,3], atom optics [4], atom interferometry [5-7], cold and ultracold collisions [8], atom holography [9], Bose-Einstein condensation [10], quantum chaos [11], optical lattices [12], trapping and guiding of atoms in hollow laser beams [13,14], atom optics with evanescent waves [15,16], integrated atom optics with magnetic and electrical microstuctures [17], and quantum information processing [18,19]. We acknowledge that this list is far from complete and consider it as a starting point for learning more about this exciting field of research. Taking advantage of the large number of high-quality reviews, we concentrate on aspects which might not have been covered before or for which we can supply first-hand information as being our own work. This approach serves the dual purpose of being concise, concentrating on some novel techniques, and at the same time avoiding lengthy repetitions of work presented elsewhere. The paper starts with a brief summary of the experimental methods applied (Sect. II) and then points to some relevant recent advances. The particular choice of the topics of the respective chapters was guided by our own research interests. In Sect. III we present the investigation of atoms in optical micro-structures, in Sect. IV we discuss recent developments in coherent atom optics (mainly with BoseEinstein condensates), and in Sect. V we describe recent advances and prospects in atom interferometry.
II. Atom Optical Tools Many recent developments in the investigation of matter wave properties of atoms have only become possible after the development of a novel set of experimental tools. In this section we briefly review the principles underlying the manipulation of atoms with optical and magnetic fields as required for the later sections of this paper.
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A. OPTICAL DIPOLE FORCE AND PHOTON SCATTERING
The optical manipulation of neutral atoms in most cases is based on the electric dipole interaction of atoms with laser light. It leads to the spontaneous scattering of photons, which allows cooling, state preparation and detection of atoms, and to an energy shift experienced by the atoms, which gives rise to the dipole potential. For an understanding of the basic properties of both effects it is sufficient to assume the atom to act as a two-level system ignoring the details of its internal substructure. A detailed treatment of laser cooling, dipole potentials, and the modifications arising for multi-level atoms can be found in [2,3,20]. The rate of spontaneous scattering processes is given by
v3yrc2 (VCO____~L~ o)o /
~
/(r),
+
O90 - - O) L
(1)
O) 0
valid for negligible saturation (Fsc << F) and large detuning IAI~ Iw0- WLI >> F. I(r), is the position dependent laser intensity, wL and w0 are the laser frequency and the atomic resonance frequency respectively, and F is the natural decay rate of the population in the excited state. A conservative, non-dissipative force acting on the atoms is derivable from the dipole potential
U(r) -
2Wo3 ~ -
+ coo
I(r),
(2)
again valid for (Fse << F) and IAI ~ F. The direction of the dipole force depends on the sign of the detuning A. In an inhomogeneous optical field the dipole force attracts atoms towards regions of high intensity if the frequency of the laser light is below an atomic resonance (A < 0, "red detuning"), and repels them if the frequency of the light is above an atomic resonance (A > 0, "blue detuning"). For typical experimental conditions, the detuning is much smaller than the atomic resonance frequency (IAl<
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B. MAGNETIC MANIPULATION
Magnetic trapping was one of the decisive elements for the achievement of BEC in dilute atomic gases. Magnetic traps eliminate the need for laser light for trapping and provide the long lifetime needed for evaporative cooling. Magnetic trapping of neutral atoms was first demonstrated in 1985 [21]. The principle of these traps relies on the interaction of the atomic dipole moment with an external magnetic field given by: cr -
= m F g F l z , lBI.
(3)
(4)
A magnetic trap therefore requires an inhomogeneous field that provides a local minimum in this energy. Usually this is accomplished by a coil arrangement carrying large currents to achieve sufficient trap depths. An early overview of the different trap geometries is given in [22]. Initial experiments with BEC added small deformations to these potentials to excite oscillations in the condensate and were able to modify the trapping potential adiabatically to change the density of the condensed cloud [26]. Various design improvements simplified magnetic traps over the past few years, providing the same magnetic confinement at lower currents and lower power consumption. These improvements resulted in a number of new traps [27,28] facilitating the experiments on BEC. However, only the recent realization of miniaturized magnetic trapping and guiding structures [29-37] has shown the path towards a greatly simplified production of BEC [38,39]. The technique bears both technical advantages and the possibility for a vast number of experiments. Due to the small distance between the current carrying wires of the trap and the atoms, very tightly confining potentials can be created with small currents and low power consumption. The tight confinement alleviates the requirements on the vacuum system, since higher collision rates and hence faster evaporation can be obtained. Once a BEC is produced close to the chip surface it can be manipulated by complex guiding or transport structures easily realized on the chip. The promises and challenges in this field have recently been reviewed in [17].
III. Atoms in Optical Micro-Structures: Integrated Atom Optics and Quantum Information Processing Beyond simplifying BEC production, state-of-the-art technology in microand nano-fabrication can be combined with the quantum optical techniques
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of laser cooling, laser trapping, and quantum control to open a new gateway for integrated matter wave optics and quantum information processing with atomic systems. Several groups have applied micro-fabricated magnetic or current carrying structures for this purpose [17,29-37]. In addition, microfabricated mechanical systems have been used for atom interferometry [5,6] and atom holography [9]. Using modern optical methods, the guiding and trapping of atoms in holographically generated hollow laser beams [13,14] and in multiple atom traps created by diffraction [40,41] have been achieved. The application of near-field atom optical elements has been investigated [15,16,42] and BoseEinstein condensation in optical traps has been achieved [43]. In the work presented here, micro-fabricated optical systems have been used to create light fields that allow to scale, parallelize, and miniaturize systems for quantum information processing and atom optics in fundamental research and application [44-47]. A large potential for integration can be foreseen. Together with systems based on miniaturized and microfabricated mechanical as well as electrostatic and magnetic devices, the application of micro-optical systems has launched a new field in atom optics which we propose to name as ATOMICS for ATom Optics with MICroStructures.
A. MICROOPTICAL ELEMENTS
A special attraction of using micro-optical elements for the study of atomic quantum systems lies in the fact, that most of the currently used techniques in atom manipulation are based on the interaction of light with atoms. The use of micro-fabricated optical elements is therefore in many ways the canonical extension of the conventional optical methods into the microregime, so that much of the knowledge and experience that has been acquired in atom optics can be applied to this new regime in a very straightforward way. There are however, as we will show in the following, a number of additional inherent advantages in using microoptics which significantly enhance the possibilities of atom manipulation and will lead to a range of new developments that were not achievable until now: The use of state-of-the-art lithographic manufacturing techniques adapted from semiconductor processing enables the optical engineer to fabricate structures with dimensions in the micrometer range and submicrometer features with a large amount of flexibility and in a large variety of materials (glass, quartz, semiconductor materials, plastics, etc.). The flexibility of the manufacturing process allows the realization of complex optical elements which create light fields not achievable with standard optical components.
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Another advantage lies in the fact that microoptics is often produced with many identical elements fabricated in parallel on the same substrate, so that multiple realizations of a single conventional setup can be created in a straightforward way (scalability). A further attraction of the flexibility in the design and manufacturing process of microoptical components results from the huge potential for integration of different elements on a single substrate, or, by using bonding techniques, for the integration of differently manufactured parts into one system. No additional restrictions arise from the small size of micro-optical components since for most applications in atom optics, the defining parameter of an optical system is its numerical aperture, which for micro-optical components can be as high as NA = 0.5, due to the small focal lengths achievable. Among the plethora of micro-optical elements that can be used for atom optical applications are refractive or diffractive microoptics, computer generated holograms, microprisms and micromirrors, liquid-crystal (LCD) phase masks, integrated waveguide optics, photonic micro-cavities, nearfield optics, and integrated techniques such as planar optics or micro-optoelectro-mechanical systems (MEMS). Excellent overviews on microoptics can be found in [49,50]. In our work, we pursue the application of micro-optical systems for several aspects in research on atomic quantum systems. In the following, we will discuss recent results in integrated atom optics and quantum information processing. We also will point out potential future directions in this field of research.
B. INTEGRATED ATOM OPTICS Because of the high intrinsic sensitivity [5,6], atom interferometers have to be built in a robust way to be applicable under a wide range of environmental conditions. A new approach to meet this challenge lies in the development of miniaturized and integrated atom optical setups based on micro-fabricated guiding structures. Using micro-fabricated current carrying wires, several configurations for atom guides and beam splitters have been realized [17,29-37]. In our work, we have achieved the experimental implementation of atom guides, beam splitters, and structures for atom interferometers based on micro-fabricated optical elements (Fig. 1) [44,47]. We have demonstrated the guiding of neutral atoms along the focal lines created by arrays of microfabricated cylindrical, lenses making use of optical dipole potentials (Fig. 2 (top left)). A key advantage of optical micro-structures is the possibility to choose whether to guide and trap atoms near a surface or far from a surface
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FIG. 1. Arrays of microlenses: (a) refractive, (b) diffractives spherical miscrolenses, and (c) refractive cylindrical microlenses (with cross section at right).
FIG. 2. Interferometer-typestructures for guided atoms based on dipole potentials created by micro-fabricated optical systems.
by re-imaging the focal plane. The latter method has been used for the work presented here and allows to place the micro-optical elements outside the vacuum system and to combine the light fields of several elements. By superimposing two arrays of cylindrical micro-lenses under a variable
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relative angle, we have realized X-shaped beam splitters as well as interferometer-type configurations like Mach-Zehnder (Fig. 2 (top right)) or Michelson-type structures [47]. Figure 2 (bottom) shows the propagation of atoms through a MachZehnder-type structure for guided atoms. We load one of the input ports with atoms from a single dipole trap. The atom sample propagates to the first beam splitter and splits into two paths. At the next intersections these split into a total of four paths. Two of the paths recombine at the the fourth intersection. This Mach-Zehnder-type structure has an enclosed area of 0.3 mm 2 with a total required area including the loading and detection stages of below 1 mm 2. It presents the first experimental demonstration of a structure suitable for atom interferometry based on atom guides. Numerical simulations show that for typical experimental conditions coherent splitting of atomic waves and matter-wave interference at the output beam splitter can be achieved [51]. As an important result of these calculations, a variation in the relative phase between the two paths of a Mach-Zehnder-type structure (e.g., by inserting a variable dip in the guiding potential as phase shifter) results in a complementary periodic variation of the atom number in the two final output ports, thus clearly predicting the existence of interference fringes. Specific to optical realization of guiding structures is the possibility to use the internal atomic structure for the splitting process of guided atoms as well. For guided atoms, state-selective splitting can be achieved by applying a state-selective optical potential in a small section of one output port shortly after the beam splitter. We demonstrated a state-selective guided-atom beam splitter for 85Rb by employing an additional laser field which is red-detuned for atoms in the 5S1/2 ( F - - 2) hyperfine ground state and blue-detuned for atoms in the 5S1/2 (F = 3) hyperfine ground state.
C. QUANTUM INFORMATIONPROCESSING Following the spectacular theoretical results in the field of quantum information processing of recent years [18], there is now also a growing number of experimental groups working in this area. Among the many currently investigated approaches, which range from schemes in quantum optics to superconducting electronics [18,19], the field of atomic physics seems to be particularly promising due to the remarkable experimentally achieved control of single qubit systems and t h e understanding of the relevant coherent and incoherent processes. While there have been successful implementations of quantum logic with charged atomic particles in ion traps [52], quantum information schemes based on neutral atoms
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FIG. 3. Micro-optical realization of 2D array of dipole traps for quantum information processing. [53-60] continue to be attractive alternatives due to the weak coupling of neutral atoms to their environment. A further attraction of neutral atoms lies in the fact that many of the requirements for the implementation of quantum computation [61] are potentially met by the newly emerging miniaturized and integrated atom optical setups. We have demonstrated important steps for the experimental implementation of micro-fabricated optical systems for quantum computing purposes with atoms [45,46,48]. Using two-dimensional arrays of spherical, refractive, and diffractive microlenses, we can trap neutral atoms in one- and two-dimensional arrays of far-detuned dipole traps (Fig. 3(a)). More than 80 traps hold 85Rb atoms in Fig. 3(b). Each trap can act as a memory site for quantum information encoded in the two hyperfine groundstates of the atoms or in the quantized vibrational states of the trapping potential. Thus, the arrays can serve as registers of atomic qubits. Beyond its scalability our approach meets an important requirement for the physical implementation of quantum information processing, namely the ability to selectively address, initialize, and read out individual qubits: the large lateral separation of 125 # m between the dipole traps enables us to selectively address the individual traps in a straightforward fashion. An example is shown in Fig. 3(c) where we focus a near-resonant laser beam onto one of the dipole traps, thus removing atoms from the addressed trap. As can be seen in Fig. 3(c), no atoms are left at the addressed site, while the atoms at the adjacent sites remain unaffected. We have also demonstrated the site-specific and state-selective initialization and readout of atomic quantum states (Fig. 3(d)). Here, we illuminate a one-dimensional atom
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array with light only resonant with the 581/2 (F = 3) --+ 5P3/2 ( F ~ = 4) transition during detection. Since the atoms are almost exclusively in the lower hyperfine groundstate 581/2 (F = 2) after the loading phase (first row), they do not scatter the detection light unless we actively pump them into the upper hyperfine groundstate 581/2 (F-" 3) during the time the atoms are stored in the dipole traps, i.e., prior to the detection phase. This has been done for one (second row) or, alternatively, all (third row) of the trap sites. It is also possible to actively control the distance between individual traps in our system, if smaller or adjustable distances are required, e.g., for quantum gate operations and the entanglement of atoms via atom-atom interactions. This can be accomplished by illuminating one microlens array with two light beams under slightly different angles, which results in two interleaved sets of arrays of trapped atoms. The separation only depends on the angle between the two laser beams and can easily be changed, especially to smaller values. By reducing the relative angle to zero, overlapping traps are created [48]. Several schemes for quantum gates based on the direct interaction of neutral atoms have been proposed theoretically [53-58]. We have shown that the requirements for the implementation of most of these gates can be fulfilled by our system [48]. Specifically, our system seems to be well-suited for the implementation of gates based on cold collisions [54] with individually addressable qubits, thus extending approaches based on optical lattices [62] to single-qubit control. In addition to that, new proposals for the implementation of quantum gates, particularly suitable for our setup, were developed together with the group of M. Lewenstein (University of Hannover) [59,60].
D. FUTURE PROSPECTS: INTEGRATION As mentioned before, key features of our approach of using microfabricated optical elements for the investigation of atomic quantum systems are design flexibility, scalability, and integrability. Noteworthy, the huge potential for integration of micro-optical components can be used for further atom optical purposes. Since the same techniques are applied for the fabrication of micro-optical and micro-structured current carrying components on surfaces, micro-optical components can be combined with the magnetic and electric structures [17,29-37,44,45]. In addition, microfabricated atom optical components can be integrated with optical fibers, waveguides, and micro-fabricated optical cavities, so that the results of atom optical operations after being read-out by optical detection can be
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further processed by optical means [44,63-65]. Another canonical extension is given by the integration of micro-optical components with optoelectronic devices such as semiconductor laser sources and photodiode detectors [44]. In this case, the communication with the outside world can take place fully electronically, with the required laser light created in situ and the optical signals converted back to electrical signals on the same integrated structure. The richness of the available micro-fabrication technologies manifests itself in even another approach to integration based on micro-opto-electromechanical systems (MEMS) [49,50,66] or spatial light modulators (SLM) based on liquid-crystal displays [67]. With these elements fast switching and steering of laser beams as well as the multiplication of individual structures via diffraction become possible, so that complex spatial and temporal field patterns can be generated. An important step towards fully integrated atom optical setups is the development of miniaturized sources of ultracold atoms. Again, microoptical components can be used to achieve this goal, once more profiting from the fact that most of the preparation techniques for atom samples are based on optical manipulation. For this purpose, we proposed a miniaturized version of the "workhorse" in atom optics, the magnetooptical trap (MOT). Our approach for developing a compact MOT [44] is based on the concept of "planar optics"[50]. In planar optics, complex optical systems are integrated monolithically on a substrate. The optical path is folded in such a way, that the light propagates along a zig-zag path inside the substrate and the light is manipulated by reflective optical components (mirrors, beam splitters, lenses, retarders, etc.) that are mounted on or machined into the surface of the substrate. Planar optical systems can be used for a broad range of atom optical applications including atom traps, waveguides, beam splitters, interferometers, networks, and systems for quantum information processing. For the integrated MOT of Fig. 4 the optical components are mounted on two parallel substrates, separated by several mm or cm. The trapping light is coupled into the lower substrate and split into four beams, which, after passing through quarter-wave plates, intersect a few mm or cm above the substrate. The beams enter the upper substrate and are retroreflected after double-passes through quarter-wave plates. Between the two substrates microfabricated coils for the MOT quadrupole fields are mounted. At the center of the upper substrate a two-dimensional microlens array is included indicating the possibility of integrating the MOT with other microoptical elements. The small size of an integrated MOT configuration might limit the achievable atom number, but with a beam diameter of several ram, atoms in
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FIG. 4. Integrated magneto-optical trap (MOT) based on planar optics. The configuration consists of two optical substrates mounted in parallel planes and a pair of quadrupole coils. All optical elements needed for the operation of a MOT are mounted on or machined into the two substrates. The substrates can also contain additional microoptical elements, e.g., a microlens array, as shown here. the order of 106 should be trappable imposing no limitations for most of the applications discussed here.
IV. Coherent Atom Optics The achievement of Bose-Einstein condensation in dilute atomic vapors in 1995 [23-26] was the beginning of a new era in atom optics. It provides a novel source of coherent matter waves that has enabled a large number of experiments probing phenomena at the heart of quantum theory. Many of these experiments served a dual purpose. They have applied methods known from atom optical experiments to coherent matter waves and tested their properties at the quantum limit. At the same time their results have offered a fascinating insight into the nature of BEC. Since then many of these methods have become firmly established in the growing community of experiments working on BEC. They are now applied in experiments to probe the nature of BEC itself and also act as tools in experiments that mainly use BEC as a source of ultracold coherent matter waves. The distinction between these two aims is not entirely appropriate for all experiments with BEC. A complete review of experimental work with BEC since 1995 surpasses the scope of this chapter. Therefore we focus on the experiments that have
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included macroscopic coherent transport of BEC. This interpretation of coherent atom optics allows us to present the central methods for the manipulation of coherent atomic ensembles:'~However it excludes some fascinating experimental work on BEC such as macroscopic excitations like solitons and vortices and the work on BEC in optical lattices. A recent summary of the development was given in [1].
A. BEC AND OPTICAL DIPOLE POTENTIALS
Similar to magnetic trapping potentials, the use of optical dipole potentials as a tool of coherent manipulation was established by one of the first experiments to obtain BEC. The group of W. Ketterle used a blue detuned repulsive laser beam to plug the hole at the origin of a quadrupolar magnetic field. This combination provided the hybrid trap that allowed for the observation of the first Na BEC [24]. Despite this initial success dipole potentials did not play a major role in initial experiments on BEC. However, after the first all optical realization of BEC [43] this situation has changed and some of the most fascinating experiments with BEC are carried out in these potentials. In current experiments with BEC they provide two main advantages. First they allow for trapping, independent of the orientation of the atomic dipole moment and therefore facilitate experiments with multi component BECs. In addition the magnetic offset field becomes a free parameter allowing for tuning of the atomic scattering length. A number of experiments also used dipole potentials to transport and guide condensates over macroscopic distances. One of these experiments is the only realization of continuous BEC to date. The group of W. Ketterle first transferred Na BEC from a magnetic trap to a dipole potential formed at the focus of a red detuned laser beam and then shifted this focus [68] to replenish a BEC in another dipole trap [69].
A.1. Reflection and guiding of BECs An initial goal of our research was an evaluation of the most fundamental atom optical elements for BEC formed by dipolar potentials such as a blue detuned light sheet. It can however serve a multitude of purposes, acting as a mirror, a beamsplitter or even a phase shifter. Our experiments were carried out with 87Rb condensates at temperatures of -~ 200 nK. Due to the magnetic trapping potential used in the production of the BECs, the condensates were cigar-shaped with a length of ~ 100/zm. The atom mirror was created by a green laser beam 0~ = 532 nm), focused to a tight spot of about 10/zm waist providing a repulsive potential for the
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FIG. 5. A series of images showing BECs bouncing off a light sheet 270 /xm below the magnetic trap. Each condensate image was taken destructively at intervals of 2 ms. The light sheet shows up as a sharp lower edge in the fourth frame. atoms (see Sect. II. A). This spot was rapidly scanned back and forth in the horizontal plane by an acousto-optic modulator to form the mirror surface. The modulation period of typically 10/xs was much shorter than the time the atoms spent close to the mirror surface. Hence this resulted in a smooth time-averaged dipole potential for the atoms and ultra cold atomic clouds dropped from a height of up to 300 ~m were thus reflected. The observed clouds bounced up to three times before moving out of the field of view due to a slight slope in the orientation of the light sheet as shown in Fig. 5. As the condensate reapproached the initial altitude, it developed a structure of bright and dark fringes (frames 6 to 8 in Fig. 5). These fringes do not occur for temperatures above the critical temperature for BEC and can only be explained as a matter-wave interference structure. Due to the expansion of the condensate and the specific shape of the potential of the mirror surface, the BEC accumulates a spatially dependent phase during the bounce. This phase leads to the observation of dark and bright interference fringes. Indeed numerical results agree well with the experimental observations and clearly explain the observed self-interference structure. Most importantly, these interferences prove the persistence of matter-wave coherence for BECs reflected off the dipole potential atom mirror [70]. In addition to creating an atom mirror with reflectivity close to unity, partially reflecting mirrors and a phase shifter can be created by reducing the intensity of the light sheet. However, the tools available to the optical engineer allow for the creation of more complicated optical potentials as shown in Sect. III. Analogous to the optical fiber for light, hollow laser beams, so called doughnut beams, can be used as waveguides for atomic samples [13,14]. Our experiment focused on the release of a BEC into such a waveguide and its consecutive evolution. To avoid heating the atoms, the final stages of RF-evaporation before creation of a BEC were carried out in a combined potential consisting of both a magnetic trap and a superimposed hollow laser beam. By ramping down the magnetic trapping field, the BEC was subsequently transferred into the pure waveguide. Figure 6 shows examples of these measurements for evolution times of up to 500 ms in the waveguide. The expansion of a BEC is in excellent agreement with the theoretical prediction
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FIG. 6. Atoms from a BEC loaded into a doughnut waveguide. (a) An artists impression of the BEC in the waveguide. (b) Images of the atoms in the waveguide after the indicated evolution times.
[71] of an expansion dominated by the energy related to the atomic interactions. This waveguide provided a possibility to study the behavior of BEC in geometries of lower dimensionality [72] where a wealth of new phenomena has since been observed [73,74].
B. BEC
IN H I G H L Y ELONGATED MAGNETIC POTENTIALS
Recently the coherence properties of BEC in systems of reduced dimensionality have attracted major interest. A reduction of the dimensionality often occurs in stiff guiding or trapping potentials and is therefore of crucial importance for many promising BEC applications, such as interferometry and atom lasers. The coherent character of trapped 3D condensates well below the BEC transition temperature Tc has been confirmed by several experiments, using interferometric [75,76] and spectroscopic methods [77]. However, recent theoretical and experimental developments have shown that phase coherence is far from being an obvious property of BEC. In particular, a phase-fluctuating BEC at equilibrium has been theoretically predicted in one-dimensional [78], two-dimensional [79,80], and even in highly elongated, but still three-dimensional [81] trapped Bose gases. These systems are commonly called quasicondensates and the amplitude
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FIG. 7. (a) Density modulations in a BEC after a time-of-flight of 24 ms. (b) Column density of image (a) showing the thermal background and the density modulations. The red line is a fit to the data according to the Thomas-Fermi model.
of phase fluctuations depends strongly on the temperature and trapping geometry of the system. We have studied these quasicondensates in highly elongated traps. A modification of our magnetic trap allowed us to obtain potentials with aspect ratios X = ~or/O~zup to 120. Depending on the number of condensed atoms in this potential the conditions can be varied from a 3D to a 1D confinement allowing for the observation of quasicondensates. The phase fluctuations were first observed in a time-of-flight measurement [72]. During the ballistic expansion of the cloud, phase fluctuations transform into density modulations due to the relationship between the local phases and velocity in a BEC. A typical recorded image is shown in Fig. 7. The dependence of the fluctuations on experimental parameters was characterized [72,82] and found to be in good agreement with the theoretical prediction. Moreover, the measured energy released during the expansion confirmed the absence of density fluctuations in the trapped cloud [73,83]. The physics of quasicondensates has also been studied by means of Bragg spectroscopy, showing that the existence of phase fluctuations leads to an observable broadening of the momentum distribution [73,84]. A further experiment has analyzed the phase coherence length of non-equilibrium BECs by means of a condensate-focusing technique [74]. In a more recent experiment we have measured the spatial correlation function of phase fluctuating BECs and hence their coherence length interferometrically. An interference pattern was recorded by splitting a BEC
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in two identical copies and interfering them with a variable displacement. It was shown that the analysis of intensity correlations in this pattern, rather than its visibility overcomes a number of experimental difficulties and provides the desired information about the phase correlations in the initial condensate [85, 86].
C. BRAGG DIFFRACTION OF BECs
Bragg diffraction has been used as a tool to manipulate Bose-Einstein condensates [87] in a number of experiments. It was used to evaluate the velocity distribution of a BEC within the magnetic trap and during timeof-flight experiments [77]. It has also served as a beam-splitter in an interferometer [88], for studies of the phase evolution of BECs [89] and even as an outcoupling mechanism for an atom laser [90]. In addition Bragg diffraction was employed as a tool for the realization of exciting experiments on non-linear effects in BECs [91] and their possible application to create entanglement [92]. Bragg diffraction is a two-photon transition used to generate a new spatial mode of a matter wave. Usually a sample is exposed to two laser beams and photons are absorbed from one and emitted into the other beam. Hence two photon momenta are transferred to the atom. Thus the atoms which have been in resonance with the Bragg-transition will be separated from the remaining atoms. Since the resonance condition depends on the initial velocity of the atom, a given difference frequency of the laser beams addresses a specific velocity class within the condensate. The width of this resonance corresponds to the Fourier transform of the applied laser pulse envelope. A detailed analysis of the Bragg process can be found in [87]. Experiments employing Bragg diffraction on BEC can be divided in two general areas. By using short, intense pulses all velocity classes within a BEC can be accessed and transferred into a moving state. This process corresponds to a variable, coherent beamsplitter for matter waves. On the other hand, long pulses are selective to the velocity in the BEC and distinct velocity classes can be addressed.
C.1. Application of Bragg pulses In our research Bragg pulses haven been used both as a coherent beamsplitter and as a spectroscopic tool. These applications of Bragg diffraction are briefly discussed here to illustrate the range of applications.
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FIG. 8. Interferometer for atomic clouds released from an optical waveguide. The broad arrows indicate the two Bragg diffraction pulses that act as beamsplitters. A sample of the observed interference signal is shown.
A key question in the experiments on guiding Bose condensed samples in dipole potentials (Sect. IV. A) is the coherence or possible destruction of coherence as it expands in the waveguide. Hence the coherence of the cloud during the first milliseconds after transfer into the waveguide were investigated with an interferometric scheme shown in Fig. 8. The interferometer consists of only two Bragg diffraction pulses, applied after switching off the waveguide potential. The duration of these pulses was chosen short enough to transfer all atoms into a superposition of a resting and a moving state. ,-The two condensate wavepackets created by the first pulse separate during the subsequent free evolution time. The second pulse then recombines the partially overlapping clouds in both exit ports of the interferometer as shown in Fig. 8. The displacement leads to the interference fringes in both exit ports due to the well-defined phase within the condensate. The existence of such a phase demonstrates the coherence of BEC after an evolution in the waveguide [93].
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V. The State-of-the-Art in Atom Interferometry Matter-wave interferometry is one of the most prominent subjects in atom optics. Concise reviews of the early work on atom interferometers is given for example in [5] and in the book by P. R. Berman [6]. The field covers distinct topics such as tests of the foundations of quantum mechanics, metrology of time and frequency as well as precise inertial sensors like accelerometers and gyroscopes. Since the achievement of Bose-Einstein condensation (BEC) of dilute gases, atom interferometry has expanded into the field of quantum engineering which summarizes all techniques a n d methods to coherently control and explore atomic quantum systems. BEC also marks the beginning of a new area of coherent matter-wave sources for atom interferometry based on degenerate atomic and molecular quantum gases [160].
A. ATOM-INTERFEROMETRIC TESTS OF QUANTUM MECHANICS
The roots of matter-wave interferometry reach back to the early days of quantum mechanics when interference phenomena served to test the most counterintuitive principles of this puzzling theory: the superposition principle and the wave-particle character of matter. These principles form also the foundation of matter-wave interferometry. The superposition principle implies that a massive particle may propagate as a coherent matter wave with different momenta along distinct classical paths at the same time. After recombining the distinct spatial modes e.g., behind a double slit, an interference pattern is formed revealing the wave nature of matter [94]. One of the most exciting recent manifestations of matter waves is the interference of a split Bose-Einstein condensate, which is the direct proof that all condensed atoms can be assigned a macroscopic wave function with a unique phase [75]. Nowadays, the superposition principle, although well-established in the quantum world, motivates the realization of interferometers at the frontier to the classical world. They are based on macroscopic quantum objects like complex He-dimers and clusters, fullerenes, or in the future perhaps even more complex systems like viruses [95,96]. These experiments extend the "classical" double-slit or which-way experiments to examine the distinct aspects of the particle-wave dualism [7] such as the collapse of the wave function or the decoherence due to interaction with the macroscopic environment [97,98]. Atom interferometry is also intimately connected with the physics of the measurement process, in which quantum objects (atoms, ions) are entangled with a macroscopic meter [99]. Finally,
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atom interferometers are a key element in the coherent control of atoms to realize quantum gates (similar to ions [100]). For this application Ramsey-type interferometers serve as a precise readout of the mutual phase shift induced by entangling two atomic quantum systems with each other (for example the phase shift caused by controlled collisions of two atoms [62]).
B. THE FOUNDATIONS OF PRECISION ATOM INTERFEROMETRY The foundations for precision atom interferometry were laid roughly between 1970 and 1990 [5,6]. At this time, research in atom optics was committed to develop techniques to coherently split matter waves and to demonstrate various concepts for atom interferometers [101,102], many of them in close analogy to neutron interferometry based on diffraction at crystals and gratings. The internal electronic structure of atoms endorsed a new technique for coherent beam splitting: the interaction of atoms with laser light permits the transfer of the kinetic momentum of the photon to the atom in order to excite a new spatial mode of a matter-wave. With this technique material gratings can be replaced by crystal-like structures or phase gratings made out of light waves [103]. Based on this method, two type of geometries proved to be most successful: The Mach-Zehndertype or symmetric interferometer used for inertial sensors and the frequency-sensitive Ramsey-Bord6-type or asymmetric atom interferometer, which is at the heart of optical clocks based on atoms. The MachZehnder type was already used for the first measurements of gravitation and rotation of the earth with neutron interferometers [104-106]. A very successful variant of the coherent beam splitter using laser light is based on the Raman interaction where matter-waves with different momenta are labeled by distinct internal electronic states. Already in 1989, C. Bord6 suggested this method [107], which was demonstrated by M. Kasevich and S. Chu for inertial sensing [108,109]. This technique became a key technology for today's inertial atomic quantum sensors. Atom interferometers based on Raman transitions are an elegant solution to combine the advantages of optical photons with state-of-the-art microwave technology. Similar to the Bragg scattering at standing light waves, the Raman-type interaction used for interferometry is a two photon transition between two atomic ground states separated by a microwave frequency. The phase imprinted onto the atomic dipole by the interaction depends on the relative phase of the two lasers driving the light field and, hence, on the performance of a microwave frequency standard rather than on the phase of the individual lasers.
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The typical Mach-Zehnder type geometry consists of a spatial and/or temporal sequence of three atom-light interactions in order to coherently split, re-direct, recombine and interfere the matter waves. The quantity measured by the interferometer is the difference in the increment of the spatial phase between the light field and the induced atomic dipole while passing from the first to the second and from the second to the third interaction zone, respectively. Hence, interferometers based on Raman transition permit a direct comparison of the phase induced by acceleration or rotation with a microwave frequency standard. The high potential of these atom interferometers for metrology was demonstrated by S. Chu and M. Kasevich [108,109]. Their pioneering work comprises the realization of a gravimeter with a resolution of 10-9 g [110], gravity gradiometer with 4 x 10-9 g differential resolution [111], an atomic gyroscope with a resolution of 10-l~ rad/s [112]. All these experiments provide attractive alternatives to other state-of-the-art technologies such as gravimeters based on falling corner cubes or highprecision active ring laser gyroscopes. Key to the high performance obtained with these experiments (apart from the gravimeter) was the concept of differential interferometry, where the physical quantity is derived from the comparison of two distinct atom interferometers which rules out a major fraction of undesired perturbations. The atomic Sagnac effect was measured for the first time, with a Ramsey-Bord6 or asymmetric atom interferometer [115] as used for optical clocks [145]. The Ramsey-Bord6-type interferometer transfers Ramsey's idea of separated oscillatory fields into the optical domain [116] and, hence, represents the other important class of atomic interferometers in metrology. In fact, Ramsey-type experiments as used for micro-wave clocks can be considered as the earliest atom interferometers. The Ramsey-Bord6 interferometer was used first by Chebotayev [149] and Hall [150] for optical precision spectroscopy. The first temporal Ramsey-Bord8 interferometer with atoms prepared in a magneto-optical trap was investigated with Magnesium atoms [146]. Apart from the Sagnac measurement, Ramsey-Bord6-type interferometers served also for many other text-book experiments such as measuring the DC- and AC-Stark effect [152-156] or geometric and topological phase shifts such as the Aharanov-Casher or the Aharanov-Bohm effect [153,157] complementing by this way the work with other matter-wave interferometers [6]. Finally, asymmetric interferometers have been the basis for the pioneering experiments on optical clocks based on cold free-falling atoms and have opened the way to future optical clocks with a high short term stability as well as to a complementary measurement of the fine-structure constant [ 113,114].
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C. FUTURE INERTIAL ATOMIC QUANTUM SENSORS
Encouraged by these achievements and fostered by the enormous progress in atom optics, today, new activities are on the way worldwide to fully explore the potential of matter-wave sensors at their quantum limit. Examples for these efforts are cold-matter-wave gyroscopes [117], gravimeters [118] used for the Watt balance or the gravity gradiometers for the measurement of the gravitational constant G [119]. To date, atomic Sagnac interferometers are based on thermal atomic beams. New approaches are based on cold atoms rather than thermal beams. In the following, the advantage of cold atoms in Sagnac interferometers will be derived from the Sagnac phase for light- and matter-wave interferometers OS~g~a~ - 4rnc A o ~2
(5)
which differs from each other by a scalar factor x reflecting the nature of the respective wave. The phase shift depends on the orientation of the surface vector A of the area enclosed by the interferometer and the rotation vector s2. Complete knowledge of the magnitude of the rotation vector requires three orthogonal oriented interferometers or additional information on the precise orientation of the sensor with respect to the rotation vector. The factor xA for the atomic matter wave is equal to the ratio of the rest mass m A and Planck's constant, XL for light waves equals the ratio of the frequency v of the light wave and the square of the speed of light c. mA
xA--
h '
v
XL----fi
(6)
For typical values (Cs- or Rb- Raman interferometer, and optical interferometer with wavelength 633 nm), the ratio k A / k L results in a large gain in sensitivity by ten to eleven orders of magnitude if one replaces light by matter waves. Today, the advantage of matter waves is balanced by the difficulty to achieve large areas with atomic interferometers and the atomic sources. Considering the typical Raman interferometer, which shares many features of the traditional Mach-Zehnder type interferometer based on Bragg diffraction, the area depends on the momentum kecf transferred by the coherent beam splitting (2 photon recoils), the drift velocity of the atoms VD as well as the square of the half length L of the interferometer. A - L 2 PBS ~,
PD
VBS=~
keff
mA
(7)
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A T O M OPTICS A N D I N T E R F E R O M E T R Y
77
Equations (5) and (7) state, t h a t - f o r this type of beam splitter- the atomic mass cancels in the Sagnac phase. For the typical Raman-type transition in Rb or Cs keff is typically of the order of 1 cm/s or less. An important motivation for work on cold atom gyroscopes is to increase the ratio of the relative velocity and the drift velocity of the matter waves VBs by several orders of magnitude rather than expanding the length of the apparatus over several meters. By using cold atoms the value can be increased from 10 -5 to 10 -2 with a low atomic speed. Similar to atomic clocks, this factor can be further increased in microgravity, which is the favorite environment for freely falling cold atoms. Cold-matter-wave gyroscopes are at present in construction at the IQ (Institut ffir Quantenoptik) and the SYRTE (Syst6mes de R6f6rence Temps-Espaces). Both devices follow different design strategies. The cold-atom sensor at SYRTE is based on two cesium fountains. The two cesium ensembles are simultaneously prepared in a magneto-optical trap and launched by the moving-molasses technique with a speed of about 2.4 m/s and 83 degrees in vertical direction such that they cross each other at the vertex. The Mach-Zehnder type interferometer is realized by a temporal equence of 7r/2-Jr-rr/2 R a m a n pulses at the vertex of the atomic parabolas. The expected sensitivity of the set-up is 4 x 10-Srad/s~-H~. The cold atom Sagnac interferometer at the IQ is based on a flat parabola design and uses intensive sources of cold 87Rb atoms (see Fig. 10). Figure 9 shows the vacuum chamber made out of aluminum and BK 7 viewports. The atomic sources on each end of the apparatus are based on a threedimensional magneto-optical trap (MOT) loaded by a two dimensional MOT. Apart from the compact design, this source will provide a high atomic flux allowing for a signal to noise ratio similar to the present thermal beam atom interferometer. The two-dimensional M O T displays a similar performance as reported previously [120] with more than 10 l~ atoms per
FIG. 9. The vacuum chamber of CASI. The chamber is tightened with lead wires and with a two-component Epoxy glue (Epotek 353ND), the vacuum will be maintained with a 35 1/s ion pump and a titan-sublimation pump.
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FIG. 10. The figure shows the schematic of CASI. Two atomic beams are formed by a two 3-DMOT, each loaded by a 2-D-MOT. The two beams are split by a spatial and temporal sequence of Raman pulses.
second. The typical loading rate of the 3-D M O T is 109 atoms per second such that 10s atoms can be loaded in the M O T in 0.1 s. Alternatively, the 3-D-MOT can be replaced by Raman cooling in optical lattices [121]. The actual interferometer has a length of up to 15 cm. The coherent manipulation of the atoms (splitting, reflection, and recombination) is performed by a temporal and/or spatially separated sequence of Ramantype interactions at the center of the apparatus. With these parameters a shot-noise limited sensitivity of about 10 -9 rad/s~H-z should be feasible with about 108 atoms per shot. Apart from lowering the atomic speed, the sensitivity of the apparatus can be enhanced by increasing the momentum transferred at the beam splitter as in higher-order Raman or Bragg transitions [111] or in magneto-optical "blazed" light gratings. Their suitability for metrological applications (reproducibility, accuracy, systematic errors), however, rests to be verified. Viewing the relatively small areas achieved by present atom interferometers, an interesting alternative for such sensors may consist in waveguides (see Sect. III) which do not deteriorate the achievable uncertainty [136]. The impressive potential of atom interferometry for the measurement of the atomic Sagnac effect was already pointed out e.g., by Clauser in 1988 [151] or M. Kasevich [6]. It offers a promising complementary approach to high-resolution state-of-the-art active laser ring gyroscopes. Applications comprise the investigation of the rotation and tectonics of the earth, angular references for star observation or the measurement of relativistic effects like the Lense-Thirring effect. The measurement of the Lense-Thirring effect was recently proposed for an European satellite mission (HYPER) based on atom-interferometers [122].
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D. OPTICAL CLOCKS: RAMSEY-BORDI~ INTERFEROMETRY
Ramsey-Bord6 interferometers are a key element of optical frequency standards based on neutral atoms. Like ions, neutral atoms are today promising candidates for precise references in future clocks in the optical domain with a relative instability of less than 1 part in 1014 for a measurement time of "gm - - 1 S [ 1 2 3 , 1 2 4 , 1 5 8 , 1 5 9 ] and a relative inaccuracy of less than 1 part in I015 [123,125]. An important step towards optical clocks was the development of the comb generator, facilitating frequency comparison and division [123]. At present, ion standards display the higher potential with respect to the achievable accuracy, while standards based on neutral atoms are expected to have a superior stability. For the Calcium standard, currently the most precise optical standard based on neutral atoms, the achievable relative instability is projected well below one part in 1016 ('t'm = 1 S), the relative uncertainty below one part in 1015 [126]. For ions, the estimated limits are placed for the relative instability at one part in 1015 (rm = 1 s) and for the relative uncertainty at one part in 1018 [127]. State-of-the-art microwave clocks, however, are still leading with respect to the accuracy (below 1 part in 1015). A concise overview of the work on ion clocks was given by P. Gill [128], and for primary standards by A. Bauch [129]. An important part of the research activities to improve accuracy and stability of optical standards are focused on the fermionic and bosonic isotopes of the alkaline earth group such as Sr, Ca, and Mg, which provide numerous narrow and ultra-narrow transitions. A further reduction of their present inaccuracy of at least one order of magnitude is expected due to new cooling and trapping techniques, which have been demonstrated for Ca and Sr: Examples for the impressive progress are the narrow line cooling [130,131] and the single-stage sub-Doppler cooling [135] of Strontium isotopes, the Doppler cooling of Calcium on ultra-narrow transitions [132,133,134] and in the metastable state [148]. A new trapping technique may open the way to precision interferometry on atoms confined in the Lamb-Dicke regime [136] instead of Ramsey-Bord6 interferometry on free falling atoms. The technique is based on dipole traps, where the ac-Stark shifts of ground and excited state of the "clock" transition are identical and precisely cancel in the frequency measurement. Our research is focused on an optical frequency standard based on laser cooled magnesium atoms. The optical frequency is generated by a highlystable dye-laser spectrometer and analyzed with a Ramsey-Bord6 interferometer tuned to the transition 3~S ~ 33p(m = 0) at a wavelength of 457.2nm. With the apparatus we have achieved resolutions as high as A v = 290 Hz which corresponds to a quality factor of Q = A v/v = 2.3 x 1012 [137]. The spectrometer permits to realize a frequency standard with a
80
[V
J. Arlt et al.
relative instability of a ( z - 1 s ) - 8 • 10-]4. The instability is defined in terms of the modified Allan standard deviation
1
V~
ay(~) -- rc Q S I N
(8)
with the signal-to-noise ratio S I N and the integration time tm for one data point of the interference pattern shown in Fig. 11. Figure 12 shows the stability as a function of the resolution of our interferometer. The stability is first improving for increasing resolutions, but finally limited by the laser instability as well as the residual motion of the atoms which strongly reduce the signal-to-noise ratio. Further improvement in the Ramsey-Bord6 spectrometer is expected from a new experiment designed for multiple-stage optical cooling and trapping of magnesium in the /zK regime and a novel solid-state-laser based spectrometer. As in the previous experiment, the first stage cooling is based on a MOT which is loaded from a slowed thermal beam. In 4 s, we trap more than 107 atoms of the Bosonic 24Mg and Fermionic 25Mg isotopes
"7~D
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V]
ATOM OPTICS AND I N T E R F E R O M E T R Y 2x10
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at temperatures of about 3 mK. The second cooling step is required to reach even lower temperatures in the # K regime. Theoretical studies revealed, that not only for calcium but also for magnesium, quench cooling is a promising avenue towards this temperature range [132,147]. This technique permits to use ultra-narrow transitions for Doppler cooling and trapping, which otherwise would be highly ineffective due to the low spontaneous decay rates. Narrow-line cooling has been already studied in the early days of laser cooling by Wallis [138] and was successfully applied for Strontium, where temperatures even below the # K have been achieved by Doppler cooling at the intercombination transition. In the case of calcium and magnesium the lines are too narrow for Doppler cooling. However, by quenching the long-lived state via excitation to a fast decaying state, the cooling rate can be enhanced by several orders of magnitude such that pre-cooled atoms can be trapped and further cooled in a Quench-MOT. Based on this technique, temperatures as low as 10 # K have been achieved for calcium by quenching the triplet state via excitation to the 1S0(4s5s) at 552.3 nm or to the 1Dz(4s4d ) at 452.7 nm. In magnesium, we identified as most favorable scheme for the quench cycle, a two step excitation scheme based on the "clock" transition 180(3s)2 ---->3Pl(3s3p) at 457 nm with a linewidth of 30 Hz and the transition 3pl(3s3p)---> 1S0(3s4s) at 462 nm with a linewidth of 3 MHz for the subsequent excitation. Simulations showed that an important fraction (ideally up to 40%) of the atoms can be transferred from the MOT into
82
J. Arlt et al.
[VI
the Quench-MOT and cooled to 10/zK for powers of typically 30 mW per laser beam for both excitations. Lowering the temperature by more than two orders of magnitude helps to reduce the systematic errors as well as to further increase the resolution of the spectrometer. The atomic expansion is, however, not the only factor limiting the possible resolution and, hence, the stability of the standard. The spectral phase noise of the laser, which is sampled by the Ramsey-Bord6 interferometer, also deteriorates the stability. At very low frequency instabilities, the sampling effect is non-negligible as pointed out by Dick [ 139-142]. For this reason, the effect is called Dick-effect. Optimization of the achievable stability requires a careful adaptation of laser source, atomic preparation, and frequency measurement. As pointed out by P. Lemonde 2003 [143], a small duty cycle defined by the ratio of the time required for the atomic preparation and the interferometer sequence lowers the requirements on the phase noise of the laser. For magnesium, new solid-state laser systems based on Nd: YVO4 [137,144] or diode lasers permit to replace the versatile dye laser spectrometer, which in general displays a high intrinsic noise. The coincidence of the second harmonic of the 4F3/2 ~ 419/2 transition in Nd:YVO4 with the magnesium clock transition was demonstrated by a heterodyne measurement with our dye laser spectrometer. The laser system comprises a thin-disc laser with a linear, semi-focal cavity, which provides an output power of about 1 W TEM00 at 914 nm, and an external resonant frequency doubling stage based on PPKTP. The new experiment aims to explore possible techniques for the application of magnesium as a frequency standard. With its unique features, magnesium remains an interesting candidate for high-precision spectroscopy, frequency standards and for frequency comparisons, which are of high relevance for tests such as the constancy of fundamental constants.
VI. Concluding Remarks Atom optics is an active and highly promising field that has reinvented itself many times in the past few decades. The level of experimental control has improved drastically and the new techniques have in turn led to the preparation of better matter-wave sources. We have summarized recent developments in the field with special emphasis on the research topics covered in our group. The first section has shown the vast applicability of micro-optical elements for the preparation and manipulation of atomic samples. This development is in many respects complementary to the use of miniaturized magnetic traps, so called atom chips. An integeration of these two
VIII]
ATOM OPTICS A N D I N T E R F E R O M E T R Y
83
techniques is a promising candidate for the next decisive steps in atom optics and neutral-atom based quantum information processing. We have also shown the vast new possibilities in coherent atom optics due to the advent of Bose-Einstein condensates. Based on the methods available for their coherent manipulation we have given a brief introduction to the field and shown some potential applications. Atom interferometry is currently surpassing some of the most sensitive measurement devices to date and may soon replace some of these. So far the best candidates for precise frequency standards and sensing devices are unclear. We have presented a brief introduction to the field and motivated our research in this area. However, it is certainly only the combination of the techniques presented here that will be able to exploit the advantages of atom optics fully. So far all the experiments here are sophisticated apparatuses requiring vacuum chambers and well-controlled experimental conditions. However, their combination may make atom optical devices available to a large number of researchers and may even allow for their use in precision sensors for a wider use.
VII. Acknowledgments The work presented is the result of a team effort. We are grateful for the commitment of a large number of colleagues. Significant contributions have been made by K. Bongs, C. Bord6, F.B.J. Buchkremer, S. Burger, L. Cacciapuoti, A. Clairon, S. Dettmer, A. Douillet, R. Dumke, K. Eckert, D. Hellweg, J. Helmcke, C. Jentsch, J. Keupp, M. Kottke, H. Kreutzmann, A. Landragin, A. Lengwenus, M. Lewenstein, T. MehlstS.ubler, J. Mompart, T. Mfiller, T. Mfither, U.V. Poulsen, N. Rehbein, J. Ries, T. Rinkleff, P. Ryytty, A. Sanpera, G. Santarelli, L. Santos, T. Schulte, K. Sengstock, N. Ubbelohde, M. Volk, J. Wykhoff, and J.J. Zondy. This work has received financial support by the SFB 407 and the Schwerpunktprogramm "Quanteninformationsverarbeitung" of the Deutsche Forschungsgemeins-chaft, by the project PROCOPE "Precision MatterWave Interferometry," and by the projects A C Q U I R E and ACQP as well as the R T N Networks CGQ and CAUAC of the European Commission.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 50
A TO M - WA L L I N TER A C TIO N D. B L O C H and M. D U C L O Y Laboratoire de Physique des Lasers, UMR 7538 du CNRS, UniversitO Parisl03, 99 Av JB Clement, F-93430 Villetaneuse, France I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. L o n g Range A t o m - S u r f a c e Interaction: Principles and Near-Field Limit . . . . . A. G r o u n d State A t o m and Perfect Reflector: from L o n d o n - v a n der Waals Interaction to the Retarded C a s i m i r - P o l d e r Limit . . . . . . . . . . . . . . . . . . B. Excited A t o m in F r o n t of a Reflector: Radiative and z -3 N e a r Field Behaviors C. vW Surface Shift and Virtual Transitions . . . . . . . . . . . . . . . . . . . . . . . . D. Interaction with a Dielectric M e d i u m . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Near-field Modification of the Lifetime of an Excited A t o m in F r o n t of a Real Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Interaction of an A t o m with an Anisotropic M e d i u m . . . . . . . . . . . . . . . . III. Experimental Approaches for the Probing of A t o m - S u r f a c e Interaction . . . . . . A. Observation of the vW Interaction T h r o u g h Mechanical Effects . . . . . . . . B. Probing the Vicinity of a Surface with Selective Reflection Spectroscopy . . C. N o n l i n e a r Selective Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Evanescent Wave Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. Spectroscopy in a Thin V a p o r Film: Micro- and Nano-cells . . . . . . . . . . . IV. SR Spectroscopy as a Diagnostics Tool of the A t o m - S u r f a c e Interaction . . . . . A. Elementary Observation of the vW Interaction in Linear SR Spectroscopy . B. The M e t h o d of Experimental M e a s u r e m e n t of the C3 Coefficient . . . . . . . . C. Observation of the R e s o n a n t Long-range Coupling Between a Surface M o d e and an Excited A t o m i c Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. F6rster-like Energy Transfer Induced by the Near-field Coupling to the Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E. A Search for A n i s o t r o p y in the vW Interaction: Studying Z e e m a n Components ............................................. V. New Developments and Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Towards the E x p l o r a t i o n of Strong Confinement to the Surface T h r o u g h Spectroscopy in a Nanocell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. T h e r m a l Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. vW A n i s o t r o p y and Surface-induced Inelastic Transfer in an A t o m i c Beam D. A t o m Interaction with N a n o b o d i e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. A c k n o w l e d g m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
92 94 95 97 97 101 103 106 107 107
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This chapter deals with atom-wall interaction occurring in the "longrange" regime (typical distances." 1-1000 nm), when the electromagnetic fluctuations of an isolated atom are modified by the vicinity with a surface.
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D. Bloch and M . Ducloy
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Various regimes of interaction are discussed in an Introductory part, from Cavity Quantum ElectroDynamics modifications of the spontaneous emission, to Casimir effect, with emphasis on the atom-surface van der Waals interaction, characterized as a near-field interaction governed by a z -3 dependence. The major part of the Chapter focuses on the experimental measurements of this van der Waals interaction, reviewing various recent techniques, and insists upon optical techniques, and notably selective reflection spectroscopy which is particularly well-suited when excited atoms are considered. A review of various experiments illustrates the specific effects associated with a resonant coupling between the atomic excitation and surface modes, from van der Waals repulsion to surface-induced resonant transfer, and with anisotropy effects, including metastability transfer induced by a quadrupole contribution in the interaction. The effects of a thermal excitation of the s u r f a c e - with a possible remote energy transfer to an atom - and of interaction with nanobodies- which are intrinsically non p l a n a r - are notably discussed among the prospects.
I. Introduction The van der Waals (vW) attraction between two bodies is an ubiquitous phenomenon in nature, notably important to explain cohesion properties of materials. It originates in the correlation between the unavoidable electromagnetic (e.m.) field fluctuations (of quantum or thermal origin) of the two facing bodies. In spite of its extreme importance, direct physical measurements of this fundamental attraction are actually scarce. These effects are intimately connected to the Casimir attraction (Casimir, 1948), a paradigm essential for Quantum Electrodynamics (QED) (for a review see e.g., Bordag et al., 2001), and of fundamental importance in many problems, including the determination of the cosmological constant. The Casimir force describes the attraction between two reflecting surfaces due to vacuum fluctuations and it includes the retardation effects (light propagation). The problem of two media separated by vacuum, can be viewed as a generalized vW attraction. Very recently, precise measurements of the Casimir attraction have appeared (for a review see e.g., Lambrecht and Reynaud, 2003), that stimulate new developments in the theory, notably justifying studies at various distance ranges, or consideration of material dispersion effects and thermal effects. An elementary situation for this interaction between two bodies is the restriction to the interaction between a surface and a single atom. The theoretical link between the two problems goes through the approximation
I]
A T O M - W A L L INTERACTION
93
of an infinitely dilute medium (see Barash and Ginzburg, 1989). One experimental advantage is the variety of investigation methods that becomes available: among others, molecular beam technology, high resolution spectroscopy, laser cooled atoms, have been found appropriate for these studies. At the other end, the atom-surface problem can be seen as an extrapolation, through an integration over the collection of atoms that is the essence of the dense media, of the atom-atom long-range interaction, known as the vW long-range tail of an interatomic potential (London, 1930; Lennard-Jones, 1932). More generally, the long-range atom-surface interaction is a topic of interest in its own right. "Long-range" here means that the atom is at such a distance from the surface- usually _> 1 nm-, that the atom does not feel the details of the atomic structure at the surface: the physical surface can be simply approximated as a planar wall, and a 2D symmetry translation is naturally introduced in the problem. This atom-wall interaction is an unvoidable feature in Cavity QED, a realm of Physics that has demonstrated the possibility of reversible exchanges of excitation between the cavity modes and the atom (see e.g., Haroche, 1992), or that permits such spectacular effects as the enhancement/inhibition of the atomic spontaneous emission with respect to the atom-surface distance (Kleppner, 1981; Heinzen et al., 1987). In addition, with emerging nanotechnologies and their possibility of atom-by-atom implantation on a substrate, the precise knowledge of the interaction governing an atom in its approach towards a surface has become an essential concern. Similarly, for the understanding of desorption processes, it should be essential to know how a departing atom evolves from the attractive trapping region, to the freespace. The knowledge of the atomic structure, at least in the free-space, is usually extremely precise. This permits a detailed description of the atomsurface interaction provided the dense medium itself is described not in an ideal manner, but realistically (dispersive dielectric medium, real metal, etc.). The present work mostly concentrates on the interaction of an excited atom with a surface. This situation, although more specific, is of an obvious interest for various applications, notably nanochemistry, and is susceptible to offer a variety of behaviors. As will be shown, it also provides a deepened insight into the effect of a possible excitation of the surface itself. In addition to the energy-shift induced by the attractive potential exerted by the wall, one predicts for excited atoms a surface-induced modification of the atomic lifetimes. Drexhage and coworkers extensively studied this problem as early as the 1970s, in the experimental situation of atomic species (Eu 3+ notably) actually embedded in organic layers (Drexhage, 1974).
94
D. Bloch and M. Ducloy
[II
An overall agreement was demonstrated between the experimental results and the theoretical predictions, that were actually based upon a model of an isolated atom evolving freely at some distance from a surface. The extension to atom-surface interaction naturally permits to explore more singular and quantized systems than those available with embedded emitting species. Among these general topics, from the early 199)s, we have been involved with the study of the problem of the near-field interaction between an excited atom and a surface, with experiment,, most often relying on dedicated optical techniques. The theoretical developments have encompassed the effects of a dielectric resonance, anisotropy in the interaction, and shape factor for interaction with microbodies and nanobodies. This review first summarizes the essential relevant results of Cavity QED, notably in its connection with the non-retarded vW interaction, and discusses the various subtleties that often make the electrostatic approach oversimplified. The following section (Sect. III) reviews the main experimental methods. The emphasis is on the optical methods, mostly relying on the monitoring of the reflected light at an interface, and on the transmission through a very thin vapor cell. This description offers the basis to the analysis, in Sect. IV, of some of our essential experimental results: the spectroscopic approach allows one to observe the atomic behavior at a typical distance to the surface in the ~ 100 nm range. Before the final conclusion, Sect. V deals with the most recent developments (both experimental and theoretical) that are in particular oriented towards the interaction of atomic systems with micro- and nano-structures on the one hand, and on the other hand, with thermal excitation of the surface.
II. Long Range Atom-Surface Interaction: Principles and Near-Field Limit The major principles that govern Cavity QED and interaction of an atom with a reflector, notably a perfect reflector, have been extensively studied in numerous works, including for example, the review by Hinds (1994). The aim of this section is to first recall major results for the nonfamiliar reader, and to emphasize theoretical results that are more specific to the experimental works reviewed in this article. Hence, we mostly focus here on the near-field limit of the surface interaction, corresponding to the vW description, and then discuss in more detail the specific case of an interaction with a real reflecting surface, describing the reflector as a dielectric medium instead of an ideal metal.
II]
95
ATOM,WALL INTERACTION
A. GROUND STATE ATOM AND PERFECT REFLECTOR: FROM LONDON-VAN DER WAALS INTERACTION TO THE RETARDED CASIMIR-POLDER LIMIT
An elementary approach of the atom-surface interaction can be traced back to Lennard-Jones (1932). It relies on the idea of a London-van der Waals dipole-dipole interaction (London, 1930) between an electric dipole d, and its electrostatic image induced in a reflector (see Fig. 1). The interaction potential is hence given by: 1 (dZ+d 2 )
V=
4rre0
(1)
16z 3
In Eq. (1), z is the dipole-to-sur~ce distance, and (dx, dy, dz) the components of the vectorial dipole d. Although an atom has in general a null permanent electric dipole (dipole quantum operator D, with (D(t)) = 0), its quantum (quadratic) fluctuations cannot be neglected ((D2(t)) --/=0). This permits to extend the electrostatic model, taking into account the instantaneous correlated fluctuations induced in the reflector. One finds an additional interaction potential Hvw to be included in the atomic Hamiltonian: (2)
1 (D 2 + D 2) Hvw - - 47reo 16z 3
Equation (2) shows that the energy shift of the ground state induced by the surface interaction is always negative,- i.e., attraction- and is governed by
iiiiiiiiii;iiiiii!!i!iii!!i!i!!i!i!i
vacuum
i i i i iiiiiiiiiil .9- . . . . . . . . . - . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . . . .
................................................-.
.9. . . . . . . . . . . . . . . 9......-.-.....-.-.-.......-.-, .9. . - . - . . . - . . . . . . . . -............................ .9- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . - . . . . . . , . . .9- . - . . . - . - . - . -...-.-.-.-.-.-.-...-.-.-.-.9............-.-...-.-......................,.... .9. . . . . . . . . -.. 9 9. . . . . . . . . . - . . . . . . - . - . - . . , . ......-..........,..,............................. .9. . - . . . . . - . - . . . - ~ -............................. .................................................. -.....................-...........................
y LZ
,,
FIG. 1. The electrostatic image induced in a reflector by a charged dipole system.
96
[II
D. Bloch and M. Ducloy
a factor (gl D2 + Dz21g)(Ig) the ground state wavefunction). Remarkably, this surface interaction potential is not isotropic; however, the anisotropy vanishes in the common situation of an atom featuring a spherical symmetry, as most of atom ground states. It had been soon predicted by Casimir and Polder (1948), in a work parallel to the study by Casimir (1948) of the electromagnetic interaction between two metal plates, that this z -3 behavior is not compatible at long distance with the noninstantaneous propagation of light. Taking into account the retardation effects, they show that the actual behavior evolves continuously from a z -3 dependence (for z---> 0) to an asymptotic z -4 (for z--+ oo), with a final coefficient becoming governed by the (isotropic) electric atomic polarizability. Experimental evidences of this deviation from z -3 behavior to the z -4 behavior at long distance have appeared only in the recent years (Sukenik et al., 1993; Landragin et al., 1996; Shimizu, 2001; for a review, see Aspect and Dalibard, 2003). An important point recognized by Casimir and Polder (1948) with these retardation effects is that the distance range in which the instantaneous (near-field) a p p r o x i m a t i o n - also called electrostatic i n t e r a c t i o n - is applicable corresponds to distances smaller than the (reduced) wavelength of the relevant quantum transitions (see Fig. 2). For a real atom, and in spite of the many transitions that can couple the ground state to excited states,
DIELECTRIC
!............. VACUUM
ii:i:i:i:!:i:i:
LONG
4 RANGE r
i iii!ii " ii!!!i!i E E
i}iiiiiii
cT
iiiiiili
o
i iiiiii iiiii!i!i
s T
NEAR-FIELD
FAR-FIELD . . . . . . . . . . . . . . . . . . . .
R E T
R
A R D
"T I C
E D
, . . . . . . . . . . . . . . . . . . . .
I 0
1 nm
X (1-10gm)
FIG. 2. The various ranges of atom-surface distance, with the corresponding type of interaction.
II]
ATOM-WALL INTERACTION
97
there are numerous situations for which a two-level approximation, limited to the ground state and the resonant level, is valid: it yields a simple estimate of the range for which the short distance approximation (i.e., instantaneous image) applies to.
B. EXCITED ATOM IN FRONT OF A REFLECTOR: RADIATIVE AND Z -3 NEAR FIELD BEHAVIORS
To describe the surface effects on an atom in an excited state, one needs to consider the radiative properties of the atom associated with spontaneous emission. This comes in addition to the quantum dipole fluctuations, that are similar in essence to those for a ground state. This spontaneous emission can be described as radiated by an atomic dipole oscillating at the transition frequency or as a sum of such radiations, if various decay channnels are opened. In the vicinity of a reflector, the boundary conditions are responsible for a "self-reaction" correction term that imposes modifications to the radiative diagram in vacuum. Indeed, the oscillating atomic dipole (object) interferes with the oscillating dipole image induced in the reflector, whose oscillation is now phase-delayed by propagation effects: this results in both a radiative energy shift, and a modified decay rate of the spontaneous emission (Dalibard et al., 1982; Meschede et al., 1990; Barton, 1994). The vacuum wavelength of the electromagnetic oscillation provides a natural scaling factor to evaluate the distance range to the surface, sorting far-field and near-field effects (see Fig. 2). In agreement with the wellknown far-field expansion of the energy radiated by an oscillating dipole (Hinds and Sandoghdar, 1991), one finds for an excited state a slowly damped oscillating behavior, evolving asymptotically as z -1 cos (kz) (k: the wavenumber associated to the considered radiative process), at odds with the Casimir-Polder limit applicable to a ground state. This oscillatory radiative shift, although it remains tiny relative to the inverse of the spontaneous emission decay time, has been notably observed with an atomic beam passing through the node or antinodes of an orthogonal Fabry-Perot interferometer (Heinzen et al., 1987). Conversely, in the near-field limit, the radiative shift is dominated by a z -3 cos (kz) term. In the electrostatic limit (kz << 1), on which we will mostly concentrate on, this contribution turns out to be nothing but the z -3 vW shift mentioned above.
C. v W SURFACE SHIFT AND VIRTUAL TRANSITIONS
Before proceeding to the quantitative evaluation of the vW surface interaction, it may be of interest to note that a pure classical atom
98
[II
D. Bloch and M. Ducloy
description, with an orbiting electron, already provides some modeling of the dipole atomic fluctuations. The more the orbiting electron is excited, the stronger are the fluctuations. As a result, optical spectroscopy can in principle be used to evidence an atom-surface interaction, with a z -3 redshift in the near-field electrostatic approximation. This has provided the basis for numerous experiments, such as the ones evoked in the following sections. Paradoxically, a pure quantum two-level model contradicts this prediction (Hinds and Sandoghdar, 1991), as, in this limited frame, the average dipole fluctuations are equal for each level, and the spectral line is not shifted. This remark may help to understand the fundamental importance of considering virtual transitions in the evaluation of the strength of the z -3 vW interaction. With the expansion 1 - ~ j ~)QI, (with 1 the identity operator), one gets: {iID2Ii)- ~-~(iIDI j ) ( j [ D I i } - Z J
l{ilDIj)I2
(3)
J
where, in Eq. (3) appears a sum over all the virtual transitions (a similar development holds for the non scalar contribution in Dz2). Remarkably, parity considerations impose that when comparing {ilD2Ii} and (jlD21j} (with Ii) and [j) connected by an allowed dipole transition), the virtual couplings relevant for each of the two levels Ii) and Ij) define two different sets of atomic levels: this confirms that a pure two-level model is essentially unable to predict the strength of the vW interaction. This strength can be conveniently described by a C3 coefficient, related to the vW Hamiltonian Hvw by: C3(1i)) - -
Z3(ilHvwli) h
(4)
(with h the Planck constant), so that :
11[
C3(1i)) - 4yre0 16 h ~
I(ilDIj)I2 + ~
J
1
I(ilDzl j)12
J
(5a)
or, assuming an isotropic interaction (e.g., spherical symmetry for the considered li) level),
1
C3(li)) - 48rre0h ~ . I(iIDIj)
12
(5b)
J
In general, the prediction for the C 3 value characterizing the vW interaction can be rather accurate, the atom being in the ground state or in
II]
ATOM-WALL INTERACTION
99
an excited state atom. This is because Atomic Physics has developed numerous and refined tools for the evaluation of atomic wavefunctions. However, a few remarks should be pointed out: (i) Contrary to the spontaneous emission, which is negligible in the far infrared (IR) range, and dominant in the UV part of the spectrum, the C3 value is often dominated by the contribution of dipole couplings associated to virtual (far) IR transitions (see e.g., Fig. 3 and table I). This is due to the X3 dependence appearing in the dipole coupling for a given oscillator strength. (ii) In most cases, the C3 value grows with the atomic excitation level: this can be seen either from the increasing dipole fluctuations when the atomic excitation increases (comparable to a stronger atomic polarizability), or from the more tightened atomic structure, with more numerous IR couplings, typical of levels close to ionization. (iii) The vW Hamiltonian Hvw is nonscalar in its essence, with a quadrupole term Dz 2 susceptible to modify atomic symmetry. Such a modification becomes quite important when the vW interaction ....'~iii..~ 8P
6F 5F 4F
:J,,7',5~7' . ,,un:i ..............~..,~=~,,. .~==,.\ %. ,,::~:~:~:~:,:,, ..................................................................
7P3/2 7P1/2
.........
12.15
6P3/2 6P1/2
~\\\\\\\\\\\\\\\\-e, Cs
-
6 S 1/2
FIG. 3. The Cs levels, with the virtual couplings for Cs(6D3/2)-in black lines- and Cs(6Ds/2) in grey-. The strength of the couplings, as estimated for an ideal reflector,- see table I - is made visible by the variable thickness of the coupling arrows.
100
[II
D. Bloch and M. Ducloy Table I
Calculated contributions of the various virtual couplings to the vW shift for a Cs (6D3/2) atom in front of an ideal reflector, or in front of a dielectric medium, with a wavelength-dependent image coefficient.
Ideal Reflector
r (co)
Sapphire c•
6 D3/2
9~ (gm)
(kHz. ktm3)
Sapphire c•
(kHz. ktm3)
6 P1/2
( - ) 0.87614
0.38
( - ) 0.92085
0.09
0.61
0.06
6.76
-15.67
-107.96
1.38
1.62
2.23
0.51
0.55
0.28
6 P3/2
7 Pll2
( - ) 12.147
7 P3/2
( - ) I5.571
0.61
0.23
8 P1/2
3.2040
8 P3/2
3.1213
0.06
0.55
0.03
9 P1/2
1.9803
0.05
0.51
0.02
4 F5/2
5.3083
15.28
0.59
9.01
5 F5/2
2.2812
0.34
0.52
0.18
6 F5/2
1.7419
0.18
0.50
0.09
7 F5/2
1.5245
0.10
0.49
0.05
8 F5/2
1.4104
0.06
0.48
0.03
9 F5/2
1.3416
0.04
0.47
0.02
Total
25.3
-95.7
compares with the energy difference between levels, notably at very short distances (see Sect. V. A.3), or when some sublevel degeneracy is removed (e.g., in the presence of a magnetic field, with Zeeman degeneracy removed), or for a polarized atomic system. However, for a statistical set of sublevels, sum rules enable the vW interaction to be simply estimated with the knowledge of the dipole fluctuations associated to the radial part of the wavefunction, and with simple angular rules (Chevrollier et al., 1992). Note that in principle, the various hyperfine components originating from the same level do not necessarily undergo an identical vW interaction potential, owing to their different angular momentum. However, for atomic states with low values of the angular orbital momentum (e.g., S or P levels, that can be coupled only to S, P, D levels) the anisotropy effect remains relatively small (see also Sect. IV.E.). More generally, as long as the magnetic component remains degenerate, the averaged vW shift is governed by the scalar vW contribution (that can be identified to the r.h.s, of Eq. (5b)), while the quadrupole
II]
ATOM-WALL INTERACTION
101
contribution, that varies with the magnetic component, is essentially susceptible to induce an hyperfine-dependent broadening (Papageorgiou, 1994). (iv) In the summation implied by Eq. (5), the transitions to high-lying states and to auto-ionizing levels are very numerous, and their influence, in spite of their unfavorable short wavelength, can be important, notably for a ground state. Derevianko et al. (1999) have estimated that for a Cs atom in its ground state, the transitions involving the external electron contribute to only ~ 60% of the vW interaction, in spite of the alkaline nature of this atom. Indeed, a large part of the C3 value originates in transitions involving excitation of the electronic core. However, the nearfield approximation is valid only in a very limited range for these contributions, located in the vacuum ultra-violet (VUV) range. Above the range of core transition wavelengths, the near-field approximation (vW interaction) still stands, provided that the short wavelength couplings are neglected. Also, the core contribution does not vary much from one energy level to the other, and its contribution to spectral lines largely cancels out.
D. INTERACTION WITH A DIELECTRIC MEDIUM With respect to the large range of wavelengths involved in the vW coupling, no material can be expected to behave as an ideal reflector on the whole spectrum of interest. Rather, any real surface, including those made of noble metals, exhibits dispersive features, that can be dealt with when considering the general problem of an atom interacting (in the near-field approximation) with a dielectric medium. In the frame of a pure electrostatic model, the induced image in a dielectric medium is simply reduced by an image coefficient r (0 < r < 1): e-1 r = -e+l
(6)
with e the (real) dielectric permittivity of the medium. Actually, the static value of the permittivity, appearing in Eq. (6), is not relevant to deal with the real properties of the reflector. Indeed, in our problem of atom-surface vW interaction, the temporal dipole fluctuations have been introduced, and developed over a set of virtual transitions. Following the work of Lifchitz (1956) for the interaction between two dielectric solid bodies, the general response for a ground state atom interacting with a surface has been approached in the 1960s (Mavroyannis, 1963;
102
D. Bloch and M. Ducloy
[II
McLachlan, 1963a,b). For each virtual transition ]i) ~ [j) contributing to the vW shift, one must introduce in Eq. (5) an image factor r(coo.) (with wij: the transition frequency, counted > 0 for an ]i) --+ [j) absorption): 1
C3(1i)) - 48~re0--------hZ . r(coij)[ (iIDI j)I 2
(7a)
J
with:
2 fo ~176 coO. e(iu)- l du r(wij) - -~ o~2 + U2 e(iu) +~
(7b)
In Eq. (7), e(iu) is the analytical extension to the complex plane of the frequency-dependent dielectric permittivity e(co). Equation (7) shows that for a fluctuation, apparently sensitive to a transition frequency co0., the response efficiency is dependent upon the whole spectrum of the material. Also, it can be shown from causality reasons (e.g., from the KramersKr6nig relation), that r(cou) decreases in a monotonic way with increasing COgj. This implies, in agreement with the pure electrostatic model, that 0 < r(o~) < 1. Moreover, far away from dielectric resonances, e(wij) is real and slowly varying, and r(oJ/j) ~ [e(oJ0.) - 1]/[ e(co/j) + 1]; this justifies that when the vW interaction depends only on transitions falling into the transparency region of the material, the image coefficient factor is approximated by r = (n 2 - 1)/(n 2 + 1), with n the refractive index of the material in the transparency region. In most of the real situations, the transparency window of a material is not large enough (relatively to the width of the absorption bands) to totally neglect the influence of the neighboring absorption bands. This incorporates some corrections to (n 2 - 1)/(n 2 + 1). This has been illustrated in the course of our work (Failache et al., 2003): while for sapphire, a material transparent from 0.2 ~m to 5 ~tm, the estimated value at X = 0.87 pm is r ,-~ 0.49, the simple (n 2 - 1)/(n 2 + 1) approximation yields r = 0.51. When an excited state interacts with a dispersive reflector, the vW interaction can still be described by a set of dielectric reflection coefficients r(co/j), but there is no longer such a restriction as 0 < r(w~) < 1. From the Wylie and Sipe (1984,1985) approach, one gets indeed (Fichet et al., 1995a):
2 fo~ wij e(iu)- l du + 2~e[~(Icoo.])-1]| r(wij) -- -~ 092. + u 2 e(iu) + ~ I~oo.I) + 1
)
(8)
with | the Heavyside function [| (co) = 1 for ~o > 0, | (co) = 0 for co < 0)] and ~te standing for "real part". While the first term in the r.h.s, of Eq. (8)
II]
ATOM-WALL INTERACTION
103
behaves as the contribution from Eq. (7), with averaging over the whole spectrum of the material, the second term in the r.h.s, of Eq. (8) appears only for a virtual emission (i.e., for co0- < 0), and has no equivalent for a ground state atom. It is calculated at the p~;ecise virtual transition frequency, and it is susceptible to take any real value, moreover without any sign restriction. The physics of this additional term relies on the possible resonant coupling between the virtual atomic emission, and a virtual absorption in a surface mode. The surface mode resonances, such as illustrated in Fig. 4 for typical windows, are derived from the bulk resonances - governed by ~(co) -, through a shape factor [ ( e - 1)/(~ + 1)]. Note that the resonant surface response can possibly induce a change of the sign of the atom-surface interaction, leading to a vW repulsion, instead of the universal attraction. This can be interpreted in the following way: instead of instantaneous image fluctuations, the resonant coupling enables giant but time-delayed dipole fluctuations in the dense medium, as induced by the atomic fluctuations in the range of the virtual transition frequency. Note that as will be discussed later on (Sect. V), the restriction (in Eq. (8)) to a virtual atomic emission is related to the standard assumption that the surface itself does not bear excitation (i.e., the temperature is assumed to be T = 0). This is legitimate as long as far IR transitions can be neglected at room temperature.
E. NEAR-FIELD MODIFICATION OF THE LIFETIME OF AN EXCITED ATOM IN FRONT OF A REAL SURFACE
The modifications of the lifetime induced in the vicinity of a reflector are also specific to the excited atom. For an ideal reflector, there appears, along with the damped oscillatory behavior of the energy shift (see Sect. II.B), an enhancement/inhibition of the spontaneous emission close to surface, depending on the dipole orientation: in the limiting situation z = 0, a dipole parallel to the wall does not radiate, because the induced image oscillates with a phase strictly opposite to the one of the dipole source, while the emission rate doubles for a dipole with a normal orientation. Such a behavior, easily derived from a classical model, has also been rigorously justified in the frame of Quantum Mechanics (Courtois et al., 1996). In front of a "real" surface, the above interference effects are attenuated because the reflection is only partial, but an additional damping must be considered, related with the opening of extra-decay channels. Indeed, for a transparent dielectric medium, and as discussed by Lukosz and Kunz (1977a), the excited atom can lose its excitation by the emission, in an evanescent mode, of a photon, that has the ability to freely propagate in the
104
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D. Bloch and M . D u c l o y 20
~ ii
SAPPHIRE
;.
10 (a)
-10
~, (gm) I
I
12
10
I
14
I
16
18
I,
20
I
22
_ F U S E D SILICA
(b)
X, (gm)
-1 I
5
I
I
10
I
15
20
I
25
I
30
4
i! ,o
(c)
-2
~ (gm) 5
I
10
,
I
15
I
20
I
25
FIG. 4. (a) ~te[(e- 1)/(e + 1)] (solid line) and ~m[(e- 1)/(e + 1)] (dashed line) for sapphire with the c-axis perpendicular to the window (i.e., c• (b) same for fused silica; (c) same for YAG. The data for e is extracted from Schubert et al. (2000) for sapphire, from Palik (1985) for fused silica, and from Gledhill et al. (1991) for YAG. t r a n s p a r e n t dielectric m e d i u m (see Fig. 5). This effect, associated with an atomic emission in the f o r b i d d e n region outside the fluorescence cone, always enhances the atomic relaxation rate, but by an a m o u n t that remains finite, even w h e n very close to the interface. This a m o u n t depends on the dipole orientation and on the dielectric m e d i u m index, but it remains
II]
ATOM-WALL INTERACTION
105
FIG. 5. Emission in the "forbidden region:" when an atomic emitter of the vapor is close enough to the interface, emission in the near-field yields observable fluorescence outside the fluorescence cone defined by sin(0c,.) = 1In.
relatively small (e.g., the enhancement does not exceed a factor ~ 3 for an index n = 3, and for the optimal dipole orientation). Its variations with the distance to the surface, originating in the standard features of evanescent wave, typically span over the relevant wavelength. The extension to a multilevel atom, with various decay channels, is straightforward with respect to the various wavelengths to be considered. When the wall is not transparent at the considered emission wavelength, the absorption prevents those extra-decay channels related with an emission propagating in the forbidden cone. However, energy can be transferred from the excited atom to the surface modes (e.m. propagation guided along the surface). This near-field coupling to a surface mode appears to be the dissipative counterpart of the vW energy shift. It is governed by a surface response that diverges as z -3 (Wylie and Sipe, 1985), and governed by a factor ~m[(e(co0.) - 1)/(e(cou) + 1)], whose variations for typical windows are illustrated in Fig. 4. This divergence establishes the possibility of dramatic changes in the relative transition probabilities for an excited atom at a small distance from a wall (Failache et aI., 2002). Also, the efficiency of this transfer depends on the line strength: as for the vW interaction, the long wavelength transitions located in the far IR, where the spontaneous emission is usually negligible, are usually dominant in this near-field process.
106
D. Bloch and M. Ducloy
[II
F. INTERACTION OF AN ATOM WITH AN ANISOTROPIC MEDIUM
The "long-range" approximation, as discussed in Sect. I, implies that the atom interacts in a system offering a perfect plane symmetry, so that the interacting Hamiltonian is governed by a cylindrical symmetry. Actually, this symmetry can disappear if the medium itself exhibits some anisotropy, e.g., if the interacting surface has finite dimensions or a spherical shape (see Sects. V.C. and V.D.), or as discussed here, in the case of a birefringent medium. Up to a recent work, performed in our group (Gorza et al., 2001) and involving a detailed treatment of the birefringent medium for an arbitrary orientation of the optical axis, this problem had been seldom tackled when the (quantized) interacting particle is an atom. Several studies, that had involved an interaction with liquid crystals, notably those of Kihara and Honda, 1965, Bruch and Watanabe, 1977, and Okano and Murakami, 1979 yield however valuable hints for an atom in the ground state (see also the work of Sarlah and Zumer, 2001). As a general result, a major modification in the interaction appears in the interaction Hamiltonian, now described by such an expansion: Hvw - - 4zrs0
16z3
(9)
with usually ot -r This introduces in the principle extra quadrupole effects in the interaction, with the additional breaking of some usual symmetry rules. In the principle, this break of symmetry within the vicinity of the surface may enable previously forbidden transitions, analogous to those observed by Boustimi et al. (2001c) and Karam et al. (2002). Even for an atom with a low angular momentum, when the effects are restricted to the scalar part of the interaction, the medium anisotropy can still induce some sensitive effects, through an orientation-dependent shift of the resonant properties. Indeed, the dielectric properties of the medium are governed by two different permittivity coefficients (respectively the permittivity s// along the birefringence axis, and s• orthogonal to this axis), whose resonance frequencies are not equal. Hence, the extrapolated surface resonances, estimated from the surface response [ ( s - 1)/(s + 1)] are also different (Fichet et al., 1995; Gorza et al., 2001; Failache et al., 2003). Within the scalar approach, an effective dielectric permittivity Self can be defined, that averages the permittivities s// and s x, with a geometrical weighting dependent on the orientation of the birefringent axis relative to the surface. As illustrated in Fig. 6, the atom-surface resonant coupling becomes tunable through an adequate choice of the c-axis orientation, and this may permit to tailor a giant and possibly repulsive vW interaction, or to impose a specific near-field quenching of the atomic excitation.
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ATOM-WALL INTERACTION 25-
107
r (12.15 gm)
20 15 10 5
i
TTRACTI
0 -5
~
-10
REPULSION
-15 -20 -25
O(degrees)
0
I
I
6'o
I
FIG. 6. Tunability of the dielectric image coefficient r (see Eq. (8)) with the orientation of the c-axis. The figure illustrates the situation for a sapphire window interacting with an atom whose virtual emission, at 12.15 gm, is in resonance with the surface modes. 0 is the angle between the c-axis and the normal to the window. The atomic state itself is assumed to be isotropic.
III.
Experimental
Approaches
Atom-Surface
for the Probing of
Interaction
A m o n g the various experimental methods that have been used for the probing of atom-surface interaction, one may distinguish between techniques relying on mechanical effects, and methods based upon optical spectroscopy. In principle there is no intrinsic limit to the spatial resolution of mechanical methods, while the optical spectroscopy methods are commonly plagued by a limited spatial resolution (on the order of ~/27r ~ 100 nm), that makes them non convenient to explore these smaller distances to the surface (down to z > 1 nm) for which the surface interaction is described as "longrange." On the other hand, mechanical methods are only well-suited to longlived levels (i.e., ground state, or Rydberg states), while high-resolution spectroscopy is very convenient to study short-lived excited states.
A. OBSERVATIONOF THE v W INTERACTION THROUGH MECHANICAL EFFECTS
A.1. Thermal beam The first observation related with the vW atom-surface interaction can be traced back to the 1960s, with the Columbia group (Raskin and Kusch,
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D. Bloch and M. Ducloy
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1969) evidencing the deflection of a thermal beam of atomic Cs, at a grazing incidence with a metallic cylinder. It was followed by comparable experiments with other species, including molecules, or with dielectric surfaces (Shih et al., 1974; Shih, 1974). However, in these pioneering experiments, a large distribution of impact parameters is involved, while only atoms flying very close to the surface undergo a notable deflection. These measurements (Shih and Parsegian, 1975), affected by the uncertainty on the quality of the polishing of the deviating cylinder, did not permit a sophisticated inversion of the potential, such as discriminating between a z -3 vW potential, a z -4 dependence (asymptotic limit of the Casimir-Polder expansion), and an hypothetical z -2 potential (e.g., for a charged surface). A series of elegant experiments was completed by the Yale group with a beam of long-lived Na (and Cs) atoms in Rydberg states (Anderson et al., 1988; Sandoghdar et al., 1992 and 1996): essentially, the transmission of the atomic beam is measured when flying between two parallel surfaces, whose relative distance is adjustable. The high polarizability of Rydberg levels make them very sensitive to the vW attraction. The transmission methods provide a specific enhanced spatial resolution in the sense that only Rydberg atoms flying in a very narrow central zone, where the two vW attractions compensate, are susceptible to escape from the attraction of the two plates, and to be transmitted and finally counted through an ionization process. This favorable transverse velocity selection also justifies that a classical trajectory model reveals to be sufficient for the analysis. Precision measurement of the z -3 behavior of the atom-surface interaction was achieved (Sandoghdar et al., 1992 and 1996) by measuring the spectral shift of the excitation resonance to the Rydberg levels, for a beam of Na atoms having entered in the ground state in the channeling zone. The quantitative comparison was performed for a plate separation ranging from 3 gm down to a 0.5 lam value, and for various (nS) Rydberg levels (n = 10 to n = 13). It was found to be in agreement with the theoretical predictions. These experiments were essentially conducted for interaction with metal-coated walls. Attempts to extend these experiments to dielectric surfaces (notably uncoated silica blocks) most often led to irreproducible results, with respect to the strong sensitivity of Rydberg levels to stray electric fields. Note that with slight modifications of the set-up, the long-distance CasimirPolder behavior (for a ground state) have been demonstrated (Sukenik et al., 1993), as well as modifications of the spontaneous emission induced by thermal effects on the wall (Lai and Hinds, 1998). It is only very recently that more numerous experiments have been implemented, based upon a mechanical signature of the vW interaction. The technological development of nanogratings have enabled the G6ttingen group (Grisenti et al., 1999) to observe the modified atomic diffraction of a
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ATOM-WALL INTERACTION
109
rare gas b e a m - in its ground state and more recently in a metastable state (Brtihl et al., 2002)- in a transmission grating. The vW interaction reduces the effective opening of the slits and induces a modification of the diffraction pattern, conveniently observed due to the high quality and reproducibility of the nanoslits involved in the grating (periodicity ~ 100 nm). Relative to the experiments on Rydberg levels, the small size of the transmission region is compensated for by the weaker interaction coefficient for a ground state. Metastable beam transmission in slits and gratings has also been used to explore the anisotropic part of the vW interaction (see Sect. V.C.) A.2. Cold atoms
The recent development of cold atom technology has opened up a new field to the study of atom-surface interaction. It is notably motivated by the fact that surface-induced effects, like decoherence, can be responsible for major limitations in the trapping and manipulation of cold atoms in integrated atom optics: in particular, at short distances, the vW attraction may be strong enough to attract cold atoms towards the surface and to accelerate them in a final phase of (surface) thermalization. However, the use of cold atoms for the study of atom-surface interaction has been rather restricted, most probably because of the unfavorable duty cycle between the duration required to prepare a bullet of cold atoms (on the order of seconds) and the short time actually spent close to the surface (at 1 lam from the surface, the velocity largely exceeds ~0.1m/s, even for a cold sample prepared 1 mm above the surface). Anyhow, the Orsay group (Landragin et al., 1996) has succeeded in probing the long-range atom-surface interaction, observing the free fall of a sample of cold atoms, down to the surface. They have provided one of the very few evidences of the retardation effects affecting the interaction with the ground state. Essentially, the attractive long-range potential exerted onto a ground state is balanced with a controlled additional repulsive potential as induced by a (blue-detuned) evanescent wave. The resulting bouncing of atomic w a v e s - occuring at a distance estimated to be 47 n m - appears to obey the Casmir-Polder expansion, rather than the simple vW attraction, valid only for z << ;~ (see Sect. II.A.). It is worth noting that, in the fitting, the atomic interaction is theoretically evaluated only with the help of the transitions involving the external electron, while neglecting transitions from the core (Derevianko et al., 1999). This is most probably justified (see Sect. II.C.) by the distance of observation, that largely exceeds the wavelength (in the VUV range) of transitions from the core, hence inducing a strong attenuation through the retardation effects; in addition, the reflectivity of the dielectric surface is most probably very weak for the VUV range.
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Further possibilities to explore a closer range of distance with cold atoms now seems opened with the recent experimental demonstration of quantum reflection, performed by Shimizu (2001) with a beam of ultra-cold Ne* atoms flying nearly parallel to the wall.
B. PROBING THE VICINITY OF A SURFACE WITH SELECTIVE REFLECTION SPECTROSCOPY
B.1. Basic principle
The basic principle of the Selective Reflection (SR) spectroscopy was devised nearly a century ago (Wood, 1909). It consists of the monitoring of a resonant change of the reflection coefficient at an interface (see Fig. 7). Indeed, when irradiating a resonant medium, like a vapor, at the interface with some transparent window, the resonant change of refractive index induces a modification of the reflection, as predicted by the Fresnel formulae. Under normal incidence, the reflection coefficient R (in intensity) obeys: - nv(~)12 ~w + nv(3)
Inw
R(3) -
(10)
with nw the refractive index of the dense window, and n~(3) the resonant index of the vapor, as evaluated for a frequency detuning 3 relatively to the atomic resonance. Assuming In~(6)- 11 < < 1, one calculates at first order the resonant reflectivity change AR(6): A R(6) -- -- 4nw(nw -- 1)~te[(nv(6) - 1] (nw + 1) 3
(11)
................................................................................... i!i!iiiii!iii!iiiiiiii!liiiiiiiiiiiiiiiiiiiiiiiiii!iiiii!iiiiiiiiiiiiiiiiiiiiiiiii!iiiiiiiiiiii!iiiii!i
ii!i!iiiii!iiiiiiiiiiii!i!i!iiiilili!iii!i!iiiiiiiiiiiiiiii!i i! i! iiiiiii!iiiii!iii!ii!iii!iiiiililiiiiii!iiiii!i!iiiiiiiiiiiiiiiiiili i i:i:i:i:i:i:i:i::: ii ::::::::~:::.~ a,:.:...:.:.::: 0)
"'"'"'"""'""
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.:iii!:0")iiiiiiii . iiiii!i!iiiililili iiii!iiiiiiiilililiiiiiiiiiiliiiiiiililiiiiiiiiiiiiiii ..................................................
...............................
!iii!i!ii!!iiiiiiiiiiiiiiiiiiii!i!iii!iii!ii iiiiiiiii i ii!iii)i!iii!iiii i!iiiiiiiililiiiiiiiiiii ~z
FIG. 7. The principle of Selective Reflection (SR) spectroscopy is the detection of a resonant change (i.e., when the irradiating frequency o~ is close to the vapor resonance at COo)A R ( a ~ ) in the field reflected at the window interface. This change originates in the field radiated, for each "slice" of the medium, by the oscillating dipole p(z) induced by the irradiating field.
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A T O M - W A L L INTERACTION
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Equation (11) shows that the SR lineshapes is governed by the dispersion (or refractive index) of the vapor, and is independent of the vapor absorption (within the first order approximation). This is why SR spectroscopy has been used as a way to probe an optically opaque vapor: as opposed to absorption or fluorescence spectroscopy, the SR signal, originating from the reflection at the interface, is insensitive to the cell length. As discussed below, the actual typical distance of observation is on the order of an optical wavelength; this point can appear somehow hindered by the assumption - as in Eq. (10) - of spatial homogeneity of the refractive index. In a microscopic description of a SR experiment, the field reflected at the interface Er(~) is the sum of the field E ~ reflected from the dielectric interface, and the field reflected by the vapor AEr(3). This AEr(3) results from the coherent summing of the field emitted by all oscillating dipoles, driven by the incident field in the resonant vapor. Under the standard assumption IAEr(~)I < < IE~ which is analogous to the one used to derivate Eq. (11), one gets: AR(~) - 2E~
(12) IE~ 2
In Eq. (12), we have conventionally assumed an optical phase such that E ~ is real; also, for purposes of simplicity, all optical fields and oscillating dipoles are expressed in the rotating frame. Note that in more complex geometries (such as a multilayer window, possibly including an absorbing layer, e.g., metallic coating), AR(~) may become proportional to a complex admixture of 9~e[AEr(~)]and~m[AEr(~)], with heavy consequences on the predicted lineshapes (Chevrollier et al., 2001). In the calculation of the resonant reflected field AEr(~), one has to sum up the field radiated by the atom dipoles, that are spatially distributed in the vapor. Hence, a phase factor exp (ikz) (with k = 27r/~ the wave number of the incident radiation) has to be taken into account for the propagation of the incident field to the locally induced dipole p(z) (see Fig. 7). A similar additional phase contribution appears for the coherent summing-up (at the interface z = 0) of the backward radiated field. One gets:
AEr(~) -
1 f~x~p(z,~)exp(2ikz)dz 2ieok
(13)
In Eq. (13), the phase modulation factor exp(2ikz), analogous to a mismatch factor in nonlinear optics, is responsible for the spatial resolution of the SR method, defining a "coherence length" (e.g., ;~/4zr), on the order of a reduced
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wavelength ,k =)~/2zr. This confirms that, when the medium response is spatially homogeneous (i.e., p(z) = p), increasing the length L (L >> )~) does not increase the reflected field. An interesting consequence of this short coherence length is that the SR signal can be dominant in the spatial regions where p(z) varies sharply (i.e., on a )~/47r scale). This is the reason for SR to appear as a convenient method for probing the surface interaction : in an homogeneous medium, only the vicinity with the surface is susceptible to induce rapid changes of p(z). Note at last that in Eq. (13), it has been essential to assume that the density of the resonant medium remains low enough, so that the propagation is unchanged at resonance (i.e., k remains real and identical to its value in vacuum). B.2. Atomic response and atomic motion
For a vapor of motionless atoms, and neglecting the surface interaction effects, the induced dipole p(z) is usually derived from a simple linear resonant response such as: B.2.1. The resonant atomic response.
y/2
p(z,8) - p(8) - P0 8 - iF~2
(14)
with F the relaxation rate of the so-assumed Lorentzian resonance, and ip0 the dipole response at resonance; note that in Eq. (14), P0 is real, so that on resonance (8 = 0), the induced dipole oscillates in quadrature with the exciting field, and radiates a field whose phase is opposite to that of the incident field, signing the absorption process. It is hence easily verified from Eqs. (12-14) that for a homogeneous semi-infinite vapor, the SR signal is purely governed by the dispersive response of the atomic dipole, justifying the elementary approach of Eq. (10). In the early descriptions of the SR spectroscopy, the effect of the atomic motion was simply described as an inhomogeneous broadening of the resonance frequency, with the detuning 8 replaced by a Doppler-shifted detuning, e.g., ( 3 - kvz) with vz the normal velocity for SR under normal incidence. This approach predicts for the SR lineshape a Dopplerbroadened dispersion (or more generally, a dispersive Voigt profile, see Fig. 8). It is actually valid only when the Doppler broadening is small compared to the homogeneous broadening y. Early high-resolution experiments performed by Cojan (1954), and confirmed in the laser spectroscopy era by Woerdman and Schuurmans (1975), have established that the lineshape is narrower than predicted by this approach. Indeed, the steady-state response given by Eq. (14) does not describe the response of atoms departing from the wall, which is a transient build-up response: as
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ATOM-WALL INTERACTION
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F = y/ku = 0.01
i I
I f i
t
-2
-1
0
1
2
FIG. 8. The theoretical SR lineshape, in the local model (dispersive Voigt profile, in dashed line), and in the nonlocal model (solid line). The horizontal frequency scale is in Doppler width (ku) units, the homogeneous width is 0.01 times the Doppler width.
long as an atom is on the wall, its energy structure is considerably perturbed, and it is insensitive to the nearly resonant excitation of the incident field. At least two notable consequences can be derived from this behavior: (i) the response in SR spectroscopy is essentially "nonlocal" due to the transient effects and the atomic motion (Schuurmans, 1976). Indeed, the atomic response of a given velocity group p(z,vz) depends not only on the incident field E0(z), but also on the field E0(z') for all the z' values included in the (classical) trajectory explored before reaching z. (ii) The exp (2ikz) modulation factor tends to scramble the contribution of atoms exploring many wavelengths. This enhances relatively the contribution of those atoms that are slow enough (along the z-axis) to reach their steady-state response within ~,~ and it is at the origin of a subDoppler contribution in the SR lineshape at normal incidence. It also shows that those atoms that spend a long time interacting with the surface bring an important contribution to the SR signal. Note that in spite of the nonlocal atomic response, the evaluation of the SR signal derived from the Fresnel formulae (such as Eqs. (10 and 11) for the normal incidence) still stands, provided that the local refractive index is replaced by an "effective index". This index relies on an "effective susceptibility" of the medium (Nienhuis et al., 1988; Schuller et al., 1991), that spatially integrates all of the atomic response, and is no more intrinsic
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to the medium. It is notably dependent upon the angular orientation of the incident beam.
B.2.2. The SR lineshape and the sub-Doppler logarithmic singularity. The standard analysis of the SR lineshape - in the absence of surface interaction - was developed by Schuurmans (1976). It is valid in the case of a Dopplerbroadened two-level atom system in the regime of a linear field-atom interaction (i.e., saturation effects are to be neglected). It essentially integrates separately the contribution of the atoms arriving onto the surface, assumed to be in a steady state of interaction with the resonant light field, and of the atoms departing from the surface, experiencing a transient regime evaluated as a function of the elapsed time r = Z/Vz since their departure from the wall. One of the major results is that, simply assuming a symmetric velocity distribution, these two separate contributions are identical. The SR lineshape (see Fig. 8) is hence the convolution of a two-level Lorentzian response with a half-Maxwellian (assuming a thermal velocity distribution). This coincidence between the two contributions, later shown to survive when a surface interaction is included in the model (Ducloy and Fichet, 1991), can be traced back to a compensation between the 2kvz Doppler shift between the two velocity groups Vz and -Vz, and the phase factor exp (2ikz) typical of SR spectroscopy. An important property of this convolution is that, due to the asymptotically slow Vz-1 dependence (for Vz--+ oe) of the dispersive Lorentzian in [(3 - kvz) - iy/2] -1, the convergence of the velocity integration is ensured only thanks to the finite tails of the velocity distribution. This means that, for a given detuning, the SR response cannot be seen as originating in the contribution of a single "velocity group", as it is the usual case in absorption (i.e., in the "large Doppler width approximation", that cannot be used here for a dispersive lineshape). Rather, the (weighted) contribution of all atomic velocities has to be included. The abrupt singularity (Vz = 0) of the half-Maxwellian distribution is responsible for the specific narrow SR signal at line center (3 = 0) whose amplitude would diverge logarithmically if the Doppler width would be asymptotically large. ( kuy/2 This narrow response, evolving like lnw+• - with u the thermal velocity - appears superimposed to a broader disperswe Doppler-broadened profile (see Fig. 8). B.2.3. The narrowing of SR lineshape with FM modulation. This remarkable sub-Doppler feature of SR spectroscopy, that singles out the Vz - 0 contribution, has been turned into an efficient Doppler-free method when the Lebedev group (Akul'shin et al., 1982) recognized that the SR
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ATOM-WALL INTERACTION
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lineshape yields a Doppler-free signal once frequency-derivated. Technically, such a derivation is conveniently performed with a FM (frequency-modulation) applied to the incident field, and demodulation of the SR signal. The (FM) SR signal turns out to be a pure Doppler-free dispersive Lorentzian in the infinite Doppler width approximation, now allowed as the derivation ensures the velocity integration convergence. The selected velocity component (k. Ivzl < 9//2) corresponds to atoms moving by less than ~ - normally to the surface- during the relaxation time 2)/-1 associated to the optical width. B.3. SR lineshapes in the presence of an atom-surface interaction potential B.3.1. The general case. Under the assumption of a linear regime of atomlight interaction, and solving the problem of the nonlocal atomic response with the assumption of atomic linear trajectories at constant velocity, a formal calculation of the SR signal has been derived in the Ducloy and Fichet (1991) paper, that accounts for a z-dependent surface interaction potential [i.e., 3 = 3(z)= w-co0(z), with co0(z) the z-dependent resonance frequency of the atom, and co the irradiating frequency], also including a possible z-dependent transition width (i.e., y = V(z)). The calculation generally requires the evaluation of a triple integral, through (i) the averaging over the velocity distribution, (ii) the spatial averaging typical of the SR spectroscopy, and (iii) the spatio-temporal integration associated with the buildup of the oscillating atomic dipole. The FM technique, shown above to emphasize the contribution of slow atoms, is particularly well-suited to the study of atom-surface interaction. because it enhances the contribution of those atoms interacting for a long time with the surface. Technically, the velocity integration is hence replaced by the sole response of the zero-velocity group i.e., atoms slow enough to exhibit a null Doppler shift, although the non local response, even for slow atoms, still demand a double spatial integration. For this simplification, it is sufficient to assume that the Doppler broadening is large compared to both the homogeneous width, and the surface interaction, as evaluated at a distance ~,~ (note that a diverging interaction at small distances remains compatible with this reduction). B.3.2. The specific case of the z -3 v W interaction. The double integral of the general FM SR signal, or at least one of the steps of integration, can sometimes be evaluated analytically. Apart from the simple case of an exponentially decaying potential- as induced by the dipole force associated to an additional evanescent field- a (vW type) z -3 potential has been shown
D. Bloch and M. Ducloy
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A=5
[III
D
A=I
A=20
A=0.2 I
//
IA:0J
A=-
IA
FIG. 9. Theoretical frequency-modulated (FM) SR lineshapes taking into account the strength of the vW interaction through the dimensionless A parameter (see Eq. 15). The calculation is "universal," due to the infinite Doppler width approximation.
(Ducloy and Fichet, 1991) to enable such an analytical integration. Hence, a single numerical integration permits to obtain universal (dimensionless) F M SR lineshapes in the presence of a vW interaction (see Fig. 9). An essential point is that under the simple approximation of infinite Doppler width, all features of these calculated lineshapes can be traced back to a single dimensionless parameter: A = 2kC3/Y
(15)
with C 3 the coefficient of the Z - 3 transient shift. Note that in this spectroscopic approach, C3 has been defined for the probed Ii) --+ [j) transition, i.e., C3 = C3([j)) - C3(]i)) and COo(Z) = (Oo - C3 Z - 3 . The optical width is here assumed to be constant with the distance (y(z) = y), i.e., it ignores the effect of a possible resonant transfer (see Sects. II.E and IV.D).
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For low values of A (0 < A << 1), the vW interaction is essentially a perturbation that imposes a combined shift and distortion to the essentially dispersive Doppler-free lineshape. In the strong vW regime (A > 1), the lineshape is so strongly modified that one cannot recognize the original antisymmetry predicted for FM SR with A - 0. Various shapes are obtained, evolving from a red-shifted absorption-like shape for moderate A values (e.g., in the A ~ 1-10 range), to multiple oscillations on the red side (for A >_ 100). The calculation can also be performed for A < 0 (Fichet et al., 1995b), as it occurs when a vW repulsion is exerted onto the excited state (see Sect. II.D) or if, for some peculiar reasons, one has C3(Ij)) < C3(1i)). Remarkably, a red-shift of the SR lineshape is still predicted in this case, although the local atomic resonance is shifted to the blue. This seemingly paradoxical result originates in the particular spatial averaging typical of SR spectroscopy (see Chevrollier et al., 1992, and notably the appendix). On the other hand, in spite of their closely resembling lineshapes in the perturbative regime IAI < 1, red-shifting (A > 0) and blue-shifting (A < 0) vW interactions can be distinguished by their amplitudes, and by their apparent width (see Failache et al., 2003).
B.4. Beyond several simplifying approximations The set of universal (FM) SR lineshapes that, as will be seen in Sect. IV, provides the basis for a large part of our experimental investigations, has implied several current approximations. It is worth discussing the major ones, in order to understand how experimental constraints may lead to a possible violation of these approximations.
B.4.1. Absorption. The validity of Eq. (13) assumes that there is no absorption, particularly because the exp(2ikz) factor assumes that in the resonant medium, the propagation does not differ from the propagation in vacuum. An expansion at first order in absorption (or, equivalently, in atomic density) is sometimes tractable, but already leads to the blue shift first predicted by Schuurmans (1976). Note that the observation of the SR signal, essentially related to a probe region of extension ~,~, often occurs in experimental conditions for which the absorption is nonnegligible on a wavelength scale. This shows that, in principle, extrapolation of the SR data to the limiting situation of a weak absorption is always needed. The problem hence becomes extremely complex, with local field (Lorentz field) corrections (Maki et al., 1991) to be taken into account, and most often a nonexponential attenuation of the irradiating field (Vartanyan et al., 1995, see also Vartanyan and Weis, 2001).
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B.4.2. Symmetry of the velocity distribution. The remarkable compensation appearing in the linear regime between the phase shift imposed by the transient response and the Doppler shift separating Vz and -Vz velocity groups, permits to calculate the SR lineshape with the sole contribution of the arriving atoms - or of the departing atoms - provided that the velocity distribution (over Vz) is symmetric (Ducloy and Fichet, 1991). Although this assumption looks reasonable, it may not be satisfied in various situations of experimental interest. For a gas sample submitted to an additional optical pumping, the atomic polarization- mostly induced on the arriving atomscan be partly destroyed through a collision onto the wall, leading to an asymmetry in the velocity distribution for a given atomic state. More generally, it is actually fascinating to note that, for a gas at equilibrium, the common idea of an isotropic Maxwellian velocity distribution may become invalid close to a surface (Comsa and David, 1985). Indeed, various reasons at the microscopic level, including the structural details of the surface, angular properties of desorption, surface roughness, or quantum effects on the atomic trajectories, may actually contribute to invalidate the Lamberttype "cos 0 " angular law for departing atoms, whose validity has been seldom tested (see however Grischkowsky, 1980; Bordo and Rubahn, 1999). Note that the selection of "slow" atoms, typical of the FM SR method, is moreover a way of testing the large angular values (i.e., trajectories at a grazing incidence with respect to the window plane, or 0 ~ Jr/2), usually out of reach for most of the mechanical methods. Let us mention that thanks to a relatively simple experiment of nonlinear selective reflection, the contribution of the slow atoms was measured to be approximately twice smaller for the arriving atoms, than for the departing atoms (Rabi et al., 1994). Unfortunately, it has not been possible, through these measurements, to attribute unambiguously this effect to a surface specificity of the velocity distribution, rather than to a differential saturation effect. B.4.3. De-excitation at the arrival onto the surface. The SR theory assumes that arriving atoms get de-excited when hitting the surface. Hence, the contribution of departing atoms is evaluated as a transient excitation, builtup from the ground state, and function of ~: = Z/Vz (with ~: the time elapsed since the atom has departed from the wall). Actually, it is conceivable that an atom, in a wall collision that would be "instantaneous" (i.e., on a time scale ~ 10-12 s), does not relax all of its internal energy. However, the SR spectroscopy performs a kind of coherent measurement, sensitive to the oscillating atomic dipole, rather than to the atomic excitation. Hence, the tremendous interaction potential exerted by the surface at close distance, which is moreover state-dependent, guarantees (Ducloy, 1993) that the prepared coherent superposition of states is washed out in a surface collision
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process, even for an atom that could remain energetically excited in the collisional process. B.4.4. Finite Doppler width. The FM SR is a genuine Doppler-free method only in the frame of the "large Doppler approximation", assuming ku/y ~ ~ , and also 6 << ku. In a realistic case, even for ku/y = 100, and as due to the rather slow evolution of SR lineshape with the ku/y factor (the "divergence" being only logarithmic), the FM SR technique does not yield a signal totally independent of the velocity distribution, and some corrections must be applied to the pure dispersive Lorentzian model (Papageorgiou et al., 1994a; Failache et al., 2003). In standard cases, these corrections affect only a contribution associated with the tails of the velocity distribution, with no essential effects on the predictions for the nearly Doppler-free SR resonance. B.4.5. Normal and oblique incidence. The sub-Doppler contribution, turned into a genuine Doppler-free signal for FM SR, has been predicted under the hypothesis of an irradiation at normal incidence. The narrowing occurs because of an identity between the "Doppler axis" (along which the velocity is counted for the estimate of the Doppler shift), and the normal axis, along which the transient effects are evaluated. Under an oblique incidence, the FM SR Doppler-free lineshape is turned into a lineshape sensitive to a "residual" Doppler broadening, on the order of kuO, with 0 the incidence angle of the irradiating beam in the vapor (Nienhuis et al., 1988; Orifi et al., 1991; Chevrollier et al., 1991 and 1992). This broadening is negligible as long as 0 << y/ku. B.4.6. Atomic trajectories." Spectroscopy vs. mechanical effects. The essence of the SR lineshape model that we have described above consists of atomic trajectories that traveled at a constant velocity. It neglects any possible curvature imposed by the normal force exerted by the atom-surface potential. Such an assumption may appear rather crude, especially with respect to the special contribution of the slowest atoms, that are most sensitive to the mechanical effects of the potential. We have attempted to enhance such a modification of the velocity distribution close to the wall by studying (Papageorgiou, 1994 and Papageorgiou et al., 1995a) the influence of an auxiliary blue-detuned repulsive evanescent wave on SR spectral lineshapes. However, the SR signal reveals sensitive not only to these possible changes in the atomic velocity, but also to the spectroscopic effect of the potential (Ducloy et al., unpublished). To discriminate between dominant mechanical or spectroscopic effects, the relative value of the Doppler shift associated with the potential-induced
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velocity change, and of the spectroscopic shift imposed by the potential, can provide a rule of thumb. For a "typical" step of the potential A U (the "step" being distributed over a distance comparable with the spatial resolution ,-~;~, notwithstanding a possible divergence of the potential very close to the wall), the velocity change A v is given by: (vo + A v)2 - ( v o f -- 2A U/m
(16)
with v0 the initial velocity, and m the atomic mass. In the F M SR approach, the typical selection of slow atoms is a restriction to velocities IVzl <_ y/k. With a specific interest to this upper boundary v0 = y/k, and assuming Av << v0, one calculates from Eq. (16):
A v - AUk/ym
(17)
According to our criterion, the Doppler shift associated with the mechanical effect dominates over the interaction potential if h kAv > A U. In our approach, this appears to be independent of the potential A U, and simplifies to: hk 2 > my
(18)
This shows that for our typical experiments on a heavy atom like Cs at )~,-~ 1 gin, and for rather broad resonance lines (),~ few (270 MHz), the spectroscopic effect is dominant. Conversely, the observation of the mechanical effects would demand a particularly light atom, along with a very narrow optical transition. More generally, the criterion defined by Eq. (18) implies that the mechanical effect dominates only when the selected atomic momentum mvo is smaller than the recoil effect hk. Such a condition seems to be at odds with the uncertainty principle: it shows convincingly that the mechanical effects of the potential should not be dealt with in the frame of classical mechanics.
C. NONLINEAR SELECTIVE REFLECTION The principle of probing an interface through SR spectroscopy can be extended from linear spectroscopy (i.e., with a single incident beam, whose intensity is assumed to be weak enough to avoid saturation) to nonlinear spectroscopy, when the medium is sensitive either to the saturation induced by the single irradiating beam or irradiated with multiple beams. However, it should be recalled that one essential peculiarity of SR spectroscopy is the logarithmic enhancement of the slowest atoms in the wall frame (and the
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genuine velocity selection in the FM mode), and that this behavior is intimately connected to the linear atomic response. C.1. Saturation with a single irradiating beam
Under a relatively strong resonant irradiation, in the same SR scheme as described in Sect. III.B.1, saturation of the optical transition can appear through optical pumping of the resonant atoms to a third level, The onset of such a pumping usually requires moderate intensities owing to the long relaxation time of the pumping (e.g., hyperfine optical pumping). For this reason, the arriving a t o m s - already in the steady-state- are much more sensitive to the optical pumping effects than the departing atoms. A related experimental situation has been analyzed by Vuleti6 et al. (1994): two different effective saturation intensities have been shown to appear, that were attributed to the different behavior of arriving and departing atoms, the arriving atoms being sensitive to saturation with an allowed hyperfine optical pumping, while the saturation for departing atoms is related with optical saturation of a pure two-level system. C.2. Multiple beams nonlinear S R spectroscopy
In volume, nonlinear (NL) spectroscopy with multiple beam irradiation, such as pump-probe spectroscopy, is a very efficient way to impose the selection of a given velocity group. Even with a system as simple as a three-level system, a large variety of schemes can be found (ladder scheme, cascade, (A-type, V-type,...). When one extends these techniques to NL SR spectroscopy at an interface, the variety of situations (see e.g., Schuller et al., 1991, 1993, 1996; Nienhuis and Schuller, 1994) is, at least, as large because propagation from the window, or to the window (with unavoidable reflections) generally induce different behaviors. In addition, the overlap of various incident beams, can sometimes generate extra nonphase-matched nonlinear emission from the bulk (Le Boiteux et al., 1987; Amy-Klein et al., 1995; Sautenkov et al., 1997). A specific point of NL SR spectroscopy is that, while it is easy for the arriving atoms to interact with the pump excitation (at least in the large region where the surface interaction is negligible), more complex features can appear in the pump interaction with the departing atoms, owing to their transient behavior. This generally means that, in addition to narrow resonances associated with velocity groups arbitrarily selected by the NL excitation, as occuring in volume spectroscopy, one still predicts, in NL SR spectroscopy, a specific NL response of the slow atoms yielding, when the surface interaction is neglected, a signal centered on the probed transition (Rabi et al., 1994; Gorris-Neveux et al., 1996).
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Up to now, the atom-surface interaction has been neglected in most of the specific theoretical approaches for NL SR. Indeed, the calculations are most often heavy (even in the lowest order limit, i.e., third order) because the transient behavior of a NL polarization should be evaluated, and then spatially integrated. Typically, the triple integral of linear SR mentioned in Sect. III.B.3 has to be replaced at least by a quintuple integral, with no obvious simplification. Another point worth mentioning is that the integrand of the NL SR response, equivalent to the p(z) exp (2ikz) term appearing in Eq. (13), includes various spatial frequencies, as a consequence of the multiple beam NL excitation. This makes the depth of the coherently probed region difficult to estimate. This may explain why no surface interaction effect has been clearly identified in experiments based upon NL SR spectroscopy, even when the excited atomic levels are supposed to undergo a strong vW response (Gorris-Neveux et al., 1996). However, when a strong spatial dispersion is induced (van Kampen et al., 1998), notably when the pumped region is confined close to the interface (e.g., pumping with a confined or evanescent wave), some specific possibilities for the probing of the atom-surface interaction may exist. Also, the possibility of selecting an arbitrary velocity group close to the surface may provide quantitative indications on the actual velocity distribution close to the surface (see sub-Sect. III.B.4.2.), with a possible differentiation between the slowly arriving and slowly departing atoms (Rabi et al., 1994). C.3. Pseudo-thermal pumping in an excited state
A convenient situation combines the linear probing on a transition between excited states, with the generation of an artificial (quasi-) thermal population, as induced thanks to an auxiliary pumping scheme. It permits indeed to benefit from the well-understood knowledge of linear SR spectroscopy, while reaching excited atomic levels by a stepwise process. Such a technique has been notably implemented in an experiment described in the Sect. IV (Failache et al., 1999 and 2003), with a broadband pumping, in an off-axis geometry (i.e., yielding Doppler-broadened pumping). Note that it may not be obvious that the population of departing and arriving atoms are equal very close to the surface, because the pumping of the departing atoms occurs in a transient regime of interaction.
D. EVANESCENTWAVE SPECTROSCOPY The general technique of Attenuated Total Reflection (ATR) consists of the coupling of an inhomogeneous field to a resonant medium: although an
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FIG. 10. The principle set-up for evanescent wave spectroscopy.
inhomogeneous field does not propagate energy, an energy transfer between the field and the medium can occur. This transfer can be detected on a propagating field coupled to the inhomogeneous one. In an elementary scheme, the evanescent wave (EW) spectroscopy set-up (see Fig. 10) consists of a traveling wave entering into a prism with an internal incidence angle exceeding the critical angle for total reflection: no traveling field emerges out in the vacuum or dilute resonant medium. On resonance, the reflected field is however attenuated (Carniglia et al., 1972; Boissel and Kerherv6, 1981). Analogous A T R observations are expected when the inhomogeneous field is the field of a surface plasmon, provided in a geometry like the one proposed by Kretschmann and Raether (1968). Inhomogeneous fields are intrinsically confined close to the surface, with an amplitude exponentially decaying with the distance to the surface. In principle, this makes EW s p e c t r o s c o p y - and generalizations- a suitable technique for the probing of an atom interacting with the surface. An essential difference with SR spectroscopy at an interface under a real incidence angle is that in the EW technique, the incident field in the vapor can be seen as propagating under an imaginary incidence: hence, the EW technique is essentially sensitive to absorption processes, rather than to the dispersion (Simoneau et al., 1986). Another difference with SR spectroscopy under normal incidence appears when atomic motion is considered: indeed, the Doppler shift in EW spectroscopy is counted along the velocity component parallel to the phase propagation (i.e., parallel to the interface) while the transient atomic
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response, intrinsic to the spatial inhomogeneity of the EW field, is counted with the motion along the normal to the window. Hence, while in regular SR spectroscopy, the transient behavior of the atoms helps to select the slowest atoms, EW spectroscopy is plagued both with transit time thermal broadening, and with Doppler broadening. Extending to the EW techniques the well-known volume Doppler-free saturated absorption, we had developed a Doppler-free EW spectroscopy (Simoneau et al., 1986), in which the pump and probe fields are evanescent fields induced with light beams that counterpropagate in the prism. However, the finite time spent in the evanescent fields strongly alters the efficiency of the velocity selection, so that the optimal spectroscopic resolution is achieved only when the evanescent fields have a large spatial extension. In this case, Doppler-free EW spectroscopy is only weakly sensitive to the region where long-range atom-surface interaction is important, limiting applications involving the monitoring of atom-surface interaction. However, atomic residence time could be evaluated through a dephasing measurement in this EW technique (Bloch et al., 1990; Orifi et al., 1992; see also de Freitas et al., 2002), establishing a possibility of probing with high resolution spectroscopy a phenomenon related to the short-range atom-surface interaction.
E. SPECTROSCOPY IN A THIN VAPOR FILM: MICRO- AND NANO-CELLS The narrow spectral features characterizing SR spectroscopy under normal incidence are not that much typical of a reflection process, but associated with the transient regime of interaction undergone by atoms located in the vicinity of the surface. Hence, an analogous enhancement of the slow atoms' contribution is expected to appear in transmission spectroscopy, as was demonstrated by Briaudeau et al. (1996, 1999 and refs. therein). Practically, such an effect is observable, under normal incidence, when the vapor cell is not too l o n g - relatively to an average distance traveled by an atom before reaching a steady-state of interaction- and when the vapor remains dilute enough so that the atoms fly from wall to wall. This last condition implies that the atomic "mean" free path in the short vapor cell is anisotropic, and justifies an overweight of atoms with small normal velocities (see Fig. 11). A major difference with SR spectroscopy is that, in transmission spectroscopy, there is no more the oscillating phase factor exp (2ikz) (see Eq. (13)), that has favored the detection of atom-surface interaction through the enhanced contribution of regions where the atomic response varies rapidly over ,~. Rather, the signal originates from the whole cell.
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A V_L
iiiiiiiiii i i ii!iiii LASER
FIG. 1 t. Spectroscopy in a thin cell: for a given modulus of the velocity (e.g., most probable thermal velocity), longer atomic trajectories and a longer interaction time with the laser light are allowed for atoms with a small velocity along the normal to the windows (i.e., small v• Note that the laser beam diameter is assumed to exceed largely the cell thickness L.
This explains why the first demonstrations of these novel sub-Doppler features in transmission spectroscopy, performed with micro-cells whose thickness spanned in the 10-1000 lam range, were insensitive to atomsurface interaction. Conversely, and as will be discussed in Sect. V with more details, the recent development of sub-micrometric vapor cells ("nanocells") (Sarkisyan et al., 2001) seems a promising tool to explore vW atomsurface interaction for a given range of distances to the surface, eventually much smaller than those currently reached with SR spectroscopy (Dutier et al., 2004a).
IV. SR Spectroscopy as a Diagnostics Tool of the Atom-Surface Interaction This section describes how SR spectroscopy has been used to measure the vW atom-surface interaction. Starting from the most elementary observations, when the dielectric image coefficient of the surface can be considered as a constant, it describes how an effective measurement of the C3 value is performed, yielding a variety of information on the atomic state parameter affecting the vW interaction. It is illustrated with some of the effects associated with the resonant coupling between the atomic excitation and the
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surface modes. It ends up with a search for anisotropic effect in the vW interaction. A. ELEMENTARY OBSERVATION OF THE v W INTERACTION IN LINEAR SR SPECTROSCOPY
A.1. Experimental set-up The observation of a SR spectroscopy signal basically requires a resonant narrow-linewidth tunable laser, a vapor cell enclosed in a container with at least one transparent window (wedged whenever possible), and a sensitive low-noise detector, in order to monitor conveniently the weak resonant change in the reflection coefficient, relatively to a non resonant reflected background on the order of several percents of the incident intensity. An auxiliary reference set-up, providing a signature of the volume resonance such as that obtained with a saturated absorption (SA) set-up, is at least convenient to monitor the effect of the vW atom-surface interaction on the SR signal. Also, due to the higher resolution provided by the F M SR technique, a F M - of a small amplitude - is often applied, or to the irradiating beam with an external modulator, or to the laser itself, notably when a semi-conductor laser is used, for which it is easy to perform a F M with a modulation of the drive current. The F M SR signal is acquired after processing of the photodetector signal through a phase-sensitive lock-in detection. Note that, relatively to an a posteriori frequency-derivation of the recorded SR lineshapes, the F M technique eliminates the d.c. noise (and low-frequency noise) of the laser source. A.2. Typical observation in linear SR In volume spectroscopy, the weakness of an absorption line is often compensated for by an increase in the absorption length, if not by a multipass scheme. In SR spectroscopy, the signal amplitude is typically comparable with the one expected for absorption on a depth as small as,~, and only an increase in the atomic density can enhance the signal magnitude above the sensitivity threshold. However, the atomic density cannot be increased too much because of the self-broadening of atomic lines, so that SR spectroscopy can hardly be applied to very weak lines; for example we are not aware of SR laser spectroscopy applied to molecular lines. Also, discriminating between pressure e f f e c t s - related to (volume) a t o m - a t o m collisions - and surface effects is a major concern for most SR measurements. Nearly all experiments in SR laser spectroscopy have dealt with alkali vapors, whose atomic density varies quickly with temperature. We provide
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here some numerical indications for the Cs D2 line (852 nm), although the Na D2 line, the first one to be studied (Woerdman and Schuurmans, 1975), exhibits a comparable behavior, but for a smaller vW interaction. A density on the order of ~ 1013 at/cm 3 (i.e., T ~ 100~ for Cs) allows a detectable reflectivity change on the order of 10- 4 - the precise values depend on the considered hyperfine components, and on the optical properties of the reflecting w i n d o w - while the pressure self-broadening (~ 10-7 Hz/at cm -3) remains negligible relatively to the natural width ( ~ 5 MHz) (see Papageorgiou et al., 1994a). On the SR lineshapes, one recognizes (see Fig. 12), superimposed to the Doppler-broadened dispersive wings, narrower peaks associated with the respective hyperfine components, that are hence partially resolved. In the FM mode and under normal incidence, one observes well-resolved Doppler-free resonances that are close to dispersive lineshapes but for a slight asymmetry, already noted by Akul'shin et al. (1982). In addition, high-resolution spectra most often reveal a small red-shift when compared to a reference SA spectrum, but its physical origin had been ignored until our work. This shift, on the order of 2-3 MHz, is only a fraction of the total width (most often in the 10-30 MHz range, depending upon the experimental conditions, and in excess of the 5 MHz natural width). As discussed in the next subsection, this combined distorted dispersive lineshape, and apparent lineshift, can be traced back to the vW atom-surface interaction (OriS. et al., 1991; Chevrollier et al., 1992). Conversely, the sole observation of an apparent frequency shift, while neglecting the distortion, cannot permit to evaluate, even approximately, the vW interaction. At higher atomic densities, the broadening of the SR lineshapes on resonance lines goes along with an increased (anti-)symmetry of the dispersive lineshape, that has even provided particular opportunities for laser frequency stabilization purposes (Ito et al., 1991; Li et al., 1998). 4-3
] 4i4
500MHz 4-5
'
" ..................
FIG. 12. A typical direct SR spectrum (i.e., without FM), recorded on the Cs D2 line 6S1/2(F= 4) --+ 6P3/a(F' = 3,4,5).
resonance
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This regime of density can provide an essential set of data to analyze the pressure broadening effects. It has also provide a way to study the Lorentz correction associated with local field effects (Maki et al., 1991). For this high density regime, the vW interaction can be taken into account as an extra-correction term (Guo et al., 1996: Ping Wang et al., 1997). Observing transitions weaker than the strong resonance lines of alkali is also possible, although more difficult. One of the narrowest FM SR lines that we have once observed has been recorded on the 791 nm intercombination line (1S0-3p1) of Ba, although the very high operating temperature - in excess of 700~ - rapidly destroyed the sapphire window, and imposed a notable broadening (~ 1-2 MHz) to a very narrow natural linewidth (100 kHz) (Failache et al, unpublished). In principle, such a narrow resonance should permit to select particularly slow atoms, and be favorable to observe mechanical effects induced by the atom-surface interaction potential (see Sect. III.B.4.6.). The second and higher resonance lines of alkali vapor exhibit weaker oscillator strengths, orders of magnitude smaller than the first resonance line: however, as discussed in Sect. II.C, the corresponding excited levels are much more polarizable and more sensitive to the vW interaction than the first excited state. In spite of the rather high atomic density usually required for the SR signal to be observable, and its correlated pressure broadening, the SR and FM SR spectra clearly exhibit special features that are the signature of the vW interaction in the "strong" regime (see Sect. III.B.3.2.) (e.g., FM SR lines that resemble a shifted absorption-lineshape, or an inverted dispersion,...).
B. THE METHOD OF EXPERIMENTAL MEASUREMENTOF THE C3 COEFFICIENT B.1. Fitting method
As discussed above (Sect. III.B.3.2.), the FM SR lineshapes for a 1photon transition much narrower than the Doppler width have been described by a family of universal (dimensionless) lineshapes depending upon a single-parameter A (see Eq. (15), and Ducloy and Fichet, 1991). For an isolated narrow FM SR experimental resonance, it is not difficult to evaluate if a given value of the A parameter (or a given range Am < A < An) is able to describe the observed lineshape. From an experimental determination of the width y, that is a priori dependent on the A value (i.e., y = y (A)), one estimates the relevant value of C3. The search for an optimal fitting (Papageorgiou, 1994; Papageorgiou, 1994a), performed with a least square fit method, involves homothetic factors between the experimental spectrum and the dimensionless model, and offset factors to locate the resonance frequency. Note that the fitting cannot allow a continuous change of the A
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FIG. 13. An example of the fitting (narrow black line) of a FM SR lineshape (in grey). The fitting includes here 3 different hyperfine components, and is performed with a single parameter for the vW strength parameter (and a single homogenous optical width). It also takes into account the frequencies of the unshifted (free-space) resonance, as revealed from the Saturated Absorption (SA) reference. The present FM SR lineshape is obtained in the situation of a repulsive interaction between Cs (6D3/2) and a sapphire (c• window (see Failache et al., 1999 and 2003). parameter, with respect to the non-analytic dependence of the A-lineshapes. Rather, the amount of the minimal error e(Ai), found when optimizing for each value of a set of A~,..., Ap parameters, provides a criterion to find the acceptable range of [Am, An] values, easily converted into a range of acceptable values of ('3. On this basis, extensive improvements, yielding a high reliability (see Fig. 13) and consistency, have been developed along the years. They are detailed in the work of Failache et al. (2003).
B.2. Checking the consistency of a v W determination In various situations, it so happens that for a given SR lineshape, the accuracy on the (73 value remains low. Aside from an insufficient sensitivity in the recorded spectra, it can happen, in the weak vW regime (A << 1), that a large range of A value seems acceptable for the lineshape, while the y value remains essentially governed by the peak-to-peak width of the quasidispersive lineshape. Two very different vW regimes can also exhibit seemingly analogous lineshapes. This is why the determination of the ('3 value is generally secured by a consistency check, comparing the lineshapes obtained under various pressure conditions (Chevrollier et al., 1991, 1992;
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FIG. 14. The consistency of the vW fitting over a pressure-induced modification of the resonance width. One has simultaneously extrapolated from the fittings a simultaneous linear pressure broadening, and a vW strength independent of the pressure. The FM SR experiments are performed in the situation of a repulsive interaction between Cs (6D3/2) and a sapphire (c• window, with spectra such as the one shown in Fig. 13. Failache et al., 1999, 2003). Varying y value in a controlled manner (e.g., by density broadening) leads to phenomenological changes for the SR lineshapes, that become very remarkable in the strong vW regime (A >> 1). In spite of the observed changes induced by (volume) a t o m - a t o m interaction, the atom-surface interaction has to remain unchanged. Such a test, illustrated in Fig. 14, is so sensitive that it has permitted to simultaneously evaluate the coefficients governing the vW interaction, and the pressure shifts (Chevrollier et al., 1991, 1992). It also provides an adequate citerion to choose between two very different evaluations of the A value (Failache, 1999; Failache et al., 2003).
B.3. Comparing the C3 experimental values with the theoretical predictions for SR experiments at the interface with a non dispersive material With the above fitting techniques, the (73 value for a given atomic transition and material at the interface, has been determined with an
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uncertainty in a 10-30 % typical range. Note that this uncertainty, though partly statistical and noise related, also originates from a systematic biasing appearing on the extrapolated values for C3, when attempting to improve the modeling of the SR lineshape. Several series of measurements have been performed on the Cs D2 line (681/2-6P3/2), that yielded C3 ~ 2 kHz.lam 3 at a fused quartz interface (Orifi et al., 1991; Chevrollier et al., 1992; Papageorgiou et al., 1994a). With respect to the dielectric response coefficient of fused quartz (r ~ 0.35 for all the virtual transitions relevant for the vW interaction exerted onto the 6S1/2 and 6P3/2 levels), there is an agreement, on the order of 30%, between the (slighlty higher) experimental and the predicted theoretical value (Chevrollier et al., 1992). Note also that the C3 contribution of the excited state 6P3/2 is about twice larger than that of the ground state 6S1/2 (with C3 = C3(6P1/2)-C3(6S1/2)). Comparable values are predicted for other resonance lines of alkali vapors, that are roughly confirmed by the experimental results, notably on the D1 line of Cs, and on the D lines of Rb (see e.g., Gorris-Neveux et al., 1997; Ping Wang et al., 1997). For the weaker transition to the more excited Cs(7P3/2) level (reached with the second resonance line, ;~ = 455 nm), the evaluation of the C3 value has required the removal of the pressure shift effects. It was found to be an order of magnitude larger (Chevrollier et al., 1991, 1992) than for the D 2 line. This C3 value originates essentially from the vW interaction exerted onto the excited level Cs(7P3/2). Although not performed systematically, a comparison between SR spectroscopy with a fused quartz window, and with a sapphire window, has evidenced a stronger interaction of the Cs(7P3/2) atoms with sapphire, as can be expected from a comparison of the [(e-1)/(e + 1)] factor. The systematic experimental evaluation of the C3 value yielded also a reasonable agreement with the theoretical prediction, although this one is also found to be slightly below the experimental value (~ 30 %) (note that the early given experimental error bar 15 % did not account for some possible systematic errors). Note that the relevant virtual transitions for the Cs(7P3/2) lie in the far IR region, and that even in the absence of a resonant coupling of the atom excitation with a surface mode, the theoretical evaluation of the dielectric image coefficient may require slight re-evaluation compared to the early and simplified estimates. Recent preliminary experiments on the even weaker transition to the more excited Cs(SP3/2) level via the third resonance line of Cs at )~ = 388 nm (Dutier et al., 2004a; Hamdi et al., 2004), shows that, with a refined fitting method, a 10% accuracy level on the C3 determination is feasible on this line, hence requiring a careful control of the frequency scan.
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C. OBSERVATIONOF THE RESONANT LONG-RANGE COUPLING BETWEEN A SURFACE MODE AND AN EXCITED ATOMIC LEVEL C.1. Predicting a resonant atom-surface coupling
As already mentioned after Eq. (8), a strong enhancement (positive or negative) of a given virtual emission contribution to the C3 value can occur for some materials, as the values of ~te[(e(co0-) - 1)/(e(wO.)+ 1)] are not limited (see Fig. 4). These resonances for this enhanced contribution are predicted to occur for the complex frequency poles of [e(wij) + 1]-1. For such poles, the material is no more an optical "window", but is extremely absorbing (absorption typically occurs on one wavelength), while the resonance sharpness strongly depends on the refractive index in this spectral region. Practically, the evaluation of the surface dielectric response r(coij) is extrapolated from tabulated data for 6(O)ij) (see e.g., Palik, 1985), or from a fitting analytical model for e, based upon a 3- or 4- parameters model for each bulk resonance. However, the uncertainty induced by this extrapolation can be notable in the resonance regions. Moreover, there remain some uncertainties about the precise resonant behavior, as due to possible differences (dopants or impurities, temperature, etc.) between the actual window, and the samples used in the literature. To illustrate the possibility of a resonance in the vW interaction, we have notably concentrated on the virtual coupling between C s ( 6 D ) a n d Cs(7P): our first demonstration of a strong vW regime in SR spectroscopy, achieved on Cs (7P), had relied indeed on the strong coupling to Cs (6D) (virtual absorption falling in the 12-15 lam range). Sapphire, whose main bulk absorption resonances are located at ~ 17 lam and ,~ 23 lam, exhibits an isolated strong surface resonance (surface-polariton) across the 12 gm region with a quality factor Q ~ 100 (Fichet et al., 1995). The real part of the surface response, associated with the vW shift, 9~e[(e(wij) - 1)/(e(coij) + 1)] exhibits a dispersion-like frequency response, while the imaginary contribution ~m[(e(wij) - 1) / (E(O.)ij) -Jl" 1)], that governs the surface-induced atomic level transfer (Sect. II.E., and below, IV.D.) exhibits an absorption-like dependence. Note also that the exact position of these resonances depends on the sapphire birefringence axis orientation (see Gorza et al., 2001, and Fig. 6). With a c-axis perpendicular to the window (c_t_), the vW contribution to the shift associated with the 12.15 gm emission Cs(6D3/2 --+ 7P1/2) is predicted to be enhanced by a factor ~ - 1 5 relative to an ideal reflector. This contribution, that would contribute to + 7 kHzgm 3 over a total of 25 kHzgm 3 for Cs(6D3/2) in front of an ideal reflector, induces a strong vW repulsion in front of a c_t_ sapphire window, that dominates over all other and nonresonant contributions (see table I). It represents ~ - 1 0 8 kHz. jam3 in a total predicted value of ~ - 9 6 kHz lam3
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(see Failache et al., 2003). For sapphire with a c-axis parallel to the window (c//), there is no more a strong repulsion, because the atomic resonance falls close to the center of the region of anomalous dispersion for 9te[(e(coij) - 1)/(~(co~) + 1)]: moreover, the detailed prediction ( i.e., weak repulsion, or weak attraction) is highly sensitive to the sapphire resonance modeling. The above predicted resonance behavior, that has led to the experimental demonstration of vW repulsion (Failache et al., 1999, 2003), relies on a specific coincidence between Cs(6D3/2--+ 7P1/2) and c2_ sapphire surface resonance. Actually such a coincidence is not so unusual. Indeed, for a high-lying excited atom, the most important virtual transitions (for the vW interaction) falls in the relatively far IR range, while transparency of the window is required in an energy range which is governed by a high atomic excitation. Moreover, the low quality factor of the surface resonance - i.e., Q < 100, relatively to the Q ~ 10 s for atomic t r a n s i t i o n - makes it easy to find an atomic transition lying in the repulsive dispersive wing of a resonance. Such a standard material as Y A G illustrates (see Fig. 4) how easy it is to obtain a resonant behavior in the vW atom-surface interaction. It exhibits indeed numerous resonances in the 10-20 gm region in spite of a transparency region spanning from the UV to ~ 5 gm. This justifies that Y A G also has been found to be repulsive for Cs(6D3/2) (Failache et al., 2003). C.2. Measuring the atom-surface interaction in resonant situations
The measurement of the vW surface interaction, even in the presence of a resonant coupling between the atom excitation and a surface polariton mode, is not intrinsically different from those measurements performed through SR spectroscopy from the ground state. However, the need to reach high-lying atomic states may require a multi-photon excitation. With respect to difficulties in the interpretations of NL SR spectra, for which the surface interaction has never been included in the theoretical modeling, see Sect. III.C.2., the experiments have rather relied on a stepwise quasi-thermal pumping of the resonant level, followed by linear SR spectroscopy between the resonant level and the high-lying state. The production of a quasi-thermal population in the resonant level requires a strong pumping and high atomic densities. This has made crucial an independent measurement of the collisional effect (broadening and shift) and poses extra-difficulties in the evaluation of the "quasi-thermal" distribution. In spite of these difficulties, we could compare the material influence on the vW shift for several atomic systems (notably Cs(6D3/2), Cs(981/2), Rb(6D)) that are sensitive to a resonance with a surface mode
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(Failache, 1999, Failache et al., 2003). The experimental accuracy can be on the order of 30%. These experimental determinations themselves are in agreement with the theoretical modeling. Note that the hypotheses of a linear atomic trajectories still holds for all the regions significantly contributing to the SR spectrum: for Cs(6D3/2) atoms with V z - 30 ms -1, located in front of a c• sapphire window the classical turning point is indeed located at z ~ 10 nm, a position that would imply a tremendous vW shift -~ 100 GHz.
D. FC)RSTER-LIKE ENERGY TRANSFER INDUCED BY THE NEAR-FIELD COUPLING TO THE SURFACE
The resonant near-field atom-surface coupling affects not only the energy of atomic states through virtual processes, but it can induce a real change in the internal state, induced by the vicinity with the surface. In this energy transfer with a surface, that can be seen as the analog of the F6rster internal energy transfer between two distant molecules, an excited atom located in an evanescent tail of a surface polariton mode, loses energy through a near-field transfer to the surface polariton. As already discussed in Sect. II.E., such an effect is governed by the same z -3 law as the vW effect, and implies that the branching ratios of the excited state are strongly dependent on the distance to the surface. It dramatically affects the behavior of an atom in a high-lying state on its route towards a surface. Moreover, noting that resonant behaviors are actually quite common for highly excited atoms (see Sect. IV.C.2.), such a surface-induced energy-level transfer can appear as nearly universal, with the strength of the surface resonance essentially governing the distance from the surface at which this remote process occurs. Note that an analogous internal energy transfer, but induced with surface plasmon modes, had been discussed for embedded "atomic" species (namely, electronically excited molecules), but its efficiency was limited to a much shorter distance range, owing to the ultraviolet nature of the considered resonances (see e.g., the review by Chance et al., 1978). The experimental demonstration of such a resonant transfer has remained qualitative, and was conducted with a comparison of different materials, at a distance to the surface controlled by the spatial resolution of a SR spectroscopy method. A SR spectroscopy experiment was conducted on the Cs 7P1/2 --+ 10D3/2 transition ()~ = 1.298 gm), in the presence of a strong (stepwise) two-photon pumping to Cs(6D3/2). This transition is normally transparent, because the relevant levels are unpopulated, but by the surfaceinduced transfer from Cs(6D3/2) to Cs(7P1/2) (the spontaneous emission, falling at 12.15 gm, yielding a negligible contribution). The experiments
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(Failache et al., 2002) evidenced a strong difference between a (nonresonant) fused quartz window (no SR signal), and the resonant situation provided with a sapphire window (c/l) or a YAG window (observable SR signal). The surface-induced transfer has been estimated to occur for z < 450 nm for sapphire and z _< 300 nm for YAG, and z < 30 nm for fused quartz. The spatial resolution of the SR diagnostics explains the observed differences. Such a difference is best seen for rather low Cs pressure, because at higher densities, energy-pooling collisions can compete with the surface-induced process, and induce a Cs (7P1/2) population in the vapor volume.
E. A SEARCH FOR ANISOTROPY IN THE vW INTERACTION: STUDYING ZEEMAN COMPONENTS
Due to a sum rule, it has been shown (Chevrollier et al., 1992) that the value of the C3(Ii, F ) ) ~ Ij, F')) coefficient for the scalar part of the vW interaction should be the same for all F ~ F' components as long as the degenerate IF, mF) levels are identically populated. Conversely, if the individual Zeeman components are resolved, nonnegligible differences in the strength of the vW interaction are predicted. We have attempted to observe these differences (Papageorgiou, 1994; Ducloy, 1994; Papageorgiou et al., 1995b), performing measurements in the regime of intermediate magnetic field, with the Zeeman degeneracy removed (Papageorgiou et al., 1994b). To escape from the difficulty of comparing the individual AmF--+m'F, values, due to the relatively large uncertainty affecting these measurements, we have implemented a differential measurement, comparing the surface effect when the magnetic field that imposes the Zeeman structure is parallel, or perpendicular, to the surface. The experimental approach (Fig. 15) used a cubic cell, with two perpendicular windows being irradiated in identical conditions (the irradiated spots being very close to each other, for the spatial homogeneity of the Zeeman effect). In these experiments, performed on the well-known Cs O2 line, reproducible differences, of the predicted order of magnitude, were observed but with details that were not in agreement with the vW nonscalar calculations. One possible interpretation of these discrepancies has relied on the simultaneous modifications of the radiative properties of an excited atom in front of a surface (see Sect. II.E.), that could affect locally the optical width of the transitions, and hence subtly modify the lineshapes. These modifications, ignored in the vW modeling, are also anisotropic, with a strong dependence on the relative orientation of the emitting dipole (Lukosz and Kunz, 1977b).
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FIG. 15. Scheme of an experiment aiming at detecting anisotropy effects in vW shift, with a resolved Zeeman structure. The two lasers have a similar polarization, perpendicular to the magnetic field B, so that they induce inside the vapor (bulk) an identical interaction. In SR spectroscopy, there remains a cylindrical symmetry for the vW interaction for the experiment with the (//)laser (B along the surface normal), that is destroyed for the (_1_)laser (B parallel to the surface.
V. New Developments and Prospects Among the various prospects that we present in this section, some are natural extensions of the works with optical techniques presented in Sects. III and IV. They include, extension from SR spectroscopy to nanocell spectroscopy, and the effects of a non-zero temperature environment. New directions, well-suited to study the atom interaction in a range of very small distance to the surface, are also presently explored, including the deflection of atomic beam with nanoslits technology, and the interaction of atoms with strongly curved surfaces, such as are nanobodies.
A. TOWARDS THE EXPLORATION OF STRONG CONFINEMENT TO THE SURFACE THROUGH SPECTROSCOPY IN A NANOCELL
A.1. Present technology and thickness measurement It recently became possible (Sarkisyan et al., 2001) to fabricate Extremely Thin vapor Cells (ETC) compatible with vacuum sealing and heating, so that an alkali vapor, of a controllable atomic density, can be studied when imprisoned in a container whose thickness can be as small as ~ 20 nm. In the
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present state-of-the-art, two thick transparent windows, carefully polished with an excellent planarity, are contacted to a ring-shaped spacer (typical thickness ~ 300 nm), and glued at a high temperature (mineral gluing). The external atmospheric pressure induces a curvature on the windows, and usually the local cell thickness varies smoothly from near contact in the central region, to ~ 1 ~tm in the peripheral regions. The challenging point of the construction is that the cell can resist, with negligible deformations, to a strong heating (up to 350 ~ C), enabling variations of the atomic density on a large range. Alternately, for a construction with thinner windows, inserting the ETC in a vacuum chamber (Sarkisyan et al., 2003) provides an adjustable local spacing, through the control of the environmental pressure (between 0 and 1 atm). The parallelism of the two windows is intrinsically excellent (typical window diameter ~ 20 mm), implying a Fabry-Perot behavior, at least for the two internal windows. On the one hand, this provides a convenient interferometric method to estimate the local cell thickness - with an accuracy currently reaching 5 n m - , on the other hand, a spectroscopic signal in such a cell is not the simple signal associated with transmissionor, in alternate schemes, with selective reflection- of a traveling wave: rather, it is a systematic combination of absorption and reflection signals (Dutier et al., 2003b).
A.2. Observation of surface induced effects When comparing the spectra obtained for various local thickness of the ETC, notable lineshape differences are predicted, even in the absence of a surface interaction, as due to the Fabry-Perot behavior, which mixes up transmission and reflection response: depending on the thickness, the observed lineshapes appear shifted, and with a variable asymmetry (Dutier et al., 2003a). However, on the Cs resonance line, one has observed notable red shifts and well-characterized lineshape distortions for a thickness typically below 100 nm (Dutier, 2003; Dutier et al., 2004a, b, and Dutier, in preparation). This behavior, easily observed with the FM technique (see Fig. 16), can no longer be traced back to the mixture of dispersive wings and absorption-like lineshapes. The frequency shift increases quickly with decreasing the thickness- roughly like 1/L 3 (L, cell thickness) -, while the observed lineshapes have been found to be in good agreement with predictions that include the estimated vW interaction (as estimated from theory or from previous SR experiments). From a more systematic comparison between the experimental lineshapes, and the family of theoretical models for various strengths of the vW interaction, it should be possible to measure effectively the vW interaction,
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1.1GHz
FIG. 16. FM reflection on the Cs D1 line in a 80 nm thick ETC. The dashed lines indicate the position of the volume resonances- as obtained from a SA reference. The large observed shift between ETC resonances, and volume resonances, illustrates the signature of the vW interaction.
as was done with SR experiments (Sect. IV.B.). Hence, with the spatial resolution intrinsically offered by such nanocells, it should be possible to test the law of spatial dependence in z -3 of the vW interaction more effectively than with the SR technique, that always averages over -~,k. Note that here, the effective vW potential results from an interaction with multiple electric images. Also, for each ETC thickness, a full set of C3-dependent lineshapes has to be calculated. Experiments with nanocells have also been performed on more excited levels, such as Cs (6D) level, either after a pumping on the D1 or D2 line or in two-photon schemes. We have already evidenced, after a nearly homogeneous pumping on the 02 line, the very large vW attraction (several ten's of GHz) exerted onto the Cs (6D5/2) level for small thickness in the 2050 nm range i.e., for an atom-wall distance remaining always below 25 nm. These observations remain however very preliminary because unwanted effects, such as dynamic Stark shifts, are often present, as the experimental conditions often require intense beams for the signal not to be too small. Also, for these distances, surface roughness of the windows could be an issue.
A.3. Possibility of a level crossing induced by a surface resonance Extrapolating at much shorter distances the C3(li))z -3 behavior asymptotically demonstrated for long distances, opens in principle the possibility of an li) - I j) level crossing as long as C3(1i)) -r C3(Ij)). This can be illustrated with Cs (6D) and sapphire (see Fig. 17). The fine structure sublevels of (6D3/2) and (6D5/2) are predicted to behave differently in front of a sapphire surface: the (6D3/2) --+ (7P1/2) virtual emission at 12.15 ~m falls in a resonance of the surface modes of sapphire, inducing a repulsive behavior (for c• sapphire and 6D3/2), while the 6D5/2-+ 7P3/2 virtual emission at 14.6 ~tm is nonresonant, so that (for C• sapphire and 6D3/2) the
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Fla. 17. The energy level scheme of Cs that could lead to a surface-induced level-crossingin the vicinity of a sapphire window (c• The 6D3/2 level is strongly repelled by the sapphire surface, while the 6D5/2level undergoes an ordinary vW attraction.
regular and relatively weak vW attraction remain unchanged (see Fig. 4). With the knowledge of the respective C3 values (associated to the asymptotic z -3 behavior at z ~ oe) for Cs(6D3/2) and Cs(6D5/2), a level crossing is hence expected for a distance to the wall z ~ 5 nm. This estimated distance is only marginally modified (Dutier, 2003) if one takes into account the local modifications affecting the wavelength of the relevant resonant virtual emissions, as induced by the vW shift. Conversely, the energy where this level crossing occurs is highly sensitive to the local details of the vW potential. Looking for a signature of such a level-crossing - which could turn to be an anti-crossing, depending on the non diagonal term of the vW interaction H a m i l t o n i a n - we have started to investigate an anomaly in the wings of the spectral lines reaching (in the free-space) the Cs(6D3/2) and Cs(6D5/z) levels. For such a purpose, spectroscopy in an ETC seems to offer much wider possibilities than SR or evanescent wave spectroscopy, as due to a spatial resolution limited only by the cell construction. The observation of such effects have been attempted, with the help of a widely tunable laser source (Yarovitski et al., in preparation), operating across the whole fine structure (~ 1 THz) of Cs(6D) from the resonant Cs(6P3/2) level. However, for the shortest cell thickness, the vicinity between the two walls, and their imperfections at short distances, may modify the conditions ensuring a resonant coupling between atom excitation and the surface modes.
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A.4. Atom-atom interaction in a tightly confined medium A significant observation of the atom-surface interaction in vapor requires to eliminate the effects of atom-atom interaction, such as pressure broadenings and shifts. These collisional effects themselves may depend on the cell thickness, a parameter that can be conveniently varied in ETC spectroscopy. Let us recall that the long-range atom-atom interaction, that scales like r -6 (r: the interatomic distance), and whose integration over a half-space leads to the atom-surface vW interaction (see Sect. I), can be viewed as a reaction of an atom to the field induced by its own e.m. fluctuations as mediated by the perturber atom. It has been predicted that this interaction should be affected by confinement in a cavity, when the dimensions of the cavity are smaller than or comparable to the relevant wavelengths of the dipole fluctuations (Cho and Silbey, 1996; Cho, 1999; Bostr6m et al., 2002). Indeed, the fluctuating dipole field can interact with the perturber atom following various propagation paths that include reflection onto the confining surfaces. Until now, these theoretical predictions had remained untested, because there were no available experimental methods to explore such a collisional regime. It also seems that these predictions have remained limited to the elementary situation of two atoms located at fixed positions, not providing an estimate of the overall effect resulting from an integration over a distribution of positions and velocities. Clearly, these atom-atom interactions that are mediated by a surface should be considered in various devices such as atom chips, and their detailed understanding will require a sufficient knowledge of the more elementary "atom-surface" interaction.
B. THERMAL EFFECTS In numerous cases, the temperature of the surface remains small enough so that the thermal energy kBT (with kB the Boltzmann constant, and T the temperature) is much smaller than the involved energy of the relevant atomic transitions. However, high-lying energy levels are usually connected to neighboring levels that are not very distant in energy, and as already noted in Sect. II.C., the far IR couplings easily become dominant as soon as the vW interaction is concerned. Hence, the T ~ 0 approximation may break down. A good demonstration of a kind of "spontaneous absorption" of a thermal photon has been given in the Lai and Hinds work (1998), when the decay time from Cs (13S) appears increased due to an excitation channel to Cs (14P) through a thermal absorption. This process, allowed in the freespace at a nonzero temperature, has been shown to be forbidden when the
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experiment is performed in too a narrow cavity, when its size is smaller than a wavelength cutoff. Alternately, the thermal field in the vicinity of a surface has been shown to exhibit unexpected coherence properties (see Greffet et al., 2002 and references therein), along with a spectral dependence that is governed by the near-field properties of the blackbody emitter. Although it is clear that the atom-surface vW interaction can be affected when the energy of the involved virtual atomic transitions falls in the range of thermal photons, only few theoretical works (see e.g., Barton, 1997; see also Henkel and Wilkens, 1999) had dealt with this problem. Very recently, the theory suitable for SR-type observation has been developed in our group (Gorza, in preparation, and Hamdi et al., 2004). One major result is that the resonant coupling between atom and surface, that was limited to an atom virtually emitting into a surface mode, can now be extended to the symmetric process in which the (hot) surface virtually emits a photon subsequently absorbed by the atom. The efficiency of this resonant process naturally depends on the thermal population factor {exp(h~oo./k~ T)/ [1 + exp(-hcoo./kB T) ]}. This emitting-surface process exhibits a notable change of the sign, relatively to the emitting-atom process considered in Eq. (8). An enhanced attraction for Cs(7P1/2) when the temperature is high enough, i.e., on the order of ~ 1000 K, should correspond to the observed repulsion of Cs(6D3/2) in front of (c2_) sapphire - associated with the (6D3/ 2)--+ 7P1/2) 12.15 ~tm emission. In addition to the thermal effect on the resonant coupling, involving thermal population of surface modes, the nonresonant contribution, such as the one appearing in Eq. (7) and featuring an integration over the whole spectrum, is replaced by a discrete summing over the Matsubara frequencies co=kT/27ch . Note that in principle, the introduction of these thermal excitations introduces new characteristic wavelengths, above which the near-field expansion may become invalid. In spite of this, an elementary z -3 interaction remains most often valid, yielding a C3(li)) value simply dependent on the temperature, i.e., C3(T). The changes induced by this nonresonant contribution seem to remain marginal, while the resonant contributions (including those only associated to wings of a resonance), are predicted to be dominant. Experimentally, it does not seem that these C3(T) variations have ever been investigated at present. Our SR studies on the 8P3/2 level of Cs are oriented in view of such an investigation. Indeed, the strong absorption couplings (8P3/2)--+ (7D3/2) and (8P3/2)~ (7D5/2) occur respectively at 39 ~tm and 36 ~tm, i.e., an energy corresponding to the practical temperatures used in SR spectroscopy. With windows in materials such as BaF2 or CaF2 (see Failache 1999, and Fig. 18) resonant effect in the atomsurface interaction may appear with temperature, with the vW attraction possibly turned into repulsion for a sufficient window thermal excitation.
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..",
~BaF2
2 0 -2 -4
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I
I
10
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FIG. 18. ~e[(e -- 1)/(e + 1)] for a BaF2 window (solid line), and a CaF2 window (dashed line). The predicted surface resonances should enable resonant coupling of a (virtual) atom absorption with a thermally excited surface. The data (see Failache (1999)) has been extrapolated from the bulk values as given in Kaiser et al. (1962).
These predictions assume that the surface modes are known phenomenologically, and that temperature variations on these modes can be neglected, at least for a given range of temperature. In principle, the real problem is more intricate, because the thermal equilibrium of the bulk material itself depends on its equilibrium at the interface with vacuum. However, the narrowness of atomic resonances should selectively filter these broad couplings to vacuum.
C. v W ANISOTROPY AND SURFACE-INDUCED INELASTIC TRANSFER IN AN ATOMIC BEAM
C.1. v W interaction and Metastability transfer The intrinsic anisotropy of the surface vW interaction, originating in the quadrupole term in Dz 2, can lead to a variety of diagonal interaction for the various Zeeman components, as it has been searched for in the experiments described in Sect. IV.E. The anisotropy of the interaction, with its nondiagonal contribution, is also susceptible to break down well-established selection rules and enable surface-induced A J - 2 transitions. This has led to a search for an inelastic transfer between the two metastable atomic states of rare gases (Ducloy, 1998; Boustimi et al., 2001a), respectively characterized by the q u a n t u m numbers J - 0 and J - 2. Due to the large amount of energy involved in such an inelastic process, governed by the same z -3 scaling factor, the metastability transfer occurs only at extremely small distances from the wall (that may fall below the "long-range approximation," see Sect. I). Owing to the long lifetime of
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metastable atoms, the experimental principle can rely on the mechanical deflection of an atomic beam, enabling one to compare the free atom trajectory before the vW interaction, and the output channels for the atoms having undergone such a surface interaction (see Fig. 19). A key point in the detection method is that the change in the internal energy transfer is totally converted into kinetic energy, i.e., there is no energy transfer to the surface; moreover, the vW interaction being invariant along the surface, the atom acquires an impulsion transfer Ap that is oriented along the surface normal.
FIG. 19. The principle of the experiment for the detection of a surface-induced metastability transfer. The detector of metastable states (e.g., initial state 3p0, or 3P 2 transfer state) can be rotated from the direction of the incident atomic beam, to the direction Of. The incident beam is here oriented parallel to the interacting surface, i.e., 0 - 0. The region of surface interaction extends over a length up to 50 gm (for a slit) down to 50 nm (for a nano-grating) (cf. Boustimi et al., 2001 a,b).
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C.2. Experimental observations F o r a monokinetic incident beam o f m~tastable atoms; ....the extreme accuracy of the energy transfer, combined with the well-defined direction for Ap, imposes that the atoms having undergone a change of internal state contribute to produce a novel atomic beam, monokinetic, and whose angular direction with respect to the incident beam is rigorously known. One has indeed: VoCOSOo -- VfGOSOf
(19)
v f - (V2o+ 2AE/m)1/2
(20)
In Eqs. (19 and 20), Vo and vf are respectively the initial and final atomic velocities, and 0o and Of the beam orientations with respect to the surface. As the energy transfer most often largely exceeds the thermal energy of the atoms (e.g., up to 650 meV for Kr, as compared to ~ 70 meV for the velocity-selected thermal energy), the angular deflection is very large (e.g., 70~ with the weak dispersion around this value yielding information on the effective state of the surface (e.g., lack of planarity as due to local corrugation, breakdown at a microscopic level of the local long-range symmetry, etc.). Experimentally, atoms cannot fly at a grazing incidence over a long distance because the interaction is attractive. Rather, the beam is deflected after transmission through a thin microslit. Experimental difficulties are many: the counting rates are very low, as due to the low density of metastable states; the impact parameter enabling an atom to undergo deflection is very limited : the typical distance where the metastability transfer is efficient is found to be ~ 5 nm. The shape of the microslit must be well-controlled for the interaction to occur during the ,-~ 100 nm long region where the atom is at grazing incidence. Anyhow, the strong angular selectivity of the process has permitted to observe this signature of vW anisotropy in various situations. The successful observation for metastable Ar and Kr atoms transmitted through a micro-slit (Boustimi et al., 200 l a) was followed by a more efficient process associated with transmission through a nano-grating (Boustimi et al., 2001b), by an extension to a molecular specie (metastable N2) (Boustimi et al., 200 lc), and even by the observation of the reverse endothermic metastability transfer (Karam et al., 2002). D. ATOM INTERACTION WITH NANOBODIES With the trend to explore shorter and shorter atom-to-surface distances (see Sect. V.A and V.C.), it becomes notably interesting to consider the
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interaction of atom with surface featuring "strong" curvatures, i.e., a curvature radius smaller than the relevant wavelengths for the atomic fluctuations. Several modifications have to be considered for the interaction of atoms with the nonplanar surfaces (see e.g., the review by Klimov et al., 2001): The geometrical factor that controls the strength of the electrostatic image from the bulk permittivity e departs from the common factor [ ( e - 1)/ (e + 1)]. It is described in general by a more complex function, that can occasionally be turned into the well-known form factor [ ( e - 1)/(e + 2)] for an atom located in the vicinity of a sphere (Klimov et al., 1996; 1997a,b; 1999a,b). In particular, the cylindrical limits of ellipsoids have been considered in this problem, with a study of the asymptotic behavior of the corresponding geometrical factors (Klimov and Ducloy, 2000). - This change in the surface response implies a frequency shift in the resonant response of the nanobody compared to the planar surface response, when the dielectric medium is dispersive. - The z -3 interaction law remains valid as long as the atom-surface distance is small compared to the curvature of the nanobody. More generally, the cylindrical symmetry of the interaction can be lost, and extra-anisotropy term naturally appears from the particular geometry of the interacting atom with a specially-shaped nanobody (Klimov et al., 2002a,b). When the curvature radius becomes shorter than the propagation wavelength, the atom-surface interaction is no more limited to a dipole expansion, coupling the atom dipole fluctuations to its induced image. Rather, the complete multipole expansion should be considered. This permits the quadrupole contribution to bring about specific resonant contributions, that could turn to be dominant in specific cases (Klimov and Ducloy, 2000). A larger variety of situations than the elementary discrimination between attractive and repulsive behaviors can even be considered. In particular, there could exist a possibility for an atom to orbit around a nanobody (Klimov et al., 1999b). Specific effects associated with the periodicity of a photonic device are also under investigation. Until now, the corresponding theoretical developments have not been followed by demonstration experiments, notably because of the lack of a general experimental method for these problems with nanobodies, that would be the equivalent of SR spectroscopy for the interaction of an atom with a plane surface. Note that the experimental developments, in progress in Paris (Treussart et al., 1994; von Klitzing et al., 2001) and in Cal'tech (Vernooy et al., 1998) have until now been more concerned with microbodies (notably microspheres with their specific resonances) whose -
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size largely exceeds the wavelength, than with genuine nanobodies. For a single nanobody, the surrounding volume is very small, and the experimental extension to a distribution of "identical" nanobodies requires homogeneity conditions that are particularly tough to realize with the present state-of-the-art of nanobody production. Also, the atomic motion strongly limits the interaction time. The use of very slow atoms (i.e., after laser cooling) could be beneficial, in spite of the already mentioned limitations, and eventually with respect to the quantum nature of the atomic motion and limits due to uncertainty principle at a very small distance from the nanobody. More generally, the resonances of an atom at a very small distance from the surface gets so broad, and the lifetime of its excited level (Klimov et al., 2001) so short, that the advantages of high resolution spectroscopy tends to be limited. Rather, the general formalism developed for such a problem can be applied to an elementary "atomic" system, such as a chromophore, in a more general situation than that of an atom freely evolving in space. In particular, these modelings may be of interest for various problems such as the modification of the fluorescence spectrum of an embedded atom (or ion) close to a nanoscope tip (Klimov et al., 2002b), or a carbone nanotube, or nanofibers (Klimov and Ducloy, 2004), etc. Further extensions should deal with the interaction of an atom with a micro- or nano- structured object, such as microstructured fibre, nanograting, etc., introducing the possibility of tailored shape factor as well as nanobody-driven response, extended over a macroscopic size. Let us also recall that the sensitivity is enhanced when a transmission slit is replaced by a transmission nano-grating as in the experiment described in the above section with metastable atoms. It would hence become conceivable that details on the quality of the structured surface are learned from the observed features of the surface interaction.
VI. Conclusion The problem of the long-range electromagnetic coupling, between an atom and a neighboring surface exhibits many facets that the optical methods are well-suited to tackle, notably because they provide a natural technique to explore the variety of situations offered by excited atoms. Although the description of the principle of vW surface interaction is apparently well-known, the effective experimental exploration has remained limited, with respect to the extremely broad range of energy covered by the z -3 interaction. The development of new techniques, enabling complementary exploration of various distance ranges, is hence an important purpose
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of fundamental interest, that is partly connected with contemporary quantitative research on the Casimir effect. Our studies have notably emphasized the importance of the spectral response of the surface, and are potentially sensitive to the various corrections such as anisotropy, lifetime and trajectory modifications, temperature corrections, and surface roughness, that invalidate very elementary predictions. In the same spirit, it should be noted that although the related problem of the vW interaction between two solids is of utmost importance for various problems of biology, like membrane problems, the various estimates derived from simple models have until now revealed too crude to describe sensitively the experimental biological values (Bostr6m et al., 2001). Similarly, one may expect that the understanding of the resonant energy transfer mechanism between molecules (see e.g., Cohen and Mukamel, 2003; Selvin, 2000) could benefit in a fundamental manner from the various observations performed with an atom and a surface, or with gaseous atoms in a confined environment.
VII. Acknowledgments This report has benefited from continuous discussions, and long-standing co-operation with J. Baudon, M. Fichet, M-P. Gorza, V. Klimov, J.R.R. Leite, V. Letokhov, G. Nienhuis, J. Robert, S. Saltiel, and F. Schuller. The results presented here would not have been obtained over the years without the essential contributions of numerous students, visitors, and co-workers from the staff, and notably A. Amy-Klein, M. Boustimi, M. Chevrollier, G. Dutier, H. Failache, O. Gorceix, M. Gorris-Neveux, I. Hamdi, J-C. Karam, M. Ori/t, N. Papageorgiou, D. Sarkisyan, V. Sautenkov, P.C.S. Segundo, P. Simoneau, T. Vartanyan, A. Yarovitski, and A. Weis. This work contributes to the objectives of the European consortium FASTNet (contract HPRN-CT-2002-00304)
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Shimizu, F. (2001). Specular Reflection of Very Slow Metastable Neon Atoms from a Solid Surface. Phys. Rev. Lett. 86, 987-990. Simoneau, P., Le Boiteux, S., de Araujo, C., Bloch, D., Leite, J.R.R., and Ducloy, M. (1986). Doppler-free Evanescent Wave Spectroscopy. Opt. Commun. 59, 103-106. Sukenik, C.I., Boshier, M.G., Cho, D., Sandoghdar, V., and Hinds, E.A. (1993). Measurement of the Casimir-Polder Force. Phys. Rev. Lett. 70, 560-563. Treussart, F., Hare, J., Collot, L., Lef6vre, V., Weiss, D.S., Sandoghdar, V., Raimond, J-M., and Haroche, S. (1994). Quantized atom-field force at the surface of a microsphere. Opt. Lett. 19, 1651-1653. van Kampen, H., Sautenkov, V.A., Eliel, E.R., and Woerdman, J.P. (1998). Probing the spatial dispersion in a dense atomic vapor near a dielectric interface. Phys. Rev. A 58, 4473-4478. Vartanyan, T., Bloch, D., and Ducloy, M. (1995). Blue shift paradox in selective reflection. In: "Spectral Line Shapes," A.D. May et al. (Eds.), AIP Conference Proceedings, Vol. 328, American Institute of Physics, New York, pp. 249-250. Vartanyan, T.A., and Weis, A. (2001). Origin of the "blueshift" in selective reflection spectroscopy and its partial compensation by the local-field correction. Phys. Rev. A 63, 063813 1-5. Vernooy, D.W., Furusawa, A., Georgiades, N.P., Ilchenko, V.S., and Kimble, H.J. (1998). Cavity QED with high-Q whispering gallery modes. Phys. Rev. 57, R2293-2296. von Klitzing, W., Long, R., Ilchenko, V.S., Hare, J., and Lef~vre-Seguin, V. (2001). Tunable whispering gallery modes for spectroscopy and CQED experiments. New J. Phys. 3, 14. Vuleti6, V., Sautenkov, V., Zimmermann, C., and H~insch, T.W. (1994). Optical pumping saturation effect in selective reflection. Opt. Commun. 108, 77-83. Woerdman, J.P., and Schuurmans, M.F.H. (1975). Spectral narrowing of selective reflection from sodium vapour. Opt. Commun. 14, 248-251. Wood, R.W. (1909). The selective reflection of monochromatic light by Mercury vapor. Phil. Mag. 18, 187-195; see also: Resonance Radiation and Specular Reflection in Mercury Vapor, Physical Optics (McMillan Company, 1911), Facsimile reproduction by Optical Society of America, 1988. Wylie, J.M., and Sipe, J.E. (1984). Quantum electrodynamics near an interface. Phys. Rev. A 30, 1185-1193. Wylie, J.M., and Sipe, J.E. (1985). Quantum electrodynamics near an interface II. Phys. Rev. A 32, 2030-2043.
ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 50
A T O M S M A D E E N T I R E L Y OF ANTIMATTER." T W O M E T H O D S P R O D UCE SLO W A N T I H Y D R O G E N G. G A B R I E L S E Harvard University, Cambridge MA 02138, USA I. I n t r o d u c t i o n and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Testing C P T Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Extensions to the S t a n d a r d Model that Violate Lorentz Invariance . . . . . . C. A n t i h y d r o g e n Gravity Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Ingredients of Slow A n t i h y d r o g e n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Cold A n t i p r o t o n s for All Slow H Experiments . . . . . . . . . . . . . . . . . . . . . B. A New Storage Ring for A n t i h y d r o g e n Experiments . . . . . . . . . . . . . . . . . C. Better Efficiency with More Deceleration . . . . . . . . . . . . . . . . . . . . . . . . . D. Five M e t h o d s to Accumulate Cold Positrons . . . . . . . . . . . . . . . . . . . . . . E. Plasma Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. P r o d u c t i o n M e t h o d I: D u r i n g e + Cooling of ~ in a Nested Penning T r a p . . . . A. Nested Penning T r a p and Positron Cooling of A n t i p r o t o n s . . . . . . . . . . . B. D e m o n s t r a t i o n and Study of Positron Cooling of A n t i p r o t o n s . . . . . . . . . C. A Variation: Driven e + Cooling of ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . D. A n t i p r o t o n Losses f r o m a Nested Penning T r a p . . . . . . . . . . . . . . . . . . . E. Two Techniques to C o u n t H A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Beyond C o u n t i n g H A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Probing Internal H Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Measured Field Ionization Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Beyond G u i d i n g Center A t o m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. First M e a s u r e m e n t of the Speed of Slow H A t o m s . . . . . . . . . . . . . . . . . . E. Deexcitation of Highly Excited States . . . . . . . . . . . . . . . . . . . . . . . . . . . VI. Three Body H F o r m a t i o n , and Related Experiments . . . . . . . . . . . . . . . . . . . VII. P r o d u c t i o n M e t h o d II: Laser-Controlled H P r o d u c t i o n . . . . . . . . . . . . . . . . . VIII. C o m p a r i n g the H P r o d u c t i o n Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IX. F u t u r e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. A n t i h y d r o g e n T r a p p i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Will Collisions with M a t t e r A t o m s Cool or Annihilate H Atoms? . . . . . . . C. C o n t i n u o u s L y m a n A l p h a Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI. A c k n o w l e d g m e n t s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Copyright 9 2005 Elsevier Inc. All rights reserved 1049-250X DOI: 10.1016/S1049-250X(04)50004-6
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G. Gabrielse An antihydrogen ~-H) atom - a positron (e +) in orbit about an antiproton ( ~ ) - is the simplest atom made entirely of antimatter. Producing H atoms that are cold enough to be trapped for precise laser spectroscopy, to compare antihydrogen and hydrogen, is a goal that has been pursued for many years. A prequel to this review summarized the techniques for accumulating cold ~ and e + that opened the way to slow H production, along with crucial devices like the nested Penning trap that was developed to bring the ~ and e + together. Several exciting years have seen the first production, observations and studies of slow H a t o m s - so far by two different methods. The demonstration of e + cooling of ~ in a nested Penning trap led to observations of slow H atoms produced in this way (method I) using two detection techniques. Field ionization detection of H produced by method I makes it possible to go beyond the simple counting of H a t o m s - to probe their internal structure and measure their velocity. The atoms identified so far are thus shown to be in highly excited states and to be traveling much too rapidly to trap. The new techniques to probe the internal state and speed are the necessary first steps towards developing methods to attain ground state H atoms that are much colder. In a very different method II, lasers control the production of H atoms via charge exchange collisions- a method that seems to naturally produce H atoms with essentially the low energy distribution of the ~ from which they form.
I. Introduction and Overview Antihydrogen (-H), the simplest of antimatter atoms, is the bound state of a positron (e +) in orbit around an antiproton (~). Are the properties of this atom made entirely of antimatter precisely the same as those of hydrogen, its matter counterpart, as CPT invariance would indicate (Sect. II)? Is there any difference between the gravitational acceleration of a matter and an antimatter atom? How dow we produce these atoms in order to look for answers to these questions? An 1986 Erice lecture (Gabrielse, 1987), shortly after ~ were trapped for the first time (Gabrielse et al., 1986a), laid out the antihydrogen goals that are now being pursued by three international collaborations at the CERN Antiproton Decelerator ( A D ) - a unique storage ring built to conduct these studies. "For me, the most attractive way ... would be to capture the antihydrogen in a neutral particle t r a p . . . The objective would be to then study the properties of a small number of [antihydrogen] atoms confined in the neutral trap for a long time."
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Inspiration came from attempts to confine neutrons (Kfigler et al., 1978) and the first trapping of atoms (Migdall et al., 1985). The trap first used for atoms would not allow the bias field that we needed to simultaneously trap and e +, but the use of a Ioffe trap (Gott et al., 1962) had been proposed for confining atoms in a nearly uniform bias field (Pritchard, 1983). Trapping of cold H still seems like the most feasible way to make optimal use of H atoms for precise measurements, since the number of H that will be produced still seems likely to be orders of magnitude less than typically used for hydrogen experiments. Trapping of charged particles and ions for precise measurements was already familiar in 1986, and atom trapping has since become just as common. A proposal to trap hydrogen as a way to produce Bose-Einstein condensates was reported about the same time as the Erice lecture (Hess, 1986), and hydrogen trapping is also now common (Hess et al., 1987; Roijen et al., 1988; Setija et al., 1993; Cesar et al., 1996). If the accuracy now achieved in the spectroscopy of hydrogen (Niering et al., 2000) could be realized with antihydrogen, a lepton and baryon CPT test of unprecedented accuracy would be possible. Gravitational studies of H seem very difficult but are not excluded in principle (Gabrielse, 1988; Walz and H~nsch, 2004). Some years later, while we were developing and demonstrating the techniques needed to make low energy H atoms, suggestions were made (Baur, 1993; Munger et al., 1993; Munger et al., 1994) to form very rapidly moving H by arranging that ~ in a storage ring pick up e + from pair production (Aste, 1994; Bertulani and Baur, 1998). This led to the first production and observation of H atoms. First, the 9 atoms observed at CERN were reported (Baur et al., 1996), and then 37 atoms were observed at Fermilab (Blanford et al., 1998). There was considerable interest in these observations both in the scientific community and beyond. Nonetheless, producing cold antihydrogen still seemed like the most feasible way to produce antihydrogen atoms that could be precisely compared to hydrogen atoms. Cold ~ and cold e + are essential ingredients (Sect. III). The prequel to this review, entitled "Comparing the Antiproton and Proton, and Opening the Way to Cold Antihydrogen" (Gabrielse, 2001), tells the 15-year story of developing the ~ techniques that now make all slow H experiments possible. Our TRAP Collaboration slowed (Gabrielse et al., 1989a), trapped (Gabrielse et al., 1986b), electron-cooled (Gabrielse et al., 1989b), and accumulated 4 K ~ (Gabrielse et al., 1990) at an energy 101~ times lower in energy than had been previously realized (Sect. III). They were then used to compare the charge-to-mass ratios of antiproton and proton to an accuracy that was nearly a million times better than had been previously achieved. Antiproton stacking techniques (Gabrielse, 2001) are now the only way to obtain large numbers of cold ~ at
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the AD (Gabrielse et al., 2002c). If all of these ~ techniques are applied after the ~ from the AD are first slowed in a decelerator, then it seems likely that many more ~ will be captured and transferred to an experiment trap. Cold e +, the other essential ingredients of cold antihydrogen, are also briefly discussed. This review contains an exciting update. Just several years later, slow antihydrogen atoms are now being regularly produced by two different methods: (1) H production in a nested Penning trap (Gabrielse et al., 1988) during positron cooling of antiprotons (Gabrielse et al., 2001) (Sect. IV). (2) Laser-controlled H production, in which lasers select the H binding energy (Storry et al., 2004) (Sect. VII). Our A T R A P Collaboration (table I) developed method I over many years (Gabrielse et al., 1988; Hall and Gabrielse, 1996; Gabrielse et al., 1999a, 2001) and method II much more recently (Hessels et al., 1998; Speck et al., 2004; Storry et al., 2004). Two different detection methods have been used (Sect. IV.E). A T R A P uses background-free, field ionization detection to count the H produced by both method I (Gabrielse et al., 2002a,b) and method II (Storry et al., 2004). The A T H E N A Collaboration produces H using method I, counting an H atom upon detecting the correlated loss of a e + and a ~ taking place within 5 las and 4- 8 mm of each other (M. Amoretti et al., 2002). Both collaborations count large numbers of H atoms.
Table I ATRAP collaboration: CERN AD-2. Harvard University: Prof. G. Gabrielse~, Dr. C.H. Storry, Dr. J.N. Tan, N.S. Bowden,
J. Estrada, N. Guise, P. Larochelle, D. LeSage, P. Oxley, A. Speck, M. Wessels, P. Yesley Institute for Atomic and Molecular Physics FOM, Amsterdam: C. Wesdorp
IKP, ForsehungszentrumJiilieh: Prof. W. Oelert, Dr. F. Goldenbaum, Dr. D. Grzonka, Dr. S. Martin, Dr. G. Schepers, Dr. T. Sefzick Max-Planek-Institut fiir Quantenoptik, Garehing: H. Pittner, J. Walz, T.W. Hfinsch2 Vrije Universiteit, Amsterdam: Dr. K.S.E. Eikema
York University: Prof. E.A. Hessels, D. Comeau Early contributions came from the Univ. of Bonn, and from the Inst. for Med. En. Phys. in Vienna. *Spokesperson. 1Also Ludwig-Maximilians-Universit/it Miinchen.
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ATRAP's field ionization detection technique (Gabrielse et al., 2002b) makes it possible to go beyond counting H atoms (Sect. V ) - revealing that it is highly excited H that are produced in large numbers (Gabrielse et al., 2004a), and that so far these are moving too rapidly to be trapped (Gabrielse et al., 2004b). The central challenge facing H research right now is in obtaining H atoms that are useful for precise spectroscopy, with at least the following two properties" (1) Useful H must be in its ground state. (2) Useful H must be moving slowly enough to be trapped, with energy much less than the 0.5 K depth of the deepest magnetic traps. m
Field ionization detection probes the internal H state by determining which H are deeply enough bound to survive an analyzing electric field. Recent theory provides the relationship between the size of the atoms produced and the electric field that they can survive (Vrinceanu et al., 2004). The H velocity is probed by making the strength of the analyzing electric field oscillate in time. The number of H that survive this field depends upon the H velocity (Gabrielse et al., 2004b) since faster atoms travel through the oscillating field without ionizing during the time that this field has a low magnitude. The ATRAP measurement of H velocity demonstrated for the first time that H formation is faster than e + cooling, so that H can be formed before the ~ and e + come into thermal equilibrium. No useful H has yet been identified. However, the new techniques to probe the H state and velocity should enable H production to be optimized for the production of the most tightly bound states, and for the lowest H velocity. Almost all observed H atoms have so far been produced using method I - during positron cooling of antiprotons in a nested Penning trap (Fig. 1) - rather than in the more recently demonstrated method II. The highly excited H states that are being produced at a high rate, revealed by field ionization detection (Gabrielse et al., 2002b, 2004a), are what was expected for H formation at low temperatures using finite-sized plasmas of e + and ~. Many years ago we pointed out that the expected high rate H production mechanism at low temperatures T should be the three body formation process (Sect. VI) whose rate varies as T-9/Z(Gabrielse et al., 1988) -p
+ e+ + e+
~ H * + e+ .
(1)
The matter counterpart of this process had been studied for the much higher temperatures of interest for astrophysical applications (Bates et al., 1962; Makin and Keck, 1963; Stevefelt et al., 1975). It was exciting to realize that the production rate could be enormous if we did the experiments
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(a) -Vp
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FIG. 1. Outline (a) and potentials (b) of a nested Penning trap used to produce positrons cooling of antiprotons, and the accompanying production slow H. Variations of this figure, taken from the original proposal (Gabrielse et al., 1988), are now familiar in papers on slow antihydrogen since most slow H has been produced in this way. w
at much lower t e m p e r a t u r e s - provided that the steep temperature scaling was valid down to much lower T than had been previously considered, and provided that the strong magnetic field used to confine the ~ and e + did not reduce the rate too badly. The questions raised about temperature scaling and the effect of fields triggered theoretical work that suggested that the temperature scaling would be valid both without (Zygelman and Dalgarno, 1989; Zygelman, 2003) and with (Glinsky and O'Neil, 1991; Men'shikov and Fedichev, 1995; Fedichev, 1997) a strong magnetic field. The strong field only decreased the high formation rate by a factor of ten (Glinsky and O'Neil, 1991) or even somewhat less (Robicheaux and Hanson, 2004). For a ~ in an infinitely extended plasma, ground state H would be the expected eventual outcome. However, it was immediately clear that for the limited interaction time of a ~ within the finite size plasmas that can be arranged in an ion trap, the three body formation would be "interrupted" when the H* left the e + plasma. H atoms in the highest excited states would be ionized by the trap fields, but the interrupted three body formation could then result in highly excited H* produced at a high rate, just as is now observed, and the theoretical work thus sought to determine the time scale. Can low temperature H be produced by H production method I? It is too early to tell. The most straight-forward positron cooling of antiprotons (used by ATRAP for its initial H observation and by A T H E N A for all of its H studies) could form H with an appreciable velocity if the H forms before the e + have completely cooled the ~. However, ATRAP almost immediately moved to a variation on method I - driving the H production through repeated cycles of e + cooling of ~ (Gabrielse et al., 2002b). This variation produces H more efficiently, and should also make it possible to give the just the minimum velocity needed to produce H. The needed optimization of the drive was not done for the initial demonstration of measuring an
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m
H velocity, so it remains to be seen if the low velocities hoped for can be realized. The weak dependence of the H formation rate upon the temperature of heated e + plasmas measured by ATHENA (Amoretti, et al., 2004) (contrary to what was expected for three body formation) was interpreted as if the ~ and e + were in thermal equilibrium. Likely it instead indicates rapid three body formation of very fast H - relatively independent of the equilibrium e + temperature, an interpretation born out of a very recent simulation (Robicheaux, 2004). The first laser-controlled H production (method II) was demonstrated only very recently (Speck et al., 2004; Storry et al., 2004), hv(852 nm) + hv(511 nm) + Cs Cs* + e + Ps* + ~
~ Cs*
(2)
~ Ps* + Cs +
(3)
~
(4)
+ e-,
Field ionization detection reveals that highly excited H* is also being formed by this process, as expected for resonant charge exchange collisions (Hessels et al., 1998). An attractive feature is that the H produced seems likely to have the energy distribution of the ~ from which it forms, though this remains to be confirmed experimentally. Although the ~ temperature can be no lower than the ambient 4 K temperature in the initial proof-ofprinciple experiment (Storry et al., 2004), the ~ temperature could be made much lower in principle, by adapting techniques which took a trapped electron to 300 mK (D'Urso et al., 2003), for example. The only calculation of laser-controlled H production is for no magnetic field (Hessels et al., 1998), so formation theory that includes a strong magnetic field is clearly needed. Other possible formation methods have been discussed. ATRAP was unable to get another promising H production m e c h a n i s m - field-assisted formation (Wesdorp et al., 2 0 0 0 ) - to work for reasons that are not completely clear. Another attractive possibility, suggested long ago, is to use a CO2 laser to stimulate trapped ~ and e + to form H n ~ 10 states (Gabrielse et al., 1988), which would then rapidly deexcite to the ground state by radiation. There may be an enhancement (Wolf, 1993) if the photon energy is tuned lower by several k T to take advantage of a deexcitation "bottleneck" predicted by a more recent theory (Glinsky and O'Neil, 1991). Some progress has been made on topics that will be important for future experiments (Sect. IX). We find it attractive to superimpose a neutral particle trap for H, in the same volume within which Penning traps contain the p and e + ingredients (Squires et al., 2001) from which H atoms
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form (Sect. IX.A). The challenge (Sect. IX.A) arises for magnetic gradient traps that destroy the cylindrical symmetry, and hence angular momentum conservation, thereby voiding a confinement theorem (O'Neil, 1980) which prevents radial diffusion of the charged ingredients from their traps. Many recent calculations investigate the feasibility of cooling H atoms in collisions with matter atoms (Sect. IX.B). In an important step on the way to the first H spectroscopy, a continuous Lyman alpha radiation source (Eikema et al., 1999) has been used for hydrogen l s-2p spectroscopy (Eikema et al., 2001), a demonstration that bodes well for the H future. Space does not permit discussing two related topics that should at least be mentioned. The first is the possibility to directly measure the ~ magnetic moment, building on techniques we developed to measure the magnetic moment of the free electron (D'Urso et al., 2004), and also on a double trap developed to measure the magnetic moment of an electron bound to an ion (Verd6 et al., 2003). The second is the discovery of a small polarization correction to the cyclotron frequency of a molecular ion (Thompson et al., 2004). When applied to the q/m comparison of the antiproton and proton (which uses an H-ion) (Gabrielse et al., 1999b), this shift slightly within its error bars the precise comparison of q/m for the antiproton and proton (Gabrielse, 2004; Thompson et al., 2004) that was summarized in the prequel to this work (Gabrielse, 2001). A conclusion (Sect. X) expresses optimism for the future, but readily admits that much remains to be done.
II. Motivations A. TESTING CPT INVARIANCE The "P" in CPT stands for a parity transformation. Suppose we perform a certain experiment and measure a certain outcome. As we do the experiment, we also watch what the experiment and outcome look like in a mirror (actually the reflection describe and a rotation by 180 degrees that we will ignore). We then build an apparatus and carry out a second experiment which is identical to the mirror image of the first. If reality is invariant under parity transformations P then we should obtain the outcome seen in the mirror for the second experiment. Until 1956 it was believed that reality was invariant under parity transformations. Then Lee and Yang noticed that this basic tenet of physicists' faith had not been tested for weak interactions, those interactions between particles which are responsible for radioactive decay of nuclei. Shortly after, Wu and collaborators, and then several other experimental groups in rapid succession, showed in fact
II]
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that experiments and mirror image experiments produced strikingly different results when weak interactions were involved. The widespread faith that reality was invariant under parity transformations P had clearly been misplaced. A new faith, that reality is invariant under CP transformations, rapidly replaced the discredited notion. The "C" stands for a charge conjugation transformation, which for our purposes is a transformation in which particles are turned into their antiparticles. To test whether reality is invariant under CP transformations, a mirror image experiment is constructed as above but this time all the particles within it are also changed into antiparticles. It was widely believed that these two different experiments could not be distinguished by their outcomes until Cronin and Fitch surprised everyone by using kaon particles to explicitly demonstrate that our reality is not invariant under CP transformations. The experiment has been repeated by different groups in different locations and related measurements are still being pursued. Now most physicists believe that reality is instead invariant under CPT transformations, the "T" standing for time reversal transformations. CPT invariance seems more well-founded insofar as theorists find it virtually impossible to construct a reasonable theory which violates this invariance. Axiomatic quantum field theory, for example, used commonly to describe all interactions except for gravity, is CPT invariant. To experimentally test for CPT invariance, one again compares the outcomes of two experiments. This time one makes a movie of the goings on in a mirror image experiment in which the particles are switched to antiparticles. The second experiment is constructed to mimic what one sees in the movie when the movie is run backwards (i.e., when "time is reversed"). In practice, the cyclotron oscillation frequencies of a proton and an antiproton oscillating in the same magnetic field would be identical if reality is invariant under CPT transformations. Our antiproton-proton frequency comparison reviewed in the prequel to this paper (Gabrielse, 2001) is by far the most precise test of CPT invariance done with baryons and antibaryons, particles made of three quark particles or three antiquark particles. The antiproton-to-proton charge-to-mass ratio comparison thus joins an experiment with kaons (made of a quark particle and an antiquark particle) and a lepton comparison of the magnetic moments of an electron and positron as one of the most precise experimental tests of whether our reality is invariant under CPT transformations. The various tests of CPT made by comparing the measured properties of particles and antiparticles are represented in Fig. 2. The stable particles and antiparticles in these tests come in several varieties which are important to distinguish. The proton (antiproton) is a baryon (antibaryon). The proton
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FIG. 2. Tests of CPT invariance.
(antiproton) is composed of three quarks (antiquarks) bound together. The K mesons, like all meson particles and antiparticles, are instead composed of a quark and an antiquark bound together. The third variety of particle is the lepton; the electron and the positron are examples of lepton particles and antiparticles. Leptons are not only not made of quarks, they seem to be perfect point particles since no experiment has yet detected any internal structure. It seems crucial to test CPT invariance in a sensitive way for at least one meson system, one baryon system and one lepton system.
II]
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FIG. 3. Relevant accuracies for precise H l s-2s spectroscopy compared to the most stringent tests of CPT invariance carried out with the three types of particles: mesons, leptons, and baryons.
The motivation for comparing the antihydrogen l s-2s transition frequencies is that the accuracy attained in measuring this interval in hydrogen (Cesar et al., 1996; Niering et al., 2000) is much higher than for any other CPT test involving leptons and baryons (Fig. 3). For example, the ratio of the Rydberg and the anti-Rydberg constants that could be deduced from such a measurement R ~ [ H ] _ m[e+___~](q[e+]]2 (q[~])21 + m[e-]/M[p]
(5)
R~[H] - m[e-] ~,q[e-]] \q[p]J 1 + m[e+]/M[~] depends upon all the ratios to the charges and masses (Hughes and Deutch, 1992) involved in antihydrogen and hydrogen. We hope and expect that such measurements will provide accurate CPT tests that are much more stringent than the most precise baryon and lepton CPT tests that are currently available. The most accurate CPT test for a baryon system, by a large factor, is the 0.09 ppb (90 x 10 -9) comparison of q/m for the antiproton and proton (Gabrielse et al., 1999b). Could it be that while the magnitude of q/m is the same for the antiproton and proton to an extremely high precision, that q and m for ~ and p may differ in just such a way as to keep q/m the same? Our measurement of q/m, combined with a determination of qZm for the (Hori et al., 2003), shows that q and m separately have the the same mass and charge magnitude to an accuracy of 10 p p b - limited by the 100 times lower accuracy of the exotic atom spectroscopy that determines qZm.
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The most accurate CPT test for a lepton system is the comparison of the dimensionless magnetic moments or g values of the electron and positron, to a precision of 2 ppt (2 x 10-12) (Van Dyck, Jr. et al., 1987). At Harvard, we are just completing the first fully quantum measurement of the electron magnetic moment, using a one-electron quantum cyclotron (Peil and Gabrielse, 1999; D'Urso et al., 2004). It looks like it may eventually be possible to get a positron-electron CPT test that is more than an order of magnitude more accurate. How many atoms are really required for accurate H spectroscopy? An experimental answer to this question is not yet available for either hydrogen or antihydrogen, but estimates suggest that small numbers may suffice (Zimmerman and Hfinsch, 1993). My own suspicion is that the most accurate spectroscopy of both hydrogen and antihydrogen will ultimately be done with one atom at a time.
B. EXTENSIONSTO THE STANDARD MODEL THAT VIOLATE LORENTZ INVARIANCE
Lorentz invariance violating extensions to the standard model have been considered and parameterized (Colladay and Kosteleck~,, 1997). Some of the possible terms cause CPT violations and some do not. The conclusion of a study of what could possibly be learnt from comparisons of hydrogen to antihydrogen (Bluhm et al., 1999) is that high accuracy comparisons could provide substantial constraints on possible Lorentz-violating additions to the Standard Model.
C. ANTIHYDROGEN GRAVITY TESTS
There have been no direct measurements of the gravitational acceleration of antimatter particles. This is not possible with charged particles because the gravitational force is so much smaller than the Coulomb force. With neutral antihydrogen there may be a chance, and it seems to me that a direct measurement would be interesting and very important. A neat review of gravitational theory and experiments summarizes the various indirect tests (Bell, 1987). Our very accurate, 90 ppt (90 parts in 1012) comparison of q/m for an antiproton and proton (Gabrielse et al., 1999b) can be interpreted (Hughes and Holzscheiter, 1991) as a comparison of an antimatter clock (the cyclotron motion of antiproton) and a matter clock (the cyclotron motion of a proton). If the gravity acts differently on the the antimatter and matter clocks, then the gravitational red shift could make them run at different
II]
ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
167
rates. If the clocks run at the same rate to within 9 x 10-11, as reported, then the accelerations due to gravity differ for antiprotons and protons by less than 1 ppm (1 part in 106). A possibility that has generated much interest is that the familiar tensor gravity of our matter world, with its spin 2 graviton, might be accompanied by an attractive scalar contribution (spin 0 graviton) and repulsive vector contribution (spin 1 graviton), that happen to cancel for matter. For antimatter, however, the scalar and vector additions would both be attractive, so an H atom would have a gravitational acceleration greater than the familiar value (Goldman et al., 1986; Nieto and Goldman, 1991). It seems that equivalence principle experiments with ordinary matter set strict limits on the size of a possible vector contribution to gravity (Bell, 1987; Adelberger et al., 1991), though the more detailed and recent version of this claim has generated some controversy (Adelberger and Heckel, 1991; Goldman et al., 1991; Morpurgo, 1991). Measuring gravitational properties of antihydrogen atoms seems to be difficult (Gabrielse, 1988; Walz and H/insch, 2004) but is not excluded in principle. The relevant energy scales are summarized in Fig. 4. A significant challenge is that it is hard to cool H atoms to the same low temperature that some other atoms can be laser-cooled. The Lyman alpha photons have more energy than the photons used to cool other atoms, and the H atoms are less massive, so the laser cooling limit is higher. One way that it may be possible to get lower temperature H atoms would be to ionize extremely cold H + ions with a laser just above the ionization threshold (Walz and Hfinsch, 2004). The challenge here is to produce the
FIG. 4. Energies involved in the production, slowing and trapping of H atoms along with the energy scale appropriate for gravitational experiments. Energies are specified in units of temperature. From (Gabrielse, 1988).
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antimatter ions, not observed so far, and then to cool them to extremely cold temperatures, perhaps via collisions with laser cooled ions. I hope that we will find some H + if we look for them carefully, just as we found the trapped H - ions that we used to compare q/m for the antiproton and proton (Gabrielse et al., 1999b), but this may not work if hydrogen molecules were involved in H - formation. Of course, if the challenge of obtaining large numbers of laK and n K H atoms can be met, then it could be that the now familiar free fall and atom interferometry experiments that can be carried out with laser cooled matter atoms, could be carried out with antihydrogen as well. Without a method to obtain such ultra-cold H atoms, however, proposing to do such experiments seems like idle exercise.
III. Ingredients of Slow Antihydrogen A. COLD ANTIPROTONS FOR ALL SLOW H EXPERIMENTS The methods to accumulate 4.2 K ~ are the basis of all efforts to produce and study cold antihydrogen. These techniques were developed by our TRAP Collaboration as summarized in the prequel (Gabrielse, 2001) to this review. Antiprotons with an energy of 5.3 MeV are ejected from a storage ring in a pulse that is typically 80 ns long. The crucial steps are (1) Slowing the ~ in a matter degrader (Gabrielse et al., 1989a). (2) Capturing the ~ in a Penning trap by rapidly applying a trapping well while the ~ are inside the trapping volume (Gabrielse et al., 1986a). (3) Electron-cooling of trapped ~ (Gabrielse et al., 1989b). (4) Stacking ~ from successive ~ injection pulses (Gabrielse et al., 1989b; Gabrielse, 2001; Gabrielse et al., 2002c). Some years later, some of these techniques were duplicated (Holzscheiter et al., 1996) by the CERN PS-200 Collaboration that later developed into ATHENA. Stacking ~ from successive pulses of ~ from the storage ring is now the only way to accumulate more than about 2 x 104 p for current experiments. Accordingly we made a careful study of what is currently possible (Gabrielse et al., 2002c), as summarized in Figs. 5 and 6. The cold ~ are readily stored in a cryogenic vacuum system. Our completely sealed and cold vacuum system produces the best vacuum used for H experiments- so good that we needed to use ~ as the vacuum gauge. We held ~ for months awaiting collisions with background gas that would cause them to annihilate. No ~ loss was detected, and the
III]
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.
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.
applied potential [V] FIG. 5. Energy spectra for antiprotons trapped from a single pulse from the AD without (a) and with (b) electron cooling. Stacking (c) yields a much larger number of cold antiprotons. From (Gabrielse et al., 2002c).
0.5 0.4 Or)
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FIG. 6. Typical numbers o f f that can be accumulated as a function of the number o f f pulses that are delivered to a trap experiment - one pulse approximately every 80 s. From (Gabrielse et hi., 2002c).
170
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uncertainty in the number of trapped ~ set a limit that the background pressure was less than 5 x 10-17 Torr (Gabrielse et al., 1990). This high vacuum allows H experiments for which the annihilations of~, e + , and H are simply not a problem. For vacuum systems that are not completely cold, the pressure will of course be higher depending upon the area and condition of warm surfaces, upon how completely the trap volume is surrounded by cold surfaces, and by how much gas has been pumped onto these surfaces.
B. A NEW STORAGE RING FOR ANTIHYDROGEN EXPERIMENTS
The LEAR facility shut down after these ~ techniques were developed and demonstrated. The ~ techniques are now being used at a new storage r i n g the Antiproton Decelerator ( A D ) - built at the C E R N Laboratory in Geneva, Switzerland so that the envisioned H studies could be pursued. The AD replaces LEAR and two other storage rings that captured and accumulated ~ at high energies. With AD ~, and the TRAP techniques for accumulating cold ~, two international collaborations (soon to be three) are pursuing the mentioned objectives of precise spectroscopic comparisons of antihydrogen and hydrogen atoms. The AD sends about a hundred times less ~ to experiments in a single pulse of typically 3 x 107 (with 4.2 • 107 being the recent record high number). However, it sends more frequent pulses, about one every 80 s. The economy of the AD is possible because our ~ accumulation techniques make it possible to do the accumulation in a trap at low energies, rather than in a storage ring at high energies. Not long before the LEAR ring was shut down, while we were busy developing the techniques that would make possible the production of slow H atoms, a small number of fast H atoms were produced and observed - first at C E R N (Baur et al., 1996) and then at Fermilab (Blanford et al., 1998), as summarized in the Introduction. The incredible publicity that was afforded to these observations, in the scientific community and beyond, was a great help in promoting the construction of the C E R N AD.
C. BETTER EFFICIENCY WITH MORE DECELERATION
Antiproton accumulation time could be greatly decreased if our accumulation techniques could be applied after a decelerator first reduces the 5.3 MeV ~ energy of the ~ from the AD. Currently about 10 -3 or less of the 5.3 MeV ~ from the AD storage ring are slowed in the degrader to
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ATOMS MADE ENTIRELY OF A N T I M A T T E R . . .
171
energies low enough that we can capture them in a trap (Gabrielse et al., 2002c). If the ~ were first decelerated to lower energies, then less slowing in a degrader would be required. With a thinner degrader there would be less straggling energy width. A much higher fraction of the ~ could then be captured in a trapping well (of order 10 keV deep) that can be applied rapidly to capture the moving ~. A radiofrequency quadrupole decelerator (RFQ) was proposed many years ago as a way to prepare ~ for traps (Coc et al., 1991) but never realized. An RFQ is currently being inserted between the AD and a much thinner degrader by the ASACUSA collaboration (Yamazaki et al., 2004). This is a very substantial and costly replacement for part of the thickness of the currently used degraders, and the low ~ acceptance of a RFQ places heavy demands on the AD and beam optics. However, the possibility to increase the number of ~ available for H experiments by one or two orders of magnitude is very attractive. The hope is to eventually be able to exceed the 2 x 104~ at 4.2 K (Gabrielse et al., 2002c) that are currently available for experiments from a single pulse of ~ from the AD. Antiprotons slowed in a decelerator will need to first be caught in a catching trap that is necessarily located right at the exit of the decelerator, and then transferred to an experiment trap. The number of ~ that can be cooled to 4.2 K within the experiment trap is the number that must be eventually compared to what is currently available for experiments from a single AD ~ pulse. Alternately, a small but otherwise conventional storage ring could decelerate ~ after the AD. It would likely have a much larger acceptance than does a RFQ, but may be prohibitively expensive. Both decelerator options could make possible a much more rapid accumulation of ~ into our trap for H experiments. The ~ that ATRAP now accumulates into its trap in an hour could likely be accumulated from a single injection of ~ from the AD. This would greatly speed up the rate at which experiments could be done, and in the future may make more H atoms available for spectroscopy. However, degraders are the currently available option, and these are extremely inexpensive and robust. It is also much easier to distribute ~ between experiments spaced far enough apart (so that their large magnetic fields do not greatly affect each other) at 5 MeV rather than at tens of keV. D. FIVE METHODS TO ACCUMULATE COLD POSITRONS
For slow H production, cold e + are needed as well as cold ~. Fortunately, e + from radioactive decay are readily available in any laboratory, unlike whose production requires large accelerators. So far, 22Na sources have been
172
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used with five e + accumulation methods, four of which have produced cryogenic e + so far. (1) At Harvard we used electronic damping to accumulate substantial numbers of 4.2 K e + (Haarsma et al., 1995) for the first time, but the accumulation rate is slower than the methods currently used for H studies. It had been thought that electronic damping had been used previously to accumulate a few e + for precision measurements (Schwinberg et al., 1981), but our work suggests that some other mechanism must be responsible. (2) A T R A P developed and uses a method in which highly excited and highly magnetized positronium is produced and then ionized inside a trap that captures the e + (Estrada et al., 2000; Gabrielse, 2001; Gabrielse et al., 2001). (3) A T H E N A uses a method developed for plasma studies (Greaves et al., 1994) in which fast e + collide with neutral gas atoms in a series of room temperature Penning traps with sequentially lower background gas pressures (Surko et al., 1997; M. Amoretti, 2004). (4) NIST demonstrated a method in which e + collide with laser-cooled Be + ions to be trapped and cooled (Wineland et al., 1993; Jelenkovic et al., 2003). (5) A very thin and dense electron plasma has been used to slow e + for capture (Oshima et al., 2003), but has not yet accumulated large numbers or low temperature e +. It is hoped that this method could have the good vacuum of method 2 with the high accumulation rate of method 3. Methods 2 and 3 are the most important in practice so far. A T R A P ' s positronium method was the first to accumulate substantial number of cold (4.2 K) e + . As currently used, up to 5 x 106 e + are available for experiments. These are accumulated during hours when ~ are not available for experiments, are hidden behind a rotatable electrode so as to be out of reach of ~ during ~ loading, are cleaned of ions by pulsing the e + from one electrode to another, and are reused from one H production experiment to another. Even for large numbers of e + the plasma is typically not so far from a spheroidal shape, as measured by an aperture method (Oxley et al., 2004). In a trap with 1.2 cm working diameter we cannot currently handle many more e + in a robust way. The e + accumulation apparatus is very simple. Also, the e + and ~ accumulation take place entirely within coaxial trap electrodes that are completely surrounded by a 4.2 K vacuum enclosure. One result is that the e + cool naturally via synchrotron radiation to thermal equilibrium at 4.2 K. A second is that the vacuum inside the trap is better than the 5 x 10 -17 Torr limit already discussed.
III]
A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
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The gas slowing method adopted by A T H E N A accumulates hot e + in a large and separate room temperature apparatus much more quickly, then transfers them several meters into the cold (15 K) H production region where they cool naturally via synchrotron radiation to 15 K. About 7.5 • 10 7 e + are stored in the larger A T H E N A trap for H production e x p e r i m e n t s - about 15 times more e + than are typically used by ATRAP. The e + are distributed in a long thin plasma. Some radial compression comes from a rotating wall technique (Huang et al., 1997; Anderegg et al., 1998), and some from the entry of the e + into the strong field of a solenoid. The vacuum in the A T H E N A apparatus is not as low as for ATRAP, owing to the coupling of warm and cold vacuum systems that is needed to admit e + into the cryogenic trap apparatus. However, the ~ lifetime is still much longer than needed for H production. A T H E N A can accumulate fresh e + to fill their larger diameter trap about every 5 min. A T R A P accumulates e + much more slowly, but reuses them over many hours. Especially when a mistake causes us to lose e + , we at A T R A P are jealous of the rapid e + accumulation rate from buffer gas loading. Of course, what really matters is the number, density and plasma geometry of e + that are available for ~ experiments; the optimal value of these parameters for producing cold, ground state H is not yet known. It also remains to be seen if the better vacuum carefully preserved by the A T R A P approach will have advantages when precision measurements begin. Cooling and trapping e + from a radioactive source by colliding them with laser cooled Be (Jelenkovic et al., 2003) has yielded fewer e + (~ 2000) than was originally hoped for (Wineland et al., 2003), though the number could likely be improved by using this method as a second step after one of the other e + accumulation mechanisms. An e + temperature limit < 5 K was established, substantially larger than the temperature of the ions. However, this temperature was realized in a room temperature apparatus. Also, very nice images clearly reveal centrifugal separation of the laser-cooled 9Be+ ions and the e +, with the e + compressed into a narrow column along a Penning trap's magnetic field axis, with density >_4 x 109 cm -3. The intriguing suggestion is made that, with better e + accumulation, it may be possible to use Mg + ions to cool up to 109 e + to similar low temperatures within a room temperature apparatus.
E. PLASMA DIAGNOSTICS A quantitative understanding of H production requires a good understanding of the density and geometry of the ~ and e + plasmas from which
174
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m
H forms. The number of trapped particles is relatively easy to measure. Trapped ~ released from the trap produce annihilation signals in surrounding scintillators that can be counted. Trapped e + released from the trap produce a measurable current when they strike an electrode. In a perfect electrostatic quadrupole potential, trapped particles in a Penning trap will fill a spheroid (an ellipsoid with cylindrical symmetry about the magnetic field direction) which has a uniform density essentially out to its boundary (Dubin and O'Neil, 1999). If the number of particles is measured, then one more parameter is needed to determine the density and spatial distribution of the charges in the spheroid. At ATRAP we have measured the additional parameter for both e + and plasmas by measuring the number of charges that make it through an aperture whose radius is smaller than the radius of the plasma (Oxley et al., 2004). This is the only method to measure the distribution of ~ in a trap so far. Real traps do not produce perfect electrostatic quadrupole potentials especially near the walls of traps made from cylindrical rings, even when the geometry of such traps is carefully chosen (Gabrielse et al., 1989c). It is thus by no means clear that trapped plasmas will form ideal spheroidal plasmas. A nice feature of the aperture method is that it does not require assumption that the charges form a spheroid distribution. In fact, the ~ distribution that we measured was not well-approximated by a spheroid. Both ATRAP (Estrada et al., 2000) and ATHENA (Amoretti et al., 2003) detect the radiofrequency currents induced by the oscillation of the e + center-of-mass along the magnetic field direction, as a nondestructive alternative to measuring the number of e + by ejecting them from the trap. (The familiar center-of-mass oscillation of trapped charges that for decades has been used to nondestructively measure the number of trapped particles is sometimes now referred to rather obliquely as the lowest hydrodynamic mode.) Using the induced radiofrequency current is fine as long as this calibration is checked often against the actual number deduced directly using the ejecting the e +. Care must be taken because we have observed that for large numbers of e + the induced radiofrequency current can depend significantly upon the distribution of charges in the trap. Another way to measure the additional parameter needed to characterize the density and spatial distribution of a trapped plasma is to measure the oscillation frequencies for internal hydrodynamic oscillation modes of the trapped plasma. These frequencies have been calculated for ideal spheroidal plasmas (Dubin, 1991), and were studied in wonderful detail for plasmas of trapped ions (Bollinger et al., 1993). Later, this method was used to analyze trapped electrons (Weimer et al., 1994) and then trapped e + (Tinkle et al., 1996).
IV]
ATOMS MADE ENTIRELY OF A N T I M A T T E R . . .
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Shifts in the lowest frequency internal oscillation mode have been used to measure increases in the e + plasma temperature (M. Amoretti, 2003; Amoretti et al., 2003), from an initial unmeasured value that is assumed to be the temperature of the trap electrodes. A spheroidal e + is assumed. Annihilation "imaging" has been used to learn about the loss of stored (Fujiwara et al., 2004), though the spatial resolution with which the annihilation vertex was measured is unfortunately not much smaller than the trap radius. However, it sufficed to show that all ~ ejected from the trap annihilated at discrete patches on the surface of the trap electrodes. The cylindrical symmetry of the Penning trap used about the magnetic field direction is thus broken by something. Whether this is a feature of the imperfections in this particular trap, or whether such imperfections are present in all traps, is not clear.
IV. Production Method I: During e+ Cooling of ~ in a Nested Penning Trap A. NESTED PENNING TRAP AND POSITRON COOLING OF ANTIPROTONS
The production of cold H requires the interaction of ~ and e +. Their opposite sign of charge makes it impossible for them to share the same potential well in a Penning trap, since one of the two species will see it as a potential hill. Many years ago the nested Penning trap was proposed as a solution (Gabrielse et al., 1988). Figure 1 in the Introduction and Overview shows ~ in a large outer well, with e + in the inverted central well. (Of course, it would be possible to reverse the particle locations by inverting the potential, as may be desirable to get colder H.) Essentially all of the large number of slow H produced by ATRAP and ATHENA so far were produced in a nested Penning trap, during the e + cooling of ~, since ATRAP has only recently demonstrated the second production method (Sect. VII). Electrons and protons were used to first demonstrate cooling of oppositely charged species in a nested Penning trap (Hall and Gabrielse, 1996). Figure 8 shows the spectrum of protons with and without cooling electrons in the center of the nested Penning trap (Fig. 7). Without cooling electrons in the central well, hotter protons retain the higher energy distributions illustrated to the right in the figure. With cooling electrons in the well the proton energy spectrum cools dramatically as shown to the left in the figure. The next big step was to get ~ and e + into such a trap structure and demonstrate their interaction (Gabrielse et al., 1999a). Figure 9 represents
176
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the nested Penning trap used, the ~ and e + locations, and the electrical signals that tell us the number o f ~ and e + in the trap. Figure 10 shows that e + are heated when ~ pass through them. This demonstration was made during the last week of LEAR's operation. B. DEMONSTRATION AND STUDY OF POSITRON COOLING OF ANTIPROTONS
The first e + cooling o f ~ was demonstrated by A T R A P at the AD (Gabrielse et al., 2001). Figure 12(a) shows the measured energy spectrum when no e + are in the center of a nested Penning trap. Figure 11 (b) shows a spectrum of
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that are cooled (i.e., shifted right in the figure) by e + in the center of the nested well. The uncooled ~ (left in Fig. 1 l(b)) do not pass through the e + plasma. The little central peak in this example are ~ that are going through the e +, with the right energy to form H. Undoubtedly H atoms were formed here. The ~ peak to the right in Fig. 11 (b) reveals p that are cooled below the energy that takes them through the e +, with a cooling time that is about ten times longer than the initial ~ cooling time. The process seems to be a lossless evaporative cooling. The ~ in the side wells of the nested Penning trap that acquire enough energy in p - p collisions will again pass through the e + and be cooled, rather than evaporating completely out of the trap. These ~ can be brought back into contact with the e + to make more H (Sect. IV.C). Because of the importance of e + cooling of ~ in the nested trap for H production we carried out a careful and detailed study of this process in 2002. Figures 12(b-e) shows examples of the ~ energy spectra after various
IV]
A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
179
cooling times. Figure 12 shows the average ~ energy as a function of e + cooling time, before the ~ cool into m a x i m u m contact with the e +. The subsequent lossless evaporative cooling of the ~ takes places on a much longer time scale. Details of A T R A P ' s progress in quantitatively understanding the e + cooling of ~ in a nested Penning trap was reported in a thesis (Bowden, 2003). Figure 13 shows ~ cooling as a function of their time in contact with the e +, and the calculated cooling using a theory developed to describe cooling in a nested Penning trap (Chang and Ordonez,
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180
G. Gabrielse
[IV
2000). The vertical sequences show quantitative agreement between theory and experiment, but only when we greatly increased a crucial cut off length from a value near the thermal cyclotron radius that was suggested in the theoretical treatment, to nearer to the Debye length, which seems to be a better choice given that axial energy is being transferred. A related theory paper has just been published (Chang and Ordonez, 2004). There are also several papers which focus on the interaction of a ~ plasma with a e + plasma (Ordonez, 1997; Ordonez et al., 2002). Very recently, ATHENA reported observations of the e + cooling process (Amoretti et al., 2004) that are similar to the examples shown in Figs. 11 and 12, except that the ~ cool faster with more e +, as expected.
C. A VARIATION: DRIVEN
e+
COOLING OF
ATRAP and ATHENA's first H observations (M. Amoretti et al., 2002; Gabrielse et at., 2002a), and all of ATHENA's subsequent H experiments, produced H using the simplest, one-time realization of e + cooling of ~. The were injected into a nested Penning trap that contained e +, and were cooled by the e + until all cooling and all H production stopped. Almost immediately, ATRAP moved to driven H production (Gabrielse et al., 2002b), in which ~ are driven through repeated cycles of e + cooling. This variation is an improvement for two reasons. (1) More H are produced for a given number of ~. (2) Antiprotons can be given no more energy than is required for them to barely move through the e + plasma, to form H atoms. The careful optimization needed to realize the second advantage is now being attempted. To drive the production of slow H (Gabrielse et al., 2002b), ~ in the right potential well are heated with a resonant radiofrequency drive until they pass through the e + in the inverted central well. Collisions of ~ and e + (which cool to 4.2 K via synchrotron radiation) cool the ~ until they settle into the left well of the nested trap. The resonant heating drive is then switched to heat the ~ out of the left well, so the e + in the center can cool them back into the right well. There is detectable ~ loss during the driving sequence (Fig. 14). Slow H atoms are produced during such repeated cycles of e + cooling of ~. The number of H produced during each drive cycle is linear in the number of ~ in the trap (Fig. 15(a)). A small ~ remnant is presumably unable to form H because of poor spatial overlap with the e + . The number of ~ in the trap, and hence the number of H detected, decreases
A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
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181
FIG. 14. Antiprotons lost while being driven from one side of the nested Penning trap to the other. From (Gabrielse et al., 2002b).
800
'i'
E 400 0
200
o
0
-o
i
~
(a)
600 c
|
l[
~ _,.jl~ "P~ .
0.4
0.0
tr
o
,~1~~--~---'- amplitude ~ halved ,I
I
0.8 1.2 1.6 antiprotons in nested well/105
.-0 9 800 ..o 600 ' ~ (1~). . . . . . . . E = 400 c 200
,~~
/
2.0
dris amplilude halvs . . . .
t
D
0
0
5
10 15 drive cycle
20
25
FIG. 15. The number of H atoms detected is linear in the number of ~ in the trap (a), even as it decreases as a function of drive cycle because of ~ losses (b).
exponentially with the number of drive cycles (Fig. 15(b)). The drive apparently heats the ~ so that some diffuse radially out of the trap, but this is not well-understood. The strong drive we typically used (Gabrielse et al., 2002b) is represented by filled squares in Fig. 15. Even stronger drives, likely to reduce the small remnant, were avoided for fear of producing H with higher velocities. A weaker drive, half the strength of the first, produces H less rapidly to start with, produces about twice as much detectable H integrated over all drive cycles, and leaves a larger ~ remnant (open squares in Fig. 15). Further reductions in drive strength decrease H production roughly in proportion to the drive amplitude, without changing the number of remnant ~ that remain out of contact. Slowly
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G. Gabrielse
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increasing the drive amplitude during each cycle could minimize the speed of the H produced, and more sophisticated variations of drive amplitude and frequency are being considered. D. ANTIPROTON LOSSES FROM A NESTED PENNING TRAP
One issue that prompted A T R A P to develop its background-free detection method (Sect. IV.E) was the observation of radial ~ losses from a nested Penning trap. These losses take place during the e + cooling of ~. In fact, they take place when the ~ have cooled to the energies which just take them through the e + plasma in the center of the nested Penning trap. At first it was tempting to identify them as H atoms that leave the trap upon forming, until we demonstrated that such ~ losses can take place with no e + in the nested Penning trap. This ~ loss unfortunately only takes place when the ~ have the energy close to that which takes them just over the potential hill from the empty e + trap. Typically if ~ are loaded into a nested Penning trap that contains no e +, then the ~ will not cool down to the energies which take them just over the potential hill that the empty e + well presents to them, with the result that no ~ losses will be observed. This is also true if the e + cooling would be turned off by heating the e + in a nested Penning trap to high temperature. At A T R A P we observed these losses in two ways. First, we waited for a much longer time that was required for e + cooling. Collisions between the ~ spread out their energies, with some of the ~ distribution being at energies where the ~ loss could take place. Second, we heated ~ in the side wells of the nested Penning trap to give them energies that took them over the central well for e + (Fig. 14). A T H E N A does not report such losses. Is this because their e + are stored much farther from trap walls? Or, is it because very highly excited H atoms are formed from rapidly moving ~ before the e + cool them to the lower energies at which some would be lost from the trap? Or, is there another explanation? E. Two TECHNIQUES TO COUNT H ATOMS As reported first in 2002, two different techniques are used to count the H atoms that are produced during e + cooling of ~ in a nested Penning trap. A T R A P uses field ionization detection (Gabrielse et al., 2002a,b) and A T H E N A uses correlated loss detection (Amoretti et al., 2002). After a brief summary of each detection technique, the two are compared.
IV]
A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
E.1. A T H E N A ' s
183
H annihilation detection
A T H E N A adopted the nested Penning trap and the e + cooling of method to produce H, but counted the atoms very differently than did A T R A P - detecting the correlated loss of ~ and e + from the nested trap (Amoretti et al., 2002). Upon forming, a neutral H is no longer confined and thus starts its drift to the electrodes of the nested Penning trap. When the H strikes a trap electrode, its ~ and its e + will annihilate at essentially the same time. A ~ and a e + annihilation taking place at the same place thus seems to be a unique signature of H annihilation. Real detectors do not have perfect space or time resolution, however. A T H E N A ' s H annihilation detection (Amoretti, 2004) thus counted any and e + annihilation that took place within 5 ~ts and + 8 m m of each other as an H atom. The resolution is very modest compared to a state-of-the-art particle detector; it is limited by the very small space available for a detector that needs be near a cold trap. Silicon strips are used to detect the pions from ~ annihilations, and CsI crystals are used to detect the back-to-back photons from e + annihilation. Unfortunately, false H events arise when a ~ annihilates, even when the is not bound in an H. Neutral pions are one product of ~ annihilation, and neutral pions decay into electron-positron pairs. In this way a ~ and a e + annihilation will occur within the time resolution of any detector. If the and a e + (from ~ annihilation) both annihilate within the spatial resolution of the detector as well, then the false event cannot be distinguished form a real H annihilation. Is a spatial resolution of • 8 m m sufficient to eliminate false H events from H that leak out of the trap at the same energies that H atoms are expected to form? Apparently the answer is yes. Only weeks after first duplicating e + cooling of ~ in a nested Penning trap, A T H E N A counted 131 "golden" H events on top of a large background (Amoretti et al., 2002). With some time to study the performance of the detector, they have very recently argued that many of the background events are also real H counts (Amoretti et al., 2004). E.2. A T R A P ' s dield ionization detection
A T R A P ' s field ionization detection is very different. Any H atom formed near the center of a nested Penning trap is free to move in the initial direction of its ~, unconfined by the nested Penning trap. H atoms passing through the ionization well (sometimes called a detection well) in a state that can be ionized by the electric field within, will leave their ~ trapped in this well. The ionization well (within electrode EET in Fig. 16(a)) is carefully constructed so that its electric field ensures that no ~ from the nested
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Fio. 16. (a) Electrodes for the nested Penning trap have an inner diameter of 1.2 cm. Inside is a representation of the magnitude of the electric field that strips H atoms. (b) The potential on axis for positron-cooling of antiprotons (solid) during which H formation takes place, with the (dashed) modification used to launch ~ into the well. (c) Antiprotons from H ionization are released from the ionization well during a 20 ms time window. (d) No background ~ are counted when no e + are in the nested Penning trap. From (Gabrielse et al., 2002a).
Penning trap can get into it (e.g., a ~ liberated from the nested well by ambipolar diffusion) except if it travels about 4 cm bound within an H atom. Any ~ heated out of the nested Penning trap escapes over the lower potential barrier in the other direction. Even if a ~ did acquire enough energy to go over the ionization well in one pass it would not be trapped because there is no mechanism to lower its energy while over this well. In addition, e + cooling lowers the energy of the ~ in the nested well, taking them further from the energy required to even pass over the ionization well. Only signals from H are detected with this field-ionization method (Gabrielse et al., 2 0 0 2 a ) - there is no background at all! Figure 16(c) shows ionized H captured in the ionization well during the course of the one initial experiment. In trials without e +, no ~ was detected in the ionization well (Fig. 16(d)). Antiprotons from H ionization are stored in the ionization well until after e + cooling is completed in the nested well, and all other ~ and e + are released in the direction away from the ionization well. We then eject the trapped ~ by ramping down the potential of the ionization well. The ejected ~ annihilate upon striking electrodes, generating pions and other charged particles that produce light pulses in the surrounding scintillators.
E.3. Comparing the detection techniques There are advantages and disadvantages to both the detection techniques. A T H E N A detects the correlated loss of ~ and e + from the nested Penning
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ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
185
trap. This technique has the advantage that H atoms with any internal state and any velocity should be detected, reduced by the efficiency of the detection process. The disadvantage is that it is thus difficult to learn about either the internal state of the H, or about the velocity of the H. The count rate for the golden events is quite low, and it seems likely that ~ detection will often be used in the future without e + detection. ATRAP's field ionization detection has the advantage of being background free, making it possible to detect very small signals if needed. Field ionization detection also makes it possible to go beyond counting H atoms (Sect. V), and the H internal state and the H center-of-mass velocity have already been probed. The disadvantage is that only excited atoms that can be field ionized are detected. We hope to use lasers to excite more deeply bound states up to excited states that can be detected by field ionization, but this remains to be demonstrated. As the time of H trapping (Sect. IX.A) approaches, the substantial metal supports for superconducting coils or permanent magnets needed near to the trap may make it impossible to spatially resolve the location of ~ and e + annihilations. The scattering of charged pions from ~ annihilation in this material, and the increased attenuation of the photons from e + annihilation, will make the marginal spatial resolution achieved so far to be much worse. ATRAP thus committed to developing alternate H detection techniques from the outset.
V. Beyond Counting H Atoms A . PROBING INTERNAL H ORBITS
The basic idea of the field ionization method used by ATRAP to probe the internal structure of H atoms is represented in Fig. 17. A small fraction of
FIG. 17. H atoms created in within a nested Penning trap must pass through an electric field region to reach and be counted in the detection well. Any H that is field ionized in this electric field region will not be detected in the detection well.
G. Gabrielse
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D
the H atoms produced in the nested Penning trap travel along the magnetic field direction to the right in Fig. 1 7 - passing first through an electric field Fz parallel to the magnetic field, and then into the detection trap volume. They are counted if they survive Fz without ionizing and are instead ionized by the stronger electric field in the detection trap. H ionized in the detection well leave their g in this well until we release them and count the ~ annihilations in surrounding scintillators- thereby detecting H with a detection efficiency of about 0.5 and no background. In Sect. V.C we discuss the example of a field ionization spectrum in Fig. 21. A recent theory paper (Vrinceanu et al., 2004) discusses field ionization in a strong magnetic field, and suggests the use of radial size as the best way to specify the state of a highly excited, highly magnetized H atom. The largest atoms detected are guiding center atoms (GCA) (Glinsky and O'Neil, 1991), and a circular GCA is represented in Fig. 18(a). Figure 18(b) shows how such atoms polarize and then field ionize as Fz increases. Figure 18(c) illustrates how the ionization potential depends upon the axial energy as well as the drift radius of the atom. Figure 19 shows that for various analytic and numerical models of GCA atoms, and also for atoms that are too tightly bound to be described in this way, that the electric field Fz at which the atoms ionize is a reliable indication of their radial size p. Atoms that survive an electric field Fz must have a radial size
a/e, /9 _< v/~V 4~so
(6)
with a - 0 . 5 a good rule of thumb (Vrinceanu et al., 2004) for the experimental circumstances. This is only a rule of thumb in that the axial binding decreases as the axial energy increases. A more detailed theoretical consideration of GCA atoms in electric fields is just being reported (Kuzmin and O'Neil, 2004b). It agrees with our H polarization and field ionization analysis for parallel electric and magnetic fields described above (Vrinceanu et al., 2004), and extends these results in two ways. First, an explicit form for the dependence of the ionization field upon axial energy is presented, a dependence illustrated in our Fig. 18(c). Second, the H polarization and the modifications of the H center-of-mass trajectory due to radial electric fields are both explored.
B. MEASURED FIELD IONIZATION SPECTRUM The number of H atoms formed increases in proportion to the number of e + that we use to form them (Fig. 20). Under ATRAP experimental conditions,
c
Y
actual orbit resulting from guiding center initial conditions / /
5
0.5
[
\ \
limit, axial energy = 0
.-c 0.4 axial energy = 0.3 meV (kT at 4.2 kelvin)
v)
W 'c
P = P3
I
a
0.2
0.0
1
guiding center orbit
I
(1OkT at 14:2kelvin) " ' " " ' " " ' " " ' " " ' " " ' ~ " " "
0
50
100
150
200
250
300
axial electric field Fz in V/cm
350
0.0
0.1
0.2
mean p(t) in pm
FIG.18. A circular guiding center atom (a) is polarized (b) and ionized (c) by an electric field F i s applied along B. Without an ionizing field, the GCA approximation breaks down at p" ~3 (d). Parts (a)-(c) are from (Vrinceanu et al., 2004). Part (d) is from (Gabrielse er al., 2004a).
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w
FIG. 19. The field at which an excited H ionizes establishes an upper limit upon its radial size. From (Vrinceanu et al., 2004).
FIG. 20. H Produced from 2.5 x l0 s ~ and detected in the normalization (a) and detection wells (b), the latter having survived a 360 V/cm field without ionizing. From (Gabrielse et al., 2004a).
the number of e + is roughly proportional to the thickness of the e + plasma along the magnetic field direction. From such measurements we construct the field ionization spectrum in Fig. 21. This spectrum shows that the number of H atoms that survive Fz decreases approximately as Fz -2 for atoms appropriately described as GCA (shaded region), indicating that the number of H that ionize at Fz goes as Fz-3. A simple argument, perhaps too simple, gives such a dependence. We might suppose that the initial three body capture varies a s p4 since two e +
v]
ATOMS MADE ENTIRELY OF A N T I M A T T E R . . .
189
FIG. 21. Number N of H that survive an ionization field F = Fz, for 2.5 x 105 ~ and 5 • 106e +, taken from measurements such as shown in Fig. 20. From (Gabrielse et al., 2004a).
are involved in the formation, and that a subsequent deexcitation collision (between the bound e + and another e + in the plasma) has a rate that goes as p2. This would suggest that the number of H that ionize at Fz goes a s p 6 Fz-3, as is observed. This argument, however, does not give a careful account of the velocity dependence of these rates, nor upon details of the formation and deexcitation process. For the largest Fz, however, just where the GCA should be breaking down (as we shall see in the following section), the number of H atoms seems like it may be larger than the power law trend. There is not yet any theoretical model which predicts either the power law trend nor any departure from it for more tightly bound atoms. It has been suggested (Driscoll, 2004) that our first field ionization spectrum (Gabrielse et al., 2002b) is well-described by a simulation of three body formation (Glinsky and O'Neil, 1991). This would be wonderful, but unfortunately does not seem to be so (Gabrielse et al., 2004)(and would be even less so for the much bigger range of Fz in Fig. 21). The simulation illustrates basic features of three body formation in a strong magnetic field very well, but was not intended to generate spectra that could be compared experimentally. Simulation results were thus simply not reported for a wide enough range of H binding energies. A more extensive simulation could possibly solve this problem and would also provide the opportunity to add in the important coupling between internal and center-of-mass motions (Vrinceanu et al., 2004; Kuzmin and O'Neil, 2004a), along with diffusiondrag collisions (Men'shikov and Fedichev, 1995; Fedichev, 1997; Bass and Dubin, 2004). There is more discussion of these processes in Sect. VI.
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C. BEYOND GUIDING CENTER ATOMS
The theoretical studies of the three body H formation and deexcitation have used a circular "guiding center atom" (GCA) model (Fig. 18(a)) (Glinsky and O'Neil, 1991; Men'shikov and Fedichev, 1995; Fedichev, 1997). Center-of-mass motion was allowed in a recent simulation (Robicheaux and Hanson, 2004) which still relies on the guiding center approximation. We now have the first indications of H atoms that are too tightly bound to be treated with the guiding center approximation (Gabrielse et al., 2004a). For a GCA, the e + "guiding center" drifts around the ~ with a drift velocity va - E x B / B 2 where the electric field is that of the ~, and B is the strong field of the trap. This yields a circular orbit with angular drift or magnetron frequency c o a - ( . O m - recZ/(cOcp3). Superimposed upon this drift motion is the much faster e + cyclotron motion at frequency oJc, a motion with its own adiabatic invariant. Also superimposed is an axial oscillation of the e + back and forth along the direction of the magnetic field due to the restoring Coulomb force from the f, with angular oscillation frequency COz - v/recZ/P 3 for small oscillation amplitude, and this motion too has its own adiabatic invariant. Larger GCA orbits are in fact not circular because the center-of-mass and internal orbits of the H are coupled (Vrinceanu et al., 2004; Kuzmin and O'Neil, 2004a) but we will not discuss these complications here. Wave functions, spectra, and decay rates for high Iml Rydberg atoms in a strong magnetic field have recently been calculated (Guest et al., 2003; Guest and Raithel, 2003). The regular cyclotron, axial and drift (i.e., magnetron) orbits are more akin to those of a particle in a Penning trap than to the familiar lower states of hydrogen, or even to the orbits of the Rydberg atoms that have been studied. The G C A model provides a useful and valid approximation when wa << COz<< COc,
(7)
a condition that is very familiar for a charge in a Penning trap (Brown and Gabrielse, 1986). Care must be taken in transforming this condition to a condition on atom size p because the frequencies vary so rapidly with p, and the circular G C A frequencies do not apply near GCA breakdown. We use the modest requirement that wa be at least three times smaller than COz,and that O~z be at least three times smaller than coc. The circular GCA frequencies should then be reasonable estimates, allowing us to obtain the requirement that the G C A is valid only if the drift radius p is greater than P3, P > P3 - [9recZ/wZc]l/3- 0.14 t.tm
(8)
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A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
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Here re is the classical electron radius and the specific value to the right is for A T R A P experimental conditions. Figure 18(d) shows that numerical calculations of internal H trajectories verify that G C A breaks down for atoms with size p smaller than this value. The slightly less stringent minimum p sometimes mentioned for GCA validity (Glinsky and O'Neil, 1991; Fedichev, 1997), which corresponds to all the circular G C A frequencies being equal, is the left vertical line in the Fig. 18(d). A T R A P detects atoms which are smaller than P3, and which are thus not appropriately described as GCA. The field ionization spectrum of Fig. 21 shows that some H atoms survive an analysis electric field F z - 360 V / c m the strongest analysis electric field we were able to produce in the current apparatus so far, given the need for stronger fields in the detection well. According to Eq. (6), such atoms have a radial size p < 0.1 ~m. We have thus entered the regime where a GCA description of such atoms is not valid. H atoms of smaller radii might well be detected if larger Fz could be used. H atoms beyond the reach of the GCA approximation are intriguing because for more tightly bound atoms it is generally assumed that the comparable strengths of the Coulomb and magnetic forces will result in chaotic trajectories (Kuzmin and O'Neil, 2004a). A technique must be found out to deexcite H atoms through the chaotic region to the more familiar, regular and manageable orbits and states that describe atoms of smaller size. Theoretical treatments of H formation and deexcitation which do not rely entirely upon the G C A are clearly needed.
D. FIRST MEASUREMENT OF THE SPEED OF SLOW H ATOMS
As discussed earlier one of the two major challenges currently facing H research is to devise ways to produce H that is slow enough to trap. The required first step is to measure H velocities. A T R A P recently measured the speed of some slow H atoms for the first time (Gabrielse et al., 2004b). The pre-ionizing, analysis electric field represented in Fig. 17 is varied sinusoidally in time, and the number of H surviving this field is measured as a function of the oscillation frequency of the sinusoidally varying field (Fig. 22). The number drops as the frequency increases because less and less atoms are moving rapidly enough to pass through the ionization region while the electric field is small enough to not ionize them. The expected decrease in the number of H that survive the oscillating field is shown by the solid curves in the figure for H atoms of several center-ofmass energies. For this first velocity measurement we measured the speed of the most weakly bound atoms in the distribution of Fig. 21. One could
192
IV
G. Gabrielse
1.2
.__>,
1.0
.
.
.
.
.
.
.
.
.
.
.
.
O.8
~ \
-~ 0 " 4 I ~
'=
100 meV ~
f\
V
OOmeV ] meV
o.ol, 0.0
..................
0.2 0.4 0.6 0.8 1.0 frequency of oscillating prestripping field in MHz m
FIG. 22. The fraction of detected H atoms decreases as the frequency w/(2n) of the oscillating electric field increases (solid points). More atoms are detected when there is no oscillating field (open square). This point is plotted on the same scale as the others but it has no frequency associated with it. The measured points are compared to a simple model discussed in the text; the solid curves apply when the oscillating electric field is applied, and the dashed curve when it is not. From (Gabrielse et al., 2004b). hope that these might have a velocity corresponding to the average thermal velocity they would have if they were at the temperature of the 4.2 K apparatus; instead their speed was a b o u t 30 times larger. W h e t h e r this is because we were simply driving the ~ too hard during the H production, or whether such a high velocity is characteristic of this m e t h o d of H formation, is not yet known. F o r a ~ traveling in the ~ direction through the e + plasma, one ~ speed that seems i m p o r t a n t is the one that equals the average axial speed of the e + that are moving in the same direction as the ~. F o r 4.2 K e + this corresponds to a ~ energy of 210 meV. This is close to what we measure, likely by coincidence given the approximate character of the estimate. One might expect increased H production at this ~ energy, but this depends in a complicated way u p o n how quickly the ~ are being cooled by the e +. A recombination rate that depends u p o n the relative velocity of the and e + will become insensitive to ~ energies below this value, since the relative velocity will be determined by the e + velocity. A n o t h e r i m p o r t a n t speed is -
(9)
v]
A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
193
This ~ speed would allow just enough time in the L,~ 1 m m thick e + plasma for there to be a deexcitation collision (Glinsky and O'Neil, 1991) between the e + initially picked up by the ~ and another e + in the plasma on average. The expected e + - e + collision rate should be of the order of ne(:rcbZ)ve where n e - 1 . 6 x 107/cm 3 is the e + density and ve is the average thermal speed for a e + at T~--4.2 K. The distance of closest approach b comes from equating the potential energy (4rCeo)-leZ/b and the thermal energy k T~. The corresponding ~ energy, and hence the H energy, is around 400 m e V - larger than what we observe. The cross section used is only an estimate, of course, and the e + may be some what heated by the ~. Notice that Vp~neLTe -3/2 suggesting that a e + plasma with a lower density, a shorter length and a higher temperature will produce H with lower velocities. With both of these speeds being of the same order, and being closer to what we measure, it seems that most highly excited states are being formed about as rapidly as can be imagined, leaving no time for further cooling. By driving the ~ so that they have just enough energy to go through the e + plasma, it should be possible to make lower energy H atoms. In addition, it may be advantageous to keep the e + in a deep potential well so that weakly bound H will strip, giving the ~ further time to cool and to form more deeply bound states. For related reasons, it may also be advantageous to use an e + plasma that is very short along the direction of the magnetic field. A T H E N A measured the rate of H production as a function of elevated e + temperatures T during e + cooling of ~ in a nested Penning trap (Amoretti et al., 2004). This measurement was interpreted as a test of the H production mechanism assuming that H was formed with ~ and e + in thermal equilibrium, with three-body H formation expected to have a T -9/2 dependence, and radiative H formation a T -1/2 dependence. The H production rate varied slowly with e + temperature, and production was observed even with room temperature e + , with a rate too fast to be radiative recombination. However, Eq. (9) suggests a non-equilibrium interpretation. The speed Vp corresponds to a ~ energy of about 1 keV, for T - - 1 5 K, L - - 3 . 2 cm and n e - 1.7 x 108/cm 3. (For higher temperatures Vp is lower.) Since this energy is larger than that of the ~ injected into the nested Penning trap, the highly excited H could form with velocities much higher than that of the e +. The unusual observed temperature dependence then arises because three-body formation (Eq. (1)) is so rapid that the assumed thermal equilibrium does not apply. With this interpretation very high speed H atoms indeed were produced by A T H E N A .
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A very recent simulation supports this interpretation (Robicheaux and Hanson, 2004; Robicheaux, 2004) for the simplest application of e + cooling of ~ used in ATRAP and ATHENA's first H observations, and in all subsequent ATHENA experiments. The variation subsequently used by ATRAP, discussed in Sect. IV.C. and in (Gabrielse et al., 2002b), cannot be easily simulated. In this method a radio frequency drive is used to gently excite the ~ into contact with the e +. The speed of the p, and hence the H that form, is thus determined by the strength and frequency of the drive. As mentioned above, our method of driving the e + cooling of ~ should produce much slower H atoms once this drive frequency and amplitude are carefully adjusted. For atoms that are moving much slower than those we have observed so far, more care will be needed to extract the H velocity from the oscillating field measurements described above. The H travels through a large electric field gradient as it enters the detection trap, and the force on the highly polarizable H* (Vrinceanu et al., 2004; Kuzmin and O'Neil, 2004c) modifies the H trajectory. We showed that the force was too small to substantially modify the motion of the 200 meV H atoms we observed (Gabrielse et al., 2004b) (using the polarizability that we had calculated for circular GCA atoms (Vrinceanu et al., 2004) to calculate H center-of-mass motion) but warned that this would not be so for atoms that move a lot more slowly. A more recent calculation (Kuzmin and O'Neil, 2004b) shows that slow H atoms that are created off the center axis of our trap, when polarized by radial electric fields, can even follow radially diverging trajectories that could keep them from reaching our detection well and being counted.
E. DEEXCITATION OF HIGHLY EXCITED STATES Three body H formation produces large numbers of guiding center H atoms. Ground state H atoms are desired. The deexcitation of highly excite H atoms is crucial, and several different methods have been mentioned. (1) Collisional deexcitation of the H within an e + plasma is discussed in Sect. V.C. (2) The lifetimes of excited H states are typically very long. They are shorter for more tightly bound states. A state with principal quantum number n < 15 will rapidly deexcite to the ground state via radiation. Collisions with e + in the plasma will change the angular momenta so the states will more quickly radiate. Radiative decays of Rydberg states have recently been considered (Flannery and Vrinceanu, 2003; Guest et al., 2003).
ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
VI]
195
(3)
Laser stimulated deexcitation is challenging because three body formation produces states with binding energies spread over a very wide range compared to the energy spread of typical laser photons, and because the spatial overlap of the highly excited states and the desired lower states seems to be very small. A first theoretical look at this is in a very recent simulation (Robicheaux and Hanson, 2004). (4) The use of sequences of half-cycle laser pulses has recently been considered (Hu and Collins, 2004). (5) Given the similarity of GCA states and circular Rydberg states, it may be possible to use adiabatic fast passage to deexcite atoms.
VI. Three Body H Formation, and Related Experiments There was much excitement and some concern when we realized many years ago (Gabrielse et al., 1988) that the likely H formation mechanism for very cold plasmas of e + and ~ was the three body process -p + e + + e +
> H * + e +.
(10)
The excitement was because simple arguments suggested that the rate for this process would vary as T -9/2. This would make an enormous rate if this scaling was valid at 4 K. I often said that this process would be either the high rate H signal (if we found a way to use it to produce useful H) or the noise we would need to avoid (if we preferred another formation process) since no other H formation process could come within orders of magnitude of competing with this rate. One concern arose because using this formation mechanism at low temperatures had never been considered before. The matter counterpart of this process had been studied, but only for the much higher temperatures of interest for astrophysical applications (Bates et al., 1962; Makin and Keck, 1963; Stevefelt et al., 1975). The second major concern was about the role of the magnetic and electric fields in the nested Penning trap (Gabrielse et al., 1988) that we had proposed as a way of realizing H formation. How would they modify the H production rate? It seemed that magnetic field might not change the density of states and the rate too much, but a proper calculation was needed. The third concern was that the matter counterpart of this process had been studied for infinitely extended plasmas and infinite time scales, while we could only manage rather small plasmas in a trap interacting for not such long time scales. How quickly would H formed in highly excited states be deexcited to the ground states that we needed for our H trapping and spectroscopy?
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Several theoretical groups took up these challenges. First, a quantum calculation suggested that the scaling was indeed valid all the way down to 4 K if no magnetic field was present (Zygelman and Dalgarno, 1989). An extended version of this work was reported much later (Zygelman, 2003). The magnetic field challenge was then taken on (Glinsky and O'Neil, 1991). The guiding center atom (discussed in Sect. V.C) was introduced as a method of dealing with highly excited states in a strong magnetic field. The encouraging conclusion was the T -9/2 scaling would hold down to 4 K even in a strong magnetic field. Moreover, the strong field would only decrease the rate by a factor of ten for the same temperature compared to what was calculated for no magnetic field. Replacement collisions were essential in maintaining the high rate. A free e + would be captured on a field line closer to the ~, than the e + that had been bound to the ~ on a field line farther away. However, the simulations suggested that that deexcitation to a low state might be a problem with finite interaction times and volume for the and e + . Interrupted three body formation and deexcitation would yield highly excited GCA. The simulation illustrates quite well general features of three body H formation in a strong magnetic field, but is not able to yet predict the distribution of excited states that can be measured. In Sect. V.C we discuss a suggestion that our ATRAP field ionization spectrum (Gabrielse et al., 2002b) could be accounted for by comparing our data to the tails of the numerical simulations (Glinsky and O'Neil, 1991). While we wish that this claim was true, Sect. V.C also reviews why we think that such comparisons are still premature (Gabrielse et al., 2004). A later analytic treatment did not include replacement collisions and thus reached a more pessimistic conclusion about the H formation rate (Men'shikov and Fedichev, 1995). However this work did include the H deexcitation caused by many gentle, long range collisions of the H and e + in the cold plasma - diffusion drag collisions - that were not included in (Glinsky and O'Neil, 1991). One of the authors then treated three body formation and deexcitation using both the replacement collisions which would initially dexcite H atoms, and the diffusion-drag collisions which then would take over for smaller H radii (Fedichev, 1997). According to this work, deexcitation would proceed very rapidly in the diffusion-drag regime. This apparently was too good to be true. A recent treatment suggests that an adiabatic invariant will prevent the diffusion-drag deexcitation process from carrying the deexcitation to much smaller radii than did the replacement collisions (Bass and Dubin, 2004). The GCA (Glinsky and O'Neil, 1991) remains an important starting point for any discussion of three body formation in a strong magnetic
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ATOMS MADE ENTIRELY OF A N T I M A T T E R . . .
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field, since it is such highly excited states that are readily formed in the experiments. This model can be extended to include the unavoidable coupling between the internal motion of an excited H and the center-ofmass motion of the H (Vrinceanu et al., 2004; Kuzmin and O'Neil, 2004a) caused by the magnetic field. A conserved pseudo momentum makes it possible to make an effective potential for the internal motion of a e + orbit within an H atom in which the coupling to center-of-mass motion takes the form of a small harmonic offset potential for the e +. For states that are more deeply bound this coupling and offset is less important. The polarization and ionization of highly excited H has been discussed (Vrinceanu et al., 2004), and very recently the motion of GCA in electric and magnetic fields has been considered (Kuzmin and O'Neil, 2004b). A very recent simulation of three body of H formation (Robicheaux and Hanson, 2004) still makes use of the guiding center approximation but does include the coupling between the center-of-mass motion and the internal motion of the H. The recombination rate for a 5.4 Tesla field is 60% larger than for B--+ ec in the earlier simulation (Glinsky and O'Neil, 1991) - whether this is because of a different magnetic field or because of the center-of-mass coupling is not clear. An extension of this calculation (Robicheaux, 2004) attempts the daunting challenge of more realistically modeling the environment of a nested Penning trap. Qualitatively consistent with the observations and discussion in (Gabrielse et al., 2004b) and in Sect. V.D, the simulation shows H form before the ~ have completely cooled, and also suggests that a shorter e + plasma produces slower H atoms. Limited statistics prevent making quantitative comparisons with measured field ionization spectrum (e.g., Fig. 21 discussed in Sect. V.A) especially for the most deeply bound states, but this may become possible. An important message of Sect. V.C is that more extensive simulations over a wider range of H binding energies are required if there is to be a meaningful comparison of theory and experiment. These should include replacement collisions and diffusion-drag collisions. They should also include the unavoidable coupling of the center-of-mass and the internal orbits of the H. Finally, the methods used must work not only for circular GCA states, but also for more tightly bound states which cannot be described as GCA, and whose orbits are expected to be chaotic. Three body formation of other Rydberg atoms has been observed and is being studied for ion-electron plasmas produced by laser ionization just above threshold (Kilian et al., 1999, 2001; Roberts et al., 2004; Simien et al., 2004). A major difference is the absence of the strong magnetic field.
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VII. Production Method II: Laser-Controlled H Production We are quite excited about our ATRAP demonstration of a new method to produce slow antihydrogen, in which lasers control the H formation (Speck et al., 2004; Storry et al., 2004). H formation via the collisions of ground state Ps and trapped ~ was proposed long ago (Humberston et al., 1987), and the counterpart process in which a proton is substituted for a ~ has been used to produce hydrogen (Merrison et al., 1997). However, the observed rate was slow and fewer than protons are available, so no attempt has been made to form H by this method. The cross section and H formation rate from collisions of highly excited Rydberg Ps* with ~ are enormously larger. The use of laser-excited Ps was thus proposed (Charlton, 1990) but never realized. We recently demonstrated (Speck et al., 2004) the alternative of producing Ps* by laser controlled charge exchange (Hessels et al., 1998). These Ps* then collide with trapped ~ to form H* (Storry et al., 2004). The three steps of this process were listed in the Introduction and Overview, in Eqs. (2-4), and Fig. 23 gives a schematic overview of how these steps are realized. Three coaxial Penning traps (yellow regions) are arranged so that they are as close together as possible. In preparation for lasercontrolled H production, 4.2 K e + are located in the first of these (left). Cold ~ are located in the adjacent trap (center). The detection trap (right) is initially empty. Two lasers excite a Cs beam so that Cs* travel perpendicular to the axis of the traps and through the trapped e + to produce highly excited Ps* via a resonant charge change collision. Some of the Ps* travel through the trapped ~ and are able to produce H* via a second resonant charge exchange collision. A small fraction of the H* enters the detection trap and is ionized by the electric field within it. The H* deposits its ~ in the detection trap for later counting. Figure 24 shows evidence that in this demonstration about 16 H were ionized in the detection well. However, if the H production is isotropic then these events signal the production of about 200 H atoms. The H formed would naturally seem to have the low temperature of the trapped ~, though this has yet to be demonstrated. This proof-of-principle experiment was carried out at the end of the 2003 ~ run at the CERN AD, with only several hours of trials. More H production is expected as the method is refined and optimized. The strong 5.3 T magnetic field is an essential part of the three traps, but it also complicates this experiment and its theoretical interpretation. First, exciting the Cs atoms from the 6P3/2 state to the Rydberg state requires
VII]
ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
199
FIG. 23. Basic scheme for laser-controlled production of cold antihydrogen. From (Storry et al., 2004). ,
in" -o
.
,
,
(a) two-fiber detection
10
0
0
,
ionized H
(average background rate is 2.2 / 40 ms)
o
.
signal
"ID
|
0 8000
,
(b)
"0 0 0
.
,
i .
.
.
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/ ~
z ..... detecti~ well depth
9 4000
.
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.
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.
.
.
,
.
.
.
.
I ~ /ca,ibrated V ~-~h,~n
200
signal ne I
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antiproton calibration 0
10
20
30
40
-~
-200
time (ms) FIG. 24. (a) H detected (peak) as the potential well containing the ionized H is ramped down. (b) ~ annihilation signal as the axial well depth is reduced through zero. From (Storry et al., 2004).
empirically varying an electric field to tune the atoms into resonance with the fixed frequency copper vapor laser since the states have not been calculated. Second, internal orbits of both the Cs* and H* atoms formed are significantly modified by B since the magnetic force is comparable to the
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Coulomb force. Third, the binding energies of Rydberg atoms moving across a strong magnetic field are not even conserved, but are instead coupled to the center of mass energy of the atoms (Vrinceanu et al., 2004; Kuzmin and O'Neil, 2004a). A calculation of this double charge exchange process which neglects the magnetic field (Hessels et al., 1998) gives a guide about what to expect, but a formation calculation that includes the crucial role of the magnetic field is needed.
VIII. Comparing the H Production Methods B
Which of the two demonstrated H production methods is more useful in producing extremely cold, ground state H that can be trapped for precise spectroscopic comparisons with hydrogen and for gravitational studies? It seems to early to tell. Laser-controlled charge exchange has the advantages of naturally producing both colder atoms and a much narrower, laser-selected distribution of excited states. However, a method to deexcite them to the ground state has yet to be demonstrated. H produced during e + cooling of ~ in a nested Penning trap produces atoms more easily and at a much higher rate, and it may be possible to collisionally deexcite them. However, now that the velocity of these H* can be measured (Gabrielse et al., 2004b), it remains to be seen if ATRAP,s method for driving H production (Gabrielse et al., 2002b) or some variant can produce very cold atoms as hoped. Other production methods, like using a CO2 laser to stimulate H formation in a trap (Gabrielse et al., 1988; Wolf, 1993), have yet to be experimented with. The best method for producing useful H is not yet clear.
IX. Future A. ANTIHYDROGEN TRAPPING
A.1. Can ground state antihydrogen and its ingredients be trapped together? A long term goal of slow antihydrogen experiments, quoted in the Introduction and Overview, is to trap ground state H atoms for precise spectroscopy experiments (Gabrielse, 1987). When these goals were laid out long ago the first atoms had only recently been trapped (Migdall et al., 1985), and a proposal to trap spin polarized hydrogen atoms was just appearing (Hess, 1986). It is very encouraging that hydrogen atoms were
IX]
ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
201
subsequently trapped (Hess et al., 1987; Roijen et al., 1988), laser cooled (Setija et al., 1993) and used for precise hydrogen spectroscopy (Cesar et al., 1996). The simplest way to load H into such a trap would be if the cold H atoms would be created directly within the trap, and thus be trapped as soon as they are created. A great concern is that the e + and ~ might be lost from their respective traps before H forms, for traps which break the axial symmetry of a Penning trap, as is the case if a Ioffe trap field is added to a Penning trap. The stability of charges in a Penning trap is closely related to axial symmetry; the resulting conservation of angular momentum gives rise to a confinement theorem (O'Neil, 1980). Neither a charged particle nor a dense single-component plasma, can spread perpendicularly to the magnetic field enough to leave a Penning or Malmberg trap. Breaking the axial symmetry voids the confinement theorem. An experimental realization of a Penning-Ioffe trap configuration (Fig. 25(a)) could direct the magnetic field of a solenoid (not pictured) along the axis of the stacked rings of an open-access Penning trap (Gabrielse et al., 1989c). The Ioffe field would come from currents through vertical Ioffe bars and through "pinch coils" above and below, or magnetic materials arranged to give the same field configuration. For simplicity of our analysis, we assume that the "pinch coils" are away from the central region where charged particles would be trapped. The addition of the radial magnetic quadrupole field of a Ioffe trap to the field Bog for the Penning trap, B -
B o [ ~ + (xic - y i O / R ] ,
(11)
FIG. 25. (a) Open access Penning trap electrodes, with vertical current bars and pinch coils of a Ioffe trap. Orbits for a charged particle in a Penning trap (b) without and (c) with a radial Ioffe field. From (Squires et al., 2001).
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then destroys the axial symmetry about ~, and introduces a distance scale, R. Axial symmetry, present for large R, is destroyed as R is reduced (e.g., by increasing the Ioffe current). Superconducting coils could produce a Ioffe gradient, C1 = Bo/R, as large as 40 T/m, even for a bias field B0 = 2 T, whereupon R = 5 cm. The well depth energy (written in terms of an effective temperature depth T) for a Bohr magneton ~t~ within a trap of radial size p is
A trap with the parameters mentioned above, at a radius p = 2 cm, would have a well depth that corresponds to 0.1 K. To investigate the breakdown of stable confinement (after trying in vain to interest real theorists in solving this problem for a number of years) we examined the motion of a charge in a Penning trap with a radial Ioffe magnetic field using a guiding-center approximation (Lehnert, 1964), a perturbation expansion using the method of multiple time scales (Bender and Orszag, 1978), and exact numerical calculations. At roughly the same time, experiments and analysis were underway for such a field superimposed upon a Malmberg trap (Gilson and Fajans, 1999). We found stable orbits and largely separated motions that are associated with adiabatic invariants (Squires et al., 2001). Figure 25(b) shows the familiar orbit of a charge in a Penning trap, and Fig. 25(c) shows how this orbit changes when the radial field of a Ioffe trap is added. The basic orbit can be understood as motion along a force-free sheet that also conserves energy, Fig. 26. Resonant instabilities arise when the period of the modified
FIG. 26. (a) The force-free sheet and an equipotential of the electrostatic quadrupole. (b) Projections of stable magnetron orbits upon the xy plane lie within a square. From (Squires et al., 2001).
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A T O M S M A D E E N T I R E L Y OF A N T I M A T T E R . . .
203
magnetron motion (sometimes called E x B drift motion) is an integer multiple of the axial oscillation period. However, we concluded that these resonances can be avoided at least for low particle densities. The stable motion of a single charge in a Penning-Ioffe trap made us cautiously optimistic that this configuration might work as long as the density of charges was low enough. Collisions are notoriously effective in breaking adiabatic invariants, and adiabatic invariants are crucial for the stable orbits that we observed. It thus seemed clear that there would be stability problems above some density. What density might this be? We do not know. The natural density to use seems to be the number of charged particles in a volume that is the cube of the Debye screening length for a charge in the plasma, n;k3. Here the number density of the particles is n, and the Debye screening length for a charge e in a single component plasma at temperature T is
/eokT ~.D - V ffje2
(13)
in SI units. For typical A T R A P parameters n = 1.6 x 107/cm 3 and T = 4.2 K, there are only 0.25 charged particles per Debye volume. Unfortunately, we do not know at what natural density the low density analysis will break down in this regime in which n)~3 < 1. Our proposal and analysis (Squires et al., 2001) provoked a rather direct response two years later based on extrapolating an experiment done in a Malmberg-Penning trap to A T R A P Penning-Ioffe conditions, in which case it is said to "contradict" our conclusion (Gilson and Fajans, 2003). What is an issue is the applicability of our one-particle analysis (which is not disputed) to the case of more than one trapped particle. Below what particle density can the resonances (that both groups had carefully considered) be avoided? Is density alone the relevant indicator of where the single particle analysis can no longer be applied to, and if so at what density? The experiment that showed significant radial transport of charged particles was done in a Malmberg-Ioffe trap using much smaller fields and gradients than we had in mind, and much hotter plasmas. Typical conditions B0 =0.021 T and C1 =0.0002 T/m, for example, correspond to an extremely large R = 100 m. The particle density n = 107/cm 3 is almost the same as at ATRAP, but the temperature T - 1 2 0 0 0 K - - 1 eV is 3000 times higher than A T R A P ' s cryogenic temperature. To extrapolate to the A T R A P high field and low temperature conditions seems like quite a stretch, for three reasons. First, the natural density for the first experiment is n)~D = 4.6 x 104. This is more than five orders of magnitude larger than what was considered above, and goes between the
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cases n)~3 >> 1 and n~ 3 < 1. Second, the trap field and gradient require that R also be extrapolated by a large factor, of about 2000, indicating much stronger axial symmetry breaking under ATRAP experimental conditions. Third, the very long plasma column in the Malmberg trap seems likely to have broader resonances, and a somewhat different charged particle transport, compared to the smaller and more spherical e + plasmas in a Penning trap that ATRAP utilizes. At ATRAP we are encouraged by recently observing that trapped electrons survive a radial Ioffe gradient for h o u r s - much longer than needed to accumulate ~ and form H. The radial field of a Ioffe trap, from a permanent magnet apparatus constructed by our Jfilich collaborators, was added to the ATRAP Penning trap. For a bias field B - 3 T, the magnets were able to maintain C 1 - 16 T/m, which corresponds to R - 19 cm. This R is larger than what we eventually hope to achieve, but still very much smaller than for the low field experiment discussed earlier. Such investigations are still underway, with much remaining to be studied.
A.2. Proposed trapping alternatives Several suggestions have been made for trap geometries (for charge particles and neutral atoms) that are axially symmetric, or have less asymmetry than the Penning-Ioffe configuration. Three axially symmetric suggestions (Dubin, 2001) seem very challenging experimentally. Higher order magnetic traps would reduce the size of the magnetic gradient over most of the trapping volume (Fajans and Schmidt, 2004), but would confine atoms in a larger volume than can likely be illuminated by spectroscopy lasers. A magnetic cusp trap has also been proposed (Mohri and Yamazaki, 2003).
A.3. Trapping excited antihydrogen states? The H trapping discussed here is for an H atom in its ground state. We are intrigued by the possibility that the highly polarizable GCA states created in large numbers during e + cooling of ~ could be trapped in electric field gradients (Gabrielse et al., 2002a) for the time needed to deexcite them to the desired low excitation states. Perhaps this could be done using the electrostatic quadrupole of a Penning trap. What is needed is enough trapping time for deexciting the H down to states with principal quantum numbers n ~ 15 which then deexcite rapidly to the ground state by radiation. The polarization of GCA states and the resulting fields required for confinement have been discussed (Vrinceanu et al., 2004). However, these elements have not yet been put together to make a workable solution for free H atoms.
IX]
ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
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More recent theory provides more information about the polarizability and motion of a GCA in electric and magnetic fields (Kuzmin and O'Neil, 2004b), and explores the possibility of two and three dimensional trapping of polarizable H GCA within the electric field produced by a dense e + plasma.
B. WILL COLLISIONS WITH MATTER ATOMS COOL OR ANNIHILATE H ATOMS? B.1. Cooling H via collisions with hydrogen atoms? Is it possible to cool H atoms by simply introducing hydrogen atoms into the vacuum system that contains them? There is no answer to this question for the highly excited states that have been produced and identified so f a r though the larger size of these atoms will make larger cross sections. However, a lot of recent theoretical work has focussed upon collisions of ground state H and H atoms since this was first discussed many years ago (Shlyapnikov et al., 1993). The elastic scattering channel that provides the cooling (Froelich et al., 2000; Jonsell et al., 2001) must be compared to several inelastic channels by which H atoms are lost. Rearrangement 9H + H Direct 9H + H
> p~ + e ~ e
> p~ § e + + e- § annihilationproducts
Lepton 9H § H
> p + ~ + photons
RadiativeAssociation 9H § H
> HH + hv
(14) (15) (16) (17)
The losses come from a rearrangement channel in Eq. (14) and a direct annihilation channel in Eq. (15) (Froelich et al., 2000; Jonsell et al., 2000, 2001; Armour and Chamberlain, 2002; Armour et al., 2004). Interestingly, when H and H collide, the annihilation of the e + and the electron in Eq. (16) takes place at a much smaller rate (Froelich, 2002; Froelich et al., 2004a). The radiative association process is notable for the unusual quasi-bound H H states that may be produced (Zygelman et al., 2001; Froelich et al., 2004b) rather than for making a substantial contribution to the inelastic cross section. Early estimates of cross sections had led to the conclusion that cooling to 0.1 K might be possible with a loss of 90% of the atoms (Froelich et al., 2000; Jonsell et al., 2001; Dalgarno et al., 2001). Improved calculations that include the rearrangement channel (but not the direct annihilation channel) lead to the conclusion that cooling to only 0.43 K results in 90% atom loss
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(Armour and Chamberlain, 2002; Zygelman et al., 2004; Voronin and Carbonell, 2004). Putting the latest rearrangement (Zygelman et al., 2004) and direct annihilation (Jonsell et al., 2004b) cross sections together now seems likely to push this critical temperature to 1 K or above (Jonsell, 2004), though there are still uncertainties in the rearrangement cross section to be addressed (Zygelman et al., 2004). A strong interaction potential is being used to calculate ~ annihilation in the elastic channel (Armour, 2004a). The possibility to use H atoms to cool H depends in a critical way upon the temperature dependent ratio of elastic and inelastic cross sections. A superconducting Ioffe trap will likely be not deeper than 0.5 K when a strong bias field is present, so cooling without annihilation to well below this temperature is required if such collisional cooling is to be practical. There are now plans to calculate ~ annihilation in the elastic channel of collisions of H with hydrogen molecules (Armour, 2004b). B.2. Cooling H via collisions with he atoms?
Can collisions with He gas be used to cool ground state H atoms? (Collisions with highly excited H* should also be considered.) Different nuclear charges produces interesting differences between H collisions with helium and hydrogen (Armour and Chamberlain, 2001). Born-Oppenheimer potentials for the H-He system are available (Strasburger and Chojnacki, 2002), and a large effort is currently underway to calculate the cross sections for all of the various channels (Jonsell et al., 2004a; Armour, 2004a). A calculation of the elastic scattering (Sinha and Ghosh, 2003) neglects the strong interaction which, however, seems to substantially modify the elastic scattering (Jonsell et al., 2004a). The production of He-~ and ot-~ is being investigated (Todd et al., 2004) Unfortunately, the annihilation rate in the elastic channel already seems to be much higher for H collisions with He compared to collisions with hydrogen atoms, making it unlikely that He will be useful for cooling H atoms. B.3. Collisions, annihilation and vacuum
The observed ~ lifetime was used many years ago to estimate that the background pressure in the cryogenic system in which store ~ was better than 5 x 10-17 Torr (Gabrielse et al., 1990)- about a million times smaller pressure than can be measured with good commercial gauges. The most likely contaminants gas in a cryogenic system is helium, with hydrogen and probably hydrogen molecules of some interest as well. The collision calculations reviewed above, when finished and taken together, should make it possible to use the observed lifetime of trapped H
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ATOMS M A D E E N T I R E L Y OF A N T I M A T T E R . . .
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as a measure of the pressure of background pressures of helium and other gasses. What is needed, for example, is an H lifetime as a function of the H energy and the helium density, for helium gas in thermal equilibrium at temperatures ranging from 0.1 to 4.2 to 15 K. The same could be done for H - H . Ideally these graphs would be contrasted to those for ~-He and ~-H, for ~ at rest. The cryopumping of helium to surfaces can be folded in separately as appropriate for particular vacuum systems.
C. CONTINUOUS LYMAN ALPHA SOURCE Extremely accurate measurements of frequency of the l s-2s transition in antihydrogen should provide the most accurate possible comparison of the simplest atoms of antimatter and matter. Spectroscopy of the H l s-2p might be an interesting place to begin with, and two-photon spectroscopy with the first of the photons being closer to the l s-2p transition frequency would follow naturally. All of these spectroscopy examples require a source of Lyman alpha photons at 121.5 n m - for either the spectroscopy itself or for cooling of the atoms that is required to get a high precision. For this purpose, the A T R A P collaborators from Garching have built and demonstrated the first continuous source of Lyman alpha radiation (Eikema et al., 1999), at 121.5 nm. A representation of the 4-wave mixing apparatus is in Fig. 27. This source was then used to observe l s-2p transitions with a linewidth that was very close to the natural linewidth for these transitions (Eikema et al., 2001), as illustrated in Fig. 28. Up to 20 nW of power was reported (enough for spectroscopy and some laser cooling),
FIG. 27. Apparatus used to generate the first continuous coherent Lyman alpha radiation by sum-frequency mixing in mercury vapor. From (Eikema et al., 2001).
208
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700 Fls = 1 --~ F2p = 1,2 600
500 d ==
400
119 MHz Fls = 0 ,,.,1~ F2p = 1
9
300
200 t 9
9
9
9_ #
mm
_
9
9
_
9
100 ""
o
i
o'oo
i
o'oo
i
ooo
,
ooo
Relative energy near 121.56 nm [MHz] FIG. 28. Hydrogen ls-2p resonances lines observed using the continuous Lyman alpha radiation source. From (Eikema et al., 2001).
with a beam quality that allows the photons to pass through a 0.5 mm pinhole.
X. Conclusions In an exciting three years, slow antihydrogen has been produced by two different production methods. In method I, H is produced during positron cooling of antiprotons in a nested Penning trap. In method II, lasers control the H production for the first time. The experiments all use the techniques our TRAP collaboration developed to accumulate cold antiprotons, at an energy that is 10 l~ times lower than ~ circulating in any storage ring. The H experiments are all being carried out at a storage ring that was specially constructed to make these experiments possible.
x]
ATOMS MADE ENTIRELY OF A N T I M A T T E R . . .
209
Most of the slow antihydrogen has been produced during positron cooling of antiproton in a nested Penning trap. Our TRAP and ATRAP collaborations developed this device and technique for this purpose over many years - first with electrons and protons, and then with positrons and antiprotons. For their first observations of slow antihydrogen, both ATRAP and ATHENA used the most straight forward, one-time positron cooling of antiprotons in a nested trap. To count the atoms, ATRAP used field ionization detection, and ATHENA used H annihilation detection. ATRAP then moved to a variation on the positron cooling production method by driving the antihydrogen production so that there are many cycles of positron cooling in the nested Penning trap. The first advantage of this variation is that more antihydrogen is produced. The second advantage is that it should be possible to give the ~ the minimum energy needed to contact the positrons if the drive amplitude and frequency are optimized, which has not yet been done. ATRAP's field ionization method shows that it is highly excited antihydrogen atoms that are being made in large numbers. The field ionization method also makes it possible to go beyond H counting to make progress on two crucial challenges now facing slow antihydrogen research. The first crucial challenge is to deexcite the highly excited atoms that are being produced in large numbers down to the ground state. The field ionization technique provides the only way to detect which states are produced, information that is needed if the production parameters are to be optimized for the production of the most deeply bound states. The second crucial challenge is to produce H atoms with a velocity that is low enough that such particles could be trapped for precise spectroscopy experiments. A variation of ATRAP's field ionization detection, with an oscillating analysis electric field, makes it possible to measure an H velocity for the first time. An H velocity substantially above the average thermal velocity for a 4 K ambient temperature was observed in the first demonstration. However, there is hope that optimizing the driven H production during positron cooling in a nested Penning trap will result in lower velocities. ATRAP has recently demonstrated a second, entirely different method to produce cold a n t i h y d r o g e n - the first laser-controlled H production mechanism. Laser frequencies determine the H binding energy. This method seems to naturally produce H atoms with the energy distribution of the from which they form. It seems possible with techniques demonstrated with electrons to make this energy very low. An interesting possibility is to capturing cold H atoms as they are produced, within a neutral particle trap. There is currently some controversy about whether the e + and ~ can remain trapped at the same time, when the
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m
fields of a Ioffe trap are added to confine H atoms. It is thus encouraging that trapped electrons seems to survive such a field for substantial times, but much yet be studied here. A great deal remains to be done before accurate spectroscopic comparisons of antihydrogen and hydrogen can begin. However, the regular production of slow antihydrogen atoms is a big step forward - even though none of these atoms has yet been shown to be useful for precise spectroscopy in a trap. A great deal has been accomplished- enough to give hope for continued progress at a similar rate.
XI. Acknowledgments It has been and remains an honor and pleasure to lead the A T R A P collaboration, as it was the T R A P collaboration from which it grew. The A T R A P team (table I) is very dedicated and skilled, as is needed for such demanding experiments. Special thanks to A T R A P members for their comments on this r e v i e w - especially to A. Speck, C. Storry, E.A. Hessels, W. Oelert and J. Walz. Thanks for helpful discussions and comments to E.A.G. Armour, J. Fajans, P. Froelich, S. Jonsell, T. O'Neil, and B. Zygelman. I am grateful to CERN, its PS Division and the AD team for building the Antiproton D e c e l e r a t o r - the only facility in the world that is capable of delivering 5.3 MeV antiprotons to us. We profited from the help and personal encouragement of the AD staff, the SPSC, the research directors and the directors general. This work was supported by the N S F and A F O S R of the US, the BMBF, M P G and FZ-J of Germany, and the NSERC, CRC, CFI and OIT of Canada. Finally I am grateful to the Harvard University and its physics department for their good natured way of accommodating to a department chair who made weekly trips to C E R N to do antihydrogen research, and to the wonderful staff, assistant, research group and family that made it all possible.
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Storry, C.H., Speck, A., Le Sage, D., Guise, N., Gabrielse, G., Grzonka, D., Oelert, W., Schepers, G., Sefzick, T., Walz, J., Pittner, H., Herrmann, M., H~insch, T.W., Comeau, D., Hessels, E.A. (2004). First laser-controlled antihdyrogen production. Phys. Rev. Lett. 93, 263401. Strasburger, K., and Chojnacki, H. (2002). Helium-antihydrogen interaction: The BornOppenheimer potential energy curve. Phys. Rev. Lett. 88, 163201. Surko, C.M., Greaves, R.G., and Charlton, M. (1997). Stored positrons for antihydrogen production. Hyperfine Interact. 109, 181-188. Thompson, J.K., Rainville, S., and Pritchard, D.E. (2004). Cyclotron frequency shifts arising from polarization forces. Nature 430, 58-61. Tinkle, M.D., Greaves, R.G., and Surko, C.M. (1996). Modes of spheroidal ion plasmas at the Brillouin limit. Phys. Plas. 3, 749-758. Todd et al., A., 2004. To be published. VanDyck, R.S.Jr., Schwinberg, P.B., and Dehmelt, H.G. (1987). New high-precision comparison of electron and positron g-factors. Phys. Rev. Lett. 59, 26-29. Verd~, J., Beier, T., Djeki6, S., H~iffner, H., Kluge, H.-J., Quint, W., Valenzuela, T., Vogel, M., and Werth, G. (2003). The magnetic moment anomaly of the electron bound in hydrogenlike oxygen 1607+. J. Phys. B 36, 655-663. Voronin, A.Y., and Carbonell, J. (2004). Hydrogen-antyhydrogen atomic interaction at subkelvin temperatures. Nuc. Inst. Meth. B 214, 139-143. Vrinceanu, D., Granger, B.E., Parrott, R., Sadeghpour, H.R., Cederbaum, L., Mody, A., Tan, J., and Gabrielse, G. (2004). Strongly magnetized antihydrogen and its field ionization. Phys. Rev. Lett. 92, 133402. Walz, J., and H~insch, T. (2004). A proposal to measure antimatter gravity using ultracold antihydrogen atoms. General Relativity and Gravitation 36, 561-570. Weimer, C.S., Bollinger, J.J., Moore, F.L., and Wineland, D.J. (1994). Electrostatic modes as a diagnostic in Penning-trap experiments. Phys. Rev. A 49, 3842-3853. Wesdorp, C., Robicheaux, F., and Noordam, L.D. (2000). Field-induced electron-ion recombination: A novel route towards neutral (anti-)matter. Phys. Rev. Lett. 84, 3799-3802. Wineland, D.J., Weimer, C.S., and Bollinger, J.J. (1993). Laser-cooled positron source. Hyperfine Interact. 76, 115-125. Wolf, A. (1993). Laser-stimulated formation and stabilization of antihydrogen atoms. Hyperfine Interact. 76, 189-201. Yamazaki, T. et al. (2004). To be published. Zimmerman, C., and H~insch, T. (1993). Laser spectroscopy of hydrogen and antihydrogen. Hyperfine Interact. 76, 47-57. Zygelman, B. Recombination of antiprotons with positrons at low temperatures. J. Phys. B 36, L31-L37. Zygelman, B., Dalgarno, A., 1989. (private communication). Zygelman, B., Saenz, A., Froelich, P., and Jonsell, S. (2004). Cold collisions of atomic hydrogen with antihydrogen atoms: An optical potential approach. Phys. Rev. A 69, 042715. Zygelman, B., Saenz, A., Froelich, P., Jonsell, S., and Dalgarno, A. (2001). Radiative association of atomic hydrogen with antihydrogen at subkelvin temperatures. Phys. Rev. A 63, 052722.
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ADVANCES IN ATOMIC, MOLECULAR, AND OPTICAL PHYSICS, VOL. 50
ULTRA FA S T EXCITA TIO N, I O N I Z A TI O N, A N D F R A G M E N T A T I O N OF Co0 I . V . H E R T E L 1'2 T. L A A R M A N N
1 a n d C.P. S C H U L Z
1
1Max-Born-Institut, Max-Born-Str. 2a, D-12489 Berlin, Germany," 2also at Free University of Berlin, Dept. of Physics, Berlin, Germany I. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. I n t r o d u c t i o n to Energetics, Kinetics, and Properties of C60 in a Nutshell . . B. A Simple M o d e l Potential for C60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Atoms, Molecules, and Clusters in Intense Laser Fields . . . . . . . . . . . . . . D. Experimental Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. Ionization, Charge States, and F r a g m e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . A. Mass Spectra and F r a g m e n t a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Intensity Dependence and Power Laws . . . . . . . . . . . . . . . . . . . . . . . . . . IV. A b o v e Threshold Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. Multielectron Excitation, Energy Redistribution, and Coupling to Nuclear Motion .................................................... A. P o p u l a t i o n of C60 R y d b e r g S t a t e s - Beyond the Single Active Electron Picture B. Ultrafast F r a g m e n t a t i o n of C60 - Beyond a Purely Statistical Description VI. Conclusion and O u t l o o k . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
219 223 223 232 233 236 240 240 250 255 260 262 273 277 279 279
I. Introduction Ever since their discovery by Kroto, Smalley, Curl, and collaborators (1985) fullerenes in general and the Buckminster fullerene C60 in particular have drawn great attention from a broad, interdisciplinary scientific community. C60 was first identified as a special molecule by mass spectra obtained from what may be described as a laser driven reactor of hot carbon atoms (giving indeed the initial clue as to the unique structure of the Bucky ball). We show in Fig. 1 (left) a sample of these mass spectra adopted from the Nobel lecture of Kroto (2003) because it already shows the key fingerprints of the formation and fragmentation patterns of C60 which will 219 1049-250X
Copyright 9 2005 Elsevier Inc. All rights reserved DOI: 10.1016/S1049-250X(04)50005-8
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I.V. H e r t e l et al. data 100 TRANSIAC 2001 1000 of 1000 shots IOF DATA 80
7000 6000 5000 4000 3000 2000 1000 0 15 20 25 30 35 40 45 50 55 60 65 9-4-1985
Time (Microseconds)
xl0 70
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3
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8O
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18:56:4.7
0
,
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2O
,
I
,
I
,
I
,
I
40 50 80 100 Cluster Size (Atoms)
,
120
FIG. 1. Historic mass spectra. Left: First mass spectrum with clearly recognized C+0 ions (Kroto, 2003) which lead to the discovery of the fullerenes by Kroto et al. (1985). The characteristic bimodal structure is again seen very clearly. Right: Mass spectrum from laser vaporized carbon as observed by the Exxon group (Rohlfing et al., 1984), showing the typical bimodal distribution of carbon cluster ions C + characteristic for fullerene formation and fragmentation: small carbon clusters with odd and even n up to about n = 28 and a long distribution of even numbered clusters starting near 40 and extending up to over 100. The paper does not mention the enhancement of mass 720 due to C60.
be one major subject of the present progress report. It is an interesting historical a n n o t a t i o n - as mentioned in the Nobel lecture of Smalley (2003) - that the crucial features were already detected in some earlier work (Rohlfing et al., 1984) as reproduced in Fig. 1 (right), but were apparently not noted or appreciated for their far reaching consequences. These mass spectra show very clearly a bimodal distribution of larger fullerenes C2, separated by C2 units ranging down to 2n > 36 and a series of small carbon clusters C, below n < 28. We will see in the present paper that these patterns are characteristic for the fragmentation of very hot C60 after interaction of C60 with charged particles or photons provided enough time is available during the interaction process to allow for redistribution of the deposited energy over the many degrees of freedom of C60. As we shall see, these patterns may change dramatically if the interaction time is sufficiently short. The isolation of pure C60 by Kr/itschmer et al. (1990) provided the basis not only for a whole new area of material science and technology but also for a host of fundamental, experimental, and theoretical research studies focusing on an understanding of the energetics and dynamics of C60 after energy deposition and charge exchange (or removal). Most of the investigation to date have been performed in the condensed phase and their relevance for new materials and processes is obvious. On the other hand, gas phase experiments offer a direct approach to study isolated, well-defined
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finite systems with many degrees of freedom and have concentrated on the mechanisms of energy deposition, redistribution and relaxation, as well as on the subsequently ensuing dynamics of ionization and fragmentation. Note that C60 has 174 degrees of freedom for the nuclear motion and 240 valence electrons (60 essentially equivalent, delocalized re- and 180 structure defining, localized a-electrons), yet its symmetry and the applicability of some simplifying models justify the hope that the observed phenomena may eventually be understood in a quantitative manner. A wide range of processes has been studied which have led to a detailed understanding of the mechanisms and dynamics involved in the energy deposition, relaxation, ionization, fragmentation, and finally cooling of C60 and other fullerenes. We mention just a few early and some recent examples out of a wealth of experimental and theoretical studies, ranging from thermal heating (Kolodney et al., 1995), single-photon (Hertel et al., 1992; Yoo et al., 1992; Reink6ster et al., 2004) or multi-photon absorption (O'Brien et al., 1988), electron impact (Foltin et al., 1998), collisions with neutral particles (Takayama, 1992), atomic ions, including highly charged ions (Walch et a/.,1994; Martin et al., 1998; Schlath61ter et al., 1999; Reink6ster et al., 2003; Jensen et al., 2004; Brauning et al., 2004) as well as molecular ions (Campbell et al., 1993; Vandenbosch et al., 1998), cluster-ions (Farizon et al., 1997) to surface collisions (Busmann et al., 1993; Yeretzian et al., 1993; Bekkerman et al., 2004). With its large number of degrees of freedom C60 is very resilient and can accommodate a substantial amount of energy before it disintegrates. Hence, different cooling mechanisms following the initial, fast dynamics have also achieved a lot of attention and essentially three types of processes have been identified: the evaporation of electrons (thermionic emission), the release of neutral or charged particles, in particular the evaporation of C2 and radiative cooling (Campbell et al., 1992; L6pine and Bordas, 2004; Rohmund et al., 2001; Anderson et al., 1996; Hansen and Campbell, 1996). For details the reader is referred to recent reviews, for example, by Campbell and Levine (2000), Campbell and Rohmund (2000) and Lifshitz (2001). In most of these studies information on the mechanisms and dynamics involved is gleaned from either the mass spectra, showing charge and mass distribution of the products, from electrons emitted or from the changes in energy, direction or charge state of the interaction partners (ions, electrons) i.e., a long time (nanoseconds (ns) or microseconds (gs)) after the primary processes have occurred. However, with the rapid development of ultrafast spectroscopy and the enhanced availability of flexible short pulse laser systems over the past years it has become an obvious challenge to follow these dynamical processes directly while they occur in the system. Moreover, with present day high intensity short pulse laser systems it has become -
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possible to create electromagnetic fields which substantially modify the physics we are used to when describing single or ("weak field") multiphoton experiments. The field strengths available with today's high intensity laser systems may exceed those of the internal atomic and molecular fields (~1016W/cm 2) by orders of magnitudes (Ditmire et al., 2004, and references therein). The interaction of intense field laser pulses ( > 1014 W/era 2) with large molecules and clusters leads to highly charged clusters, Coulomb explosion and fast particle emission (see, e.g., K611er et al., 1999; Card et al., 2002; D6ppner et al., 2003). The latter is discussed and studied even in the context of nuclear fusion, both experimentally (Ditmire et al., 1999) and theoretically (Last and Jortner, 2002; Krainov and Smirnov, 2002, 2003). At somewhat more moderate but still high intensities, the dynamics is still dominated by the field, which may deposit a large number of photons into the system and the atomic or molecular system itself is substantially modified. The ensuing nonadiabatic multielectron dynamics (NMED) and the possibility to control molecular reactions in strong fields is of high current interest (see, e.g., Lezius et al., 2002; Levis and Rabitz, 2002; Stolow, 2003; Itakura et al., 2003; Wang et al., 2003; Markevitch et al., 2004, and references therein). It is this intensity region (lO 15 W/cm 2 > I > 1011 W/cm 2) which we will address in the present progress report. We will concentrate on the dynamics of C60 interacting with short laser pulses as a proven, experimentally well accessible and fruitful testing ground for the dynamics of complex and yet well defined systems. In that sense we view C6o as a prototype large finite system and an interesting intermediate between a molecule with an extended electronic ~ system and a semiconductor surface. In the past years very informative and challenging experimental and theoretical work has emerged and we aim at a comprehensive progress report on the interaction of short pulse lasers with C60 at intermediate intensities. This chapter is structured as follows: in Sect. II a few notions, facts, and findings on C60 and the fullerenes are introduced. However, we do not attempt to review these wide fields of ongoing research. We then familiarize the reader with some important basic terminology and concepts from the area of atoms and molecules in strong fields. Finally, some experimental aspects of studying molecules in intense, short pulse laser fields will need to be addressed. In Sect. III we discuss the ionization process, charge states, and fragmentation after short pulse laser interaction with C60 as observed by mass spectroscopy. We address the intensity dependence of these processes in some detail and dwell on a comparison of saturation intensities for the ionization processes in comparison with what has been established in the past for simple atomic systems. In Sect. IV the so-called above threshold ionization (ATI) which has been observed experimentally in photoelectron
II]
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spectra at various short pulse laser intensities are discussed and compared with the recent theoretical results. Theoretical comparison already leads us to a critical discussion of the primary excitation mechanism in an intense laser pulse. The single active electron (SAE) picture which is generally used to describe atoms interacting with low intensity light pulses is, generally speaking, no longer adequate when describing a system with many active electrons interacting with an intense laser pulse. It turns out that many electrons are active (MAE) and may be excited during one laser pulse. This leads us to a description very similar to the band structure model in condensed matter, i.e., for a semiconductor in the case of C60. Sect. V.A illustrates this with a particularly interesting example: the non-resonant excitation of Rydberg states in C6o. Finally, in Sect. V.B, we address the fast fragmentation processes of C60 beyond the well established statistical fragmentation processes known to occur on the ns to gs time scale. The report ends (Sect. VI) with a brief conclusion and outlook.
II. Preliminaries A. INTRODUCTION TO ENERGETICS, KINETICS, AND PROPERTIES OF C60 IN A NUTSHELL
The cleanest methods of studying the electronic properties of C60 are certainly based on single photon absorption: a known amount of energy hv is deposited and the resulting processes can be directly attributed to transitions between molecular states. Unfortunately, the optical vis-uv absorption spectra of C60 are rather blurred as illustrated in Fig. 2 and show only broad bands owing to the many internal degrees of freedom. As can be seen, the absorption bands are somewhat broader in the gas phase than in liquid solution but otherwise essentially identical. C60 has the shape of a truncated icosahedron and is characterized by the point group Ih. The level designations given below refer to elements of that symmetry group - small letters referring to single electron orbitals, capital letters define electronic states. The level diagram displayed in Fig. 2 refers to single electron levels and has been adopted from Wilk et al. (1995) and Zhang et al. (2003). For this system with its 60 rc and 180 ~ valence electrons this level scheme may be seen as an equivalent to a band structure in the condensed phase and has to be distinguished from the energies of the (multielectron) molecular states to which the designations in the spectra refer (indicated are the final states in transitions from the lAg ground state). Owing to the lack of high resolution vis-uv spectroscopic information, the electronically excited states of C60 are
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absorbance
,~ne~:~ : : ~ -t " q I / I 6"--i
81T'u _ / 61Tlu ( " ' i " ..
I
~
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~
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(
.......................CCC96
!/
'
levels~ :.! ~ : : hu+gg
0
,, (LUMO)tlu
-i/
i/
(HOMO) hu (HOMO-l) gg+hg
FIG. 2. Optical absorption spectrum of C60 and single electron energy level diagram. The absorption spectra and designations of transitions from the lAg ground state (full multielectron picture) are adopted from Bauernschmitt et al. (1998) ( solution in hexane) and Coheur et al. (1996) ( . . . . . gas phase). The level designations and ordering have been adopted from Wilk et al. (1995) and Zhang et al. (2003), their energetic positions have been adjusted to the absorption spectra. The Rydberg levels from Boyle et al. (2001) are drawn roughly to scale. The ionization potential is adopted from De Vries et al. (1992). Note that in the single electron picture the first optically allowed line arises from the HOMO to LUMO + 1 transition and is very weak, while the next strong absorption maximum is from the HOMO-1 to LUMO transition as indicated by dotted arrows. The association of the optically observed transitions between states with certain orbitals is justified by recent calculations from Xie et al. (2004).
still r a t h e r v a g u e l y k n o w n . In a d d i t i o n to the singlet u states i n d i c a t e d in the optical spectra one expects, for e x a m p l e , singlet g states as well as triplet states o f the molecule, w h i c h are n o t accessible to optical transitions. T h e lowest lying triplet states at 1.6 a n d 1.7eV ( H a u f l e r e t al., 1991) p l a y an i m p o r t a n t role in the d e s c r i p t i o n o f statistical decay processes o f the molecule, such as t h e r m i o n i c emission ( H 6 d e n e t al., 2003; D e n g e t al., 2003).
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In contrast to the optical spectra, rich structure is observed in Raman and IR spectra which allows to assign the vibrational modes of C60 with high accuracy (Dresselhaus et al., 1996). For the present subject it suffices to mention the two fully symmetric vibrational modes, the ag(1) radial breathing mode at 497 cm-1 (corresponding to an oscillation period of 67 fs) and the ag(2) pentagonal pinch mode at 1470 cm -1 (22 fs), and the hg(1) prolate-oblate mode with 273 cm -1 (122 fs) - as all other modes with much higher frequencies cannot be observed directly in the time domain with present day fs-laser systems. One important aspect to bear in mind while studying C60 is the high internal energy content Ev~-b~174 x k B T due to its 174 degrees of freedom in nuclear motion. To study the isolated C60 molecule it has to be brought into the gas phase, i.e., the material must be evaporated and at a typical oven temperature of 770 K we have already E ~ 4.5 eV in the system (Rohmund et al., 1996). Even when cooled by liquid nitrogen to 80 K we are still left with about 0.5 eV. It will be a subject for discussion whether, when and how this internal energy can be exploited in an electronic excitation process and will influence the dynamics of the system. For the time being, it may suffice to remark that for statistical reasons it is extremely unlikely to channel all this energy into, say, one particular chemical bond, and initiate, e.g., C2 evaporation. It is now well established (Lifshitz, 2000) that the binding or evaporation energy for C2 emission from neutral C60 is Ea > 9.5 eV and for emission from the C~-0 is ion E a - 1 0 4-0.2 eV (Matt et al., 2001). This is an exceptionally large dissociation energy and it is a unique property of C60 that its C2 binding energy is larger than the ionization potential EI < Ea. The cleanest determination of the ionization threshold can be achieved by single photon ionization, but much work has also been done with electron impact. Well established are the values for C60 ~ C~-g which is E l ( C 6 0 ) - 7.58 eV (De Vries et al., 1992), for double ionization C60 ~ C~-0 with 19.00 eV, i.e., EI(C~-0) - 11.42eV (Steger et al., 1992), and triple ionization requires (35.64- 1) eV, i.e., E/(C~-+) - 16.6eV (Scheier et al., 1994). As an example, Fig. 3 shows the photo-ion yield from threshold to 36 eV from early synchrotron work of Hertel et al. (1992) (see also Yoo et al., 1992). Two remarkable observations warrant discussion: (1) The broad feature with a maximum from 16 to 24 eV was recognized as a giant plasmon excitation with contributions from many electrons. The main aspects of this feature can be understood by a charged sphere model, as Bertsch et al. (1991) point out. Their tight binding calculations, local density approximation, LDA, (Alasia et al., 1994) and time dependent LDA (Yabana and Bertsch, 1996) show reasonably
226
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I.V. H e r t e l et al. 1.0 0.8 0.6
40
0.4 0.2
- 35
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"c~
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~._=
10
s
O- , 0
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, 8
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, 24
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photon energy / eV FIG. 3. Photoion yield in single photon ionization of C60 as measured at BESSY I by Hertel et al. (1992). Note the steep rise of the signal at threshold and the giant plasmon resonance with
a broad maximum at 16-24 eV.
good agreement with the observed features, considering that in this experiment the ion yield is due to autoionization and can only arise above the ionization threshold. LDA predicts this mode to carry an oscillator strength of ~ 160 (!). Alasia et al. (1994) find that the optical/ UV part of the dipole response of C60 is dominated by particle hole transitions among ~ orbitals, however, the agreement with the spectrum shown in Fig. 2 is less favorable than for the Mie resonance at 20 eV (Fig. 3) arising not only from ~-~ transitions but also, and to a large extent, from particle-hole excitations connecting a with rc and ~ orbitals, as well as final states with a higher number of nodes. The width of the Mie resonance is explained due to the decay of the plasmon into single-particle configurations. In the context of these calculations Bertsch et al. (1991) estimated for the polarizability of C60 a value of ot ~ 37/~k3. Alasia et al. (1994) obtained c~= 8 8 . 8 , 3 , while more recent calculations by Norman et al. (1997) give o r - 85.8 ~3. Only very recently a value of ot = 79 4-4 /~3 was reported from a sophisticated experiment (Ballard et al., 2000). We will refer to the latter in later discussions. Considering C60 as a conducting sphere this value would correspond to a radius R - 4.29 * which roughly corresponds to the outer diameter of the Buckminster fullerene cage. (2) The ion signal rises relatively steep directly at the ionization threshold (7.58 eV). No long tail below is observed, no hot bands are seen. We take
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F~G. 4. Schematic of photoionization (left) and a hypothetic resonant excitation of Rydberg states (right) in a one photon process. The Franck-Condon factors in C60 are such that a strict propensity rule Av=0 holds in either case. this as a strong indication that the ionic potential is very similar to that of the neutral ground state and F r a n c k - C o n d o n factors strongly favor transitions with A v = 0 for all vibrational modes. Schematically this is illustrated in Fig. 4: each vibrational level which is populated in the neutral ground state will also be populated in the ionic ground state. No shift of the ionization potential due to the energy content in the neutral ground state will be observed. We discuss this aspect here in detail since it is relevant while discussing the excitation of Rydberg states in Sect. V.A. Much work has been devoted to the energetics and kinetics of ionization and fragmentation in C60. Pertinent results from these efforts will be discussed later in this report as they are related to the investigations with fs-laser pulses. Here we just communicate some key results which may help us to understand observations seen in the mass spectra with short pulse multiphoton experiments in Sect. III. A typical example from electron impact ionization and fragmentation is shown in Fig. 5 as derived from Matt et al. (1996) and Foltin et al. (1998). As clearly seen in Fig. 5, C~-0 is observed for impact energies Eet from threshold with an approximately linear rise of the ion yield up to a broad maximum at about 50-100 eV which falls off smoothly for higher impact + energies. In contrast fragments C60_2m are only observed above an appearance potential EA = EI + m Ea + E~hift
(1)
far above the energetic threshold, with a so-called kinetic shift (Esmft). While the energetic threshold for C~-s would be at about 17 eV, a significant ion
228
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.-.-. . . . . . . . . . . . ~. . . . . . . . . . . :: . . . . . . . . . . . . * . . . . . . . . . . . ~. . . . . . . . . . . . . ~. . . . . . . . . . . . . ~ . . . . . . . . . . . . ~ . . . . . . . . . .
20
30
40
50
!
60
FIG. 5. Cross sections for electron impact ionization (C~-0) followed by fragmentation (C~-8) over a wide range of electron energies adapted from Foltin et al. (1998) and (C~-8) yield on an expanded scale near threshold from Matt et al. (1996) (lower panel). The insert in the latter shows also a two step process (full line) and was only recorded when increasing the electron current by a factor of 10.
yield is only observed for Eez > 47 eV as shown in Fig. 5, lower panel. The C~-8 signal then rises rather steeply and after reaching a maximum at about 60 eV falls off again much more rapidly than the parent ion (see Fig. 5 top right panel). For larger fragments a similar behavior is observed, the onset of the signals just being shifted by an addition of 10 eV for each ejected C2 unit. To understand this shift we note that these fragmentation processes do not occur as direct dissociation but rather as a kind of afterthought of the molecule to the initial process of energy deposition by the impact. A large amount of excess energy is distributed in this process over all degrees of freedom of the molecule which acquires thus an effective temperature T > 3000 K. One finds that even up to 4000 K the system still remains partially intact for a long time. The process observed may schematically be written as C60 + e -
C~-0###
C+s##
> C~-0### + 2 e -
(2a)
> C+8## + C2
(2b)
> C~-6#+ C2
etc.
(2c)
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where # stands for internal excitation. (Several # are meant to indicate that for each additional evaporation an additional initial energy of > 10 eV is required). The sequential evaporation of C2 units (Eqs. 2b, 2c) occurs long after the electron impact process is over and time scales of ns, las or even ms may be involved, resulting finally in mass spectra very much like those seen in Fig. 1. This unusual stability of C60 is again a result of the many internal degrees of freedom. Quite sophisticated R R K M calculation belongs today to the worktools for describing these fragmentation mechanisms as, for example, reviewed by Scheier et al. (1996), Campbell and Levine (2000), and Lifshitz (2001). Probably the most reliable and extended sets of ionisation potentials and dissociation energies for singly and multiply charged fullerenes have been calculated by Diaz-Tendero et al. (2003 and 2005). Of some special interest in our present context is the feature shown in the insert of the lower panel in Fig. 5. There, following a controversy in the literature, Matt et al. (1996) studied the threshold behavior of the fragments at different currents of the electron gun. At high electron current, 2-step collisions may occur where a second electron hits a molecule which has already been ionized or excited in a first collision. Obviously in that case, the appearance energy is dramatically shifted downwards, a fragment signal is seen just above threshold and the yield peaks at ca. 35 eV. Matt et al. (1996) suggest that the following steps may be responsible"
C60 -~-eC~-0# + e-
> C~-0# + 2e-
(3a)
> Cf8 --1--C2 + e-
(3b)
In this context we draw attention to the more recent studies on electronimpact induced fragmentation of ions by Hathiramani et al. (2000) shown in Fig. 6. In contrast to electron impact on neutral C60 the fragmentation occurs here without an additional ionization step (essentially following Eq. 3b). Here, the fragment yield rises directly from threshold without an extra kinetic shift. The strong resonance peaking at about 30 eV for all charge states studied resembles very much the giant plasmon resonance observed in the C~-0 photo ion yield from neutral C60 as shown in Fig. 3. As Hathiramani et al. (2000) point out, this suggests that the electron impact induced fragmentation process in the ions at low energies is predominantly caused by a plasmon excitation. The fragment ion yield from neutral C60 (Fig. 5) shows a similar peak, shifted however to about 60 eV and decreasing more rapidly and to a lower level with electron energy. The peak width in Fig. 6 is also much larger than in the photon ionization experiment (Fig. 3). To understand this, one has to bear in mind that in contrast to the
230
I.V. H e r t e l et al.
[II
FIG. 6. Absolute cross sections a for the electron-impact induced C2 fragmentation of C~from Hathiramani et al. (2000). Circles, q = 1; squares, q--2; triangles, q = 3. The solid lines are fits through the respective data points at energies higher than 120 eV.
investigations where neutral fullerenes were used as a target, the internal energy of the C q+ 6o ions will contain at least the energy of one plasmon from the ionization in the ECR ion source used in these studies. Hence, they will decay upon excitation of only one additional plasmon. It still remains surprising that fragmentation of these hot C q+ 6o ions begins without kinetic shift at threshold. For later discussion we just keep in mind that hot C q+ 6o ions readily fragment when some additional energy is deposited. Very recently Reink6ster et al. (2004) reported ion yields from single photon ionization experiment of C60 as a function or photon energy hv covering a wide energy range from hv - 26 eV to 130 eV by using synchrotron radiation. A survey of the mass spectra is displayed in Fig. 7 showing C q+ 60 ions with q up to 3 and their respective fragments C q+ 60-2m" Again, fragments are only observed at photon energies hv >_ EA far above their energetic thresholds, i.e., with high kinetic shifts Esh~ft, which are even systematically 3-7eV larger than those observed for electron impact ionization and fragmentation by Scheier et al. (1994). This may be due to the fact that in photoionization a larger part of energy is shared by the electron emitted from the C60. For later comparison with fs-laser induced mass spectra (Sect. III) we draw particular attention to the fact that doubly charged fragments are significantly more abundant than singly charged
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FIG. 7. Mass spectrum from C60 after ionization with a single photon of 26-130 eV energy adopted from Reink6ster et al. (2004). The density of points indicates the ion yield at the q+ different parent and fragment masses C60_2 m. For clarity the appearance energies for C~-s and C+6 are indicated by dashed arrows, illustrating a kinetic shift of about 30 eV to their respective energetic thresholds. f r a g m e n t s - and even triply charged fragments are clearly visible. We also note that the singly charged fragments decrease substantially as the photon energy increases while the doubly charged ones remain more or less constant. It appears suggestive to connect these findings with the ease of fragments formed from e + C q+ 6o collisions just discussed. It may well be that one of the electrons emitted in the process hv + C6o
, C2~- + 2e
(4)
contributes by some kind of an internal post-collisional or better postionization effect to the fragmentation. Now, while in single photon ionization the energy of the ejected electron rises with photon energy and the cross section for fragmentation decreases (see Fig. 6) in double photoionization there is a strong probability that one of the ejected electrons carries only a low energy (Lafon et al., 2001) and hence can efficiently excite the plasmon resonance which in turn leads to fragmentation. Reink6ster et al. (2004) have also discussed the mechanism for the formation of doubly and triply charged ions, invoking shake p r o c e s s e s which may or may not be pertinent to the generation of multiply charged ions created by fs-laser pulse interaction (Sect. III). In this process the electron "sees" the suddenly changed potential of the ionic core due to the ionization and has to adapt to this change via excitation or ionization
232
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L V. Hertel et al.
of another electron, the so-called shake up or shake off. The probability of this process is proportional to the overlap between the electron orbital in the undisturbed atom and higher lying orbitals including the continuum of the singly charged ion, which are contracted relative to the neutral atom. This describes the situation in the sudden limit and Reink6ster et al. (2004) can explain the shape of the multiply charged ion yields as a function of energy sufficiently well in the framework of a simple model developed by Thomas (1984) using essentially one parameter.
B.
A SIMPLE MODEL
POTENTIAL FOR C6o
In the previous subsection, we have already mentioned a few theoretical approaches to a quantitative understanding of the electronic structure of C60. The spectroscopy and dynamics of the molecule is determined by its 240 valence electrons for which a rigorous theoretical treatment is perhaps just possible with state-of-the-art quantum chemical methods (including TDLDA) and present computers but require a substantial effort. For a number of purposes it is, however, very useful to employ a simple model potential derived from considering the system in a first approximation as charged hollow, polarizable sphere with a radius of R = 8.1 l a0 = 4.29 A (as derived from the polarizability). Based on such a jellium type of approach a number of theoretical studies have been reported in the literature. Puska and Nieminen (1993), for example, used such a model potential to derive an estimate for the ionization potential and the plasmon resonance and based on this potential with slight modifications, Frank and Rost (1997) and Rfidel et al. (2002) were able to describe very precisely a complex oscillatory structure in the photoionization cross section of C60. These oscillations which were first reported by Xu et al. (1996) arise from interferences of electrons originating from different parts of the C+0 ion cage and may be considered a very rigorous test to any model potential. In its present, improved form also used for calculating energies of C60 Rydberg states to be discussed in Sect. V.A this one-electron potential reads i _2e-6.691r-6.691
Vo(r)
=
l
1
1r-6.691
if r < 5 13
-1.5 1+e Ir-6.691-1.558 0.006
if 5.13 < r < 5.15
0.012(6.69- r) 4 - 1.50
if 5.15 < r _< 8.23
-1.5 Ir-6.691-1.558 1-t-e 0.006
if 8.23 < r m < 8.25
_2e-6.691r-6.691
1
1r-6.691
if 8.25 < r
(5)
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FIG. 8. 3-dimensional view of the model potential for C~-0 according to Eq. (5).
converging to 1/r for large electron distances from the cage and reproduces the ionization potential of C60 in a single active electron (SAE) picture. It can also be used as a basis for a multiactive electron (MAE) description by using it as a starting point for a jellium model of all active electrons. This approach has for example, been used by Bauer et al. (2001) (see also Bauer, 2002) with a slightly simpler but similar expression. A 3D representation of this potential is illustrated in Fig. 8.
C. ATOMS, MOLECULES, AND CLUSTERS IN INTENSE LASER FIELDS
Some concepts and notions to establish the theme of discussion in the next sections are communicated here in a nutshell. Our first concern is to define what is meant by a "strong" laser field. We will discuss this in a pragmatic manner and see that this notion depends very much on the process and system studied. On an absolute scale an electromagnetic field may be considered strong if its electric field amplitude E o - v/2I/(eoc) is small comparable to the inner-atomic field. With e0 the vacuum dielectric constant, and c the velocity of light we find for a ground state H-atom (with its electron in a distance of 1 Bohr radius a0 from the nucleus) that the field is strong if the intensity is I > 3.5 x 1016 W/cm 2, while above some 1017 W/ cm 2 relativistic effects as well as the magnetic field component of the field become important. Present state of the art high intensity laser facilities can provide such intensities up to 102~ W/cm 2, using 800 nm Ti" Sapphire lasers with sub 50 fs pulse duration at a comfortable 10 Hz repetition rate (see, for example, Kalachnikov et al., 2001). However, it turns out that our present object of interest, C60, already completely disintegrates at intensities above
I.V. Hertel et al.
234
[II
1016 W/cm 2, ejecting essentially fast carbon ions with charge states up to q = 4 (Kou et al., 2000). Since we are concerned here with essentially intact C60, our present focus will be on an intensity range from 1011 W/cm 2 to 1015 W/cm 2. As we shall see, even at 1011 W/cm 2 and below, multiphoton processes dominate the energy deposition and C60 is easily ionized by 5 or more photons of 800 nm at this intensity. Hence, in the present context we consider a field to be strong if the object under study is significantly modified by the field. One relevant quantity is then the average oscillation energy which a free electron acquires in the radiation field of the laser pulse. This ponderomotive potential is given by e2 I (x ~2I Up - 2meeoCco2
(6)
and numerically by
Vp=
9.34 x 10 -20 ()~/nm)ZI/(W cm -2) eV.
with me the mass of the electron, col the angular frequency of the laser radiation. Note that the ponderomotive potential depends quadratically on the laser wave length )~, i.e., the most significant in the infrared wavelength region. To determine whether a field is strong we have thus to compare Up with the atomic or molecular energy in question. While discussing ionization processes we would consider the strong field regime to begin at
Up > EI
(7)
where EI is the ionization potential of the system. For C60 with EI = 7.58 eV (De Vries et al., 1992) an 800 nm Ti : Sapphire pulse would in that sense be "strong" when I > 1.3 x 1014 W / c m 2-Icrit, which conveniently may be achieved by focusing a 50 fs pulse of 400 laJ onto a spot size of 100 ~tm diameter. Typical multiphoton processes occur for I << Icrit as illustrated for an atom Fig. 9 (left panel). Indicated are the kinetic electron (e-) energies expected in above threshold ionization (ATI) as well as the possibility to generate high harmonics of the frequency of the interacting laser pulse. At intensities I>~Icrit the atomic or molecular potentials are significantly deformed by the field as depicted in Fig. 9 (right panel). The electron ecan escape from the atom in an above barrier process and is accelerated in the oscillating laser field. While a completely free electron would not be able to gain energy from the laser pulse (for energy and momentum conservation reasons) with the atom present this is possible. As first pointed out by Corkum (1993), the electron can accumulate energy a n d - depending on its
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FIG. 9. Schematic illustration of an atom in a strong field with electron energetics an high harmonic generation. Left: multiphoton ionization (upward arrows indicate photon energies), electron energies (full downward arrows) in above threshold ionization (ATI), and high harmonics generation (dotted downward arrow). Right: above barrier ionization in a strong field, indicating the recolliding electron with a maximum energy of 3.2 Up.
starting phase with respect to the laser field - may return to the atom with kinetic energies up to about 3.2 Up. This is schematically illustrated by the trajectory in Fig. 9 (right panel) showing an electron starting at the barrier. This so called recollision process has been established to be instrumental in high harmonic generation (HHG) and explains the experimentally observed plateau and cutoff of H H G towards high energies (Schafer et al., 1993; Corkum, 1993). As we shall discuss in Sect. III recollision may also contribute to fragmentation of molecules and clusters such as C60 in strong laser fields. Traditionally one also defines a dimensionless quantity, the so called Keldysh parameter, introduced by Keldysh (1965)
_~p
/EISomeco) 2
tzR
EI/eV
2.31 • 109/
(8)
/ / W cm-2)()~/nm) 2
V(
to differentiate between the high and low intensity regime. One can show that 9/ is also proportional to the ratio of the tunneling time tzR of the electron through the barrier in a zero range potential and the period of the laser tL -- 2rt/co0. Hence, in the strong field regime y << 1 the electron escapes from the atom in a time shorter than the field inversion time. In contrast, a
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I.V. Hertel et al.
[II
weaker field (y _> 1) reverses before the electron can tunnel through the barrier. Apart from the very dramatic deformations of the atomic (or molecular) potential just discussed we also have to consider the dynamic Stark effect caused by the laser field which may shift atomic and molecular energy levels in a significant manner. For molecules, sufficiently strong fields can thus cause potential energy crossings and consequently lead to laser field induced nonadiabatic transitions, a subject of very active current research in many experimental and theoretical studies (DeWitt and Levis 1998; Kawata et al., 2001; Kono et al., 2002, 2003, 2004; Lezius et al., 2002, Sato et al., 2003; Markevitch et al., 2003, 2004). Such behavior will be most efficient if the laser frequency is close to a resonance of the system studied. Such manifestations of the Autler-Townes effect have long been known in studies of ATI processes (LaGattuta, 1993) and definitely need to be considered for molecules in intense laser fields also. The AutlerTownes (1955) splitting is hdikeO with dik being the dipole transition moment between the resonant levels. One easily estimates that such splitting can be in the eV region at rather moderate intensities of 1011 W/cm 2, providing the laser frequency is in resonance with a transition of significant oscillator strength. We will have to keep this in mind while discussing excitation mechanisms in C60.
D. EXPERIMENTAL ASPECTS A few experimental aspects of fs laser pulse interaction studies with C60 deserve to be mentioned. Figure 10 illustrates, as an example, a selfexplaining schematic of a typical experimental setup used by the group at the Max Born Institute. Time of flight (TOF) instruments are used to study both the electron energy distributions and the mass spectra of the fullerenes. Presently, no simultaneous (coincident) detection of ions and electrons is employed, although possible in principle as shown by Stert et al. (1999). A molecular beam of C60 is usually generated by effusive heating from an oven. In a special study also a liquid nitrogen cooled C60 beam from an aggregation cell was used by Hansen et al. (1997). We mention that the reflectron used here for analyzing the ion masses has a resolution of better than 1000, hence enabling isotope identification in C60 and allowing to study metastable fragmentation on the gs time scale. The energy resolution of the electron spectrometer ranges from 5 meV at E e l - 1 eV to 400 meV at E~l--20 eV. We will not discuss the various laser systems and experimental methods of ultrafast physics. It suffices to say that typically the basis of all table top
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FIG. 10. Typical experimental setup for studying C60 interacting with ultrafast laser pulses used in the present work. Both electrons and ions can be detected by time-of-flight electron and mass spectrometers, respectively. The laser pulses originate from a Ti : Sapphire fs laser, using various frequency conversion, stretching, and shaping methods. A computer facilitates the control of the laser pulses and other experimental parameters as well as data collection.
short pulsed laser systems used in these studies is the Ti : Sapphire laser at 800 nm which may be converted conveniently to the second harmonics and by using other nonlinear conversion schemes, orange or near infrared laser wavelength can be employed. Present state-of-the-art techniques are used to manipulate, stretch, shape, and to characterize the laser pulses. We will discuss, however, a few subtleties concerning the definition of intensities, calibrating them, measuring signal yields as a function of intensity and defining the so-called "saturation intensities" in the high intensity limit. Intensity calibration with short pulse lasers is a non trivial problem. What can be measured directly is the pulse energy Ep. But since we never have a constant spatial and temporal distribution of intensity it is important to define clearly to which quantity a given intensity refers to. In the most favorable case the spatial and temporal distribution is Gaussian and the intensity I (mostly given in W/cm 2) is
I(r, t) = Im exp(--(r/co) 2) exp(--(t/r) 2)
(9)
with Im giving the maximum intensity at t = r = 0 with r and co characterizing the temporal and spatial beam profile- quantities which can, in principle, be measured experimentally by determining the autocorrelation function (for r)
238
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I.V. H e r t e l et al.
and e.g., the total energy passing a knife edge which is moved into the beam (for co). For a Gaussian, one easily works out that
or
(10) = 0.83 E,,
with th and dh being F W H M of the temporal and spatial pulse width, respectively. We note that the maximum intensity at the pulse center corresponds to a hypothetical circular beam of constant intensity of radius co. Note, however, that co is the 1/e beam waist radius, not the 1/e 2 radius often given for laser beams. Since the beam parameters are difficult to determine quantitatively, the intensity in typical ion yield experiments is usually not measured absolutely. Rather, one calibrates the intensity with a known intensity dependence for a standard ion (typically Xe +) or compares photoelectron spectra with known data from the literature (see, e.g., Larochelle et al., 1998; Schyja et al., 1998). One may be worried about the effect the spatial and temporal intensity distribution has on the experimental intensities, especially while comparing them with theoretical work which typically assumes a well-defined, constant intensity. Indeed, a careful examination of the geometry for each experiment is necessary and the lack of it may explain many discrepancies reported in the literature. However, well-defined Gaussian beams are often best suited to account for this properly. We consider the ion yield expected in a multiphoton ionization process with n photons. For not too high intensities the theoretical prediction (see, e.g., Lambropoulus, 1985) for the ionization probability is W ( I ) = a n ( I / h v ) n with an n photon "cross section" an. We assume a Gaussian laser beam focussed such that the Rayleigh length is significantly larger than the target length g illuminated- a situation which is typical for well-collimated molecular beams and not too strong focussing. In this case, the laser intensity a particular target molecule experiences depends only on its radial position and time. 1 The signal is then derived from
S-
flgNo~n • 2To
f/o dt
rdr[I(r, t)/hv] ~
(11)
1Note, however, that in experiments with extremely intense fields one often uses very tight focussing. In that case the evaluation of the signal has to account for a modification of the laser intensity in two dimensions (Larochelle et al., 1998).
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with /3 an experimental sensitivity parameter and No the target density. Using the laser pulse profile Eq. (9) one obtains after integration s- =w eUo . •
(12)
with the maximum intensity Im given by Eq. (10). This is a nice result, showing that the signal still follows a power law and is proportional to the pulse duration T and beam area at 1/e intensity. The only difference compared to a hypothetical laser pulse of uniform intensity in space and time is a reduction of the total signal by a factor 1/(n~/-n). Hence, it appears a good idea to use Gaussian beams when determining, e.g., the slope of a power law for ionization of C60 by a short laser pulse, rather than trying to spatially shape the laser pulse for constant intensity with possibly problematic consequences from diffraction etc. Slightly more complex is the determination of saturation intensities, i.e., the determination of an intensity at which most of the molecules have undergone the process investigated, i.e., for high intensities and transition probabilities. Hankin et al. (2000) and Lezius et al. (2001) pointed out that the signal for a Gaussian beam may for the general case be written as
S - fl g~No rcwZ qb fo Im 1 - eI-w~l)~ dI
(13)
where in addition an ionization branching ratio 4~ has been introduced. 2 Note, that once Im, the maximum intensity of the laser pulse is greater than the saturation intensity, Isat to ionize an atom with probability W(Isat)r = 1, any further increase of the signal essentially originates from an increase of the beam diameter for which saturation is reached as Im is further increased. To derive a saturation intensity Hankin et al. (2000) assumed that for I ( r ) > I~at one may set e-W(z)r=O and that outside the thus defined beam volume Vsat no signal is generated. With this assumption the lower limit in Eq. (13) becomes I~at and one derives
SThis would imply intensity from the on In I) with the use this somewhat
flg~Nor~w2ck[ln I - lnlsat]
(14)
that in a lin-log plot one may determine the saturation intersection of the observed signal (linearly depending abscissa. In agreement with current literature, we will pragmatic approach in the present report, defining thus
2Note that this assumes a pulse of constant intensity over a time r. More precisely, to be replaced by an integral over the temporal pulse shape.
W(I)r has
240
[III
I.V. H e r t e l et al.
an experimental measure for the readiness of a system to achieve a certain charge state in a laser field. We note, however, that we have lost on the way the obvious dependence of a saturation intensity on pulse duration still seen in Eq. (13) and we have neglected that for I < Isat i.e., from the wings of the Gaussian beam a signal is generated. Both effects make the derived saturation intensities slightly dependent on the experimental setup and on the (power) law valid in the intensity regime below saturation.
III. Ionization, Charge States, and Fragmentation A. MASS SPECTRA AND FRAGMENTATION Already the early photofragmentation experiments by O'Brien et al. (1988) showed that fullerenes have very special ionization and fragmentation properties. A typical example of these mass spectra is shown in Fig. 11. As already recognizable in the first mass spectra as obtained from hot carbon soot (see Fig. 1) two distinct regimes can be distinguished: (i) from the
,
!", 10
~, 20
"'
I' 30
~, 40
'
!
50
'"
;
"
-
60
Atoms per cluster FIG. l 1. Mass spectrum from the first photofragmentation study of mass selected C+0 obtained with ns laser pulses at 353 nm with a fluence of 59 mJ/cm 2 from O'Brien et al. (1988).
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parent ion C~-0 down to C~-2 only fragments with an even number of C atoms are observed while (ii) between C + and C~-s mass peaks are separated by one C + unit. This bimodal mass distribution has also been observed in various experiments using different excitation mechanisms, e.g., in collision between C+0 and neutral rare gas atoms (Ehlich et al., 1996). It is now generally accepted that the dominant mechanism for the formation of the large fragments from C~-0 is by sequential fragmentation, C6+0###
c,+##
> "--/60-2 -q- C2
> C~-0#__4-}-2C2
>
etc.
(15)
starting with a highly excited ion. The recent photoionization mass spectra of Reink6ster et al. (2004) shown in Fig. 7 appear to support such a view rather nicely. One clearly sees, particularly so for the doubly charged ions, that each stage of fragmentation needs an additional energy of about the C2 evaporation energy of 10 e V - in addition to the threshold energy plus the kinetic shift. However, emission of large neutrals has been regularly invoked to explain the observed loss of large-n clusters (see, e.g., DeMuro et al. (1992) or Hohmann et al. (1994)) and has even been observed in reionization experiments. For details the reader is referred to a recent, comprehensive study by Rentenier et al. (2004), and references there in. In particular for the fragmentation of multiply charged ions, a number of mechanisms have been discussed in the literature, e.g., auto-charge transfer (ACT) and asymmetric fission (AF) such as: C~- --~ C r+ + C~ (r-l)+
or +
C~-
~ C m,
C~
(r-l)+ + ), C m, --]--C n --]-mC2
+C~
or
(16)
Obviously, this type of process is necessary to explain the small C + ions observed in the mass spectra with odd and even n. The particular resilience of C60 has led to the observation of a number of general phenomena which are, however, particularly pronounced in C60 photoionization studies. Delayed ionization (or thermionic emission) which occurs microseconds after excitation, e.g., with ns laser pulses at photon energies far below the ionization limit (Campbell et al., 1991) has drawn a lot of attention during recent years (see, for example, Campbell and Levine, 2000, and references therein). Delayed ionization in photoabsorption experiments occurs subject to conditions. First, a fast energy redistribution between the electronic excitation energy and the vibrational modes enables the photoexcited species to absorb sequentially many photons and heats up quickly. While this is true for most larger molecules
242
[III
I.V. Hertel et al.
and clusters, usually these systems undergo a fast neutral dissociation since the binding energy between some molecular subunits or cluster constituents is normally much smaller than the ionization potential. For some metallic and metcar clusters and fullerenes in particular the reverse is true as discussed above (Sect. II.A.): for C60 the binding energy of the C2 is Ea >_ 9.5 eV while the ionization potential is EI--- 7.58 eV. Under these conditions the delayed electron emission is one possible decay channel in competition with other decay modes, such as fragmentation or radiative cooling (see, e.g., Rohmund et al., 2001). Mass spectra from multi-photon ionization (MPI) of C60 have been studied with various laser parameters (Hohmann et al., 1994; Hunsche et al., 1996; Baumert and Gerber, 1997; Kou et al., 1998), but only relatively recently, systematic studies with short pulse lasers and varying pulse widths have been performed (Tchaplyguine et al., 2000; Campbell et al., 2001a,b). Figure 12 shows two typical mass spectra obtained for 795 nm excitation
~11 +
C 15+
.
C. o o +
C 50+ C 19+
m
r ffl r 0
n
I
Xe +
n
Lt,,
C603+
J
9
,
:
!
. ~
044*1 I! I | l . . I1. l . i
~
,
C 2+ i 60
,
-
,
xool .[
,
~ C 6 ~
/ c 04§
I
I 5~ :
' mass [12u] ...... .. , , 20
30
40
,,~ ~
~ 5~
10
720 724 728 mass [u]
50
720 724 728 mass [u] 60
mass/q [12u] FIG. 12. Typical mass spectra obtained from C60 by ionizing with laser pulses of 765 nm wavelength with 25 fs pulse duration (bottom) and 5 ps (top). The spectra were recorded at roughly equal laser fluence, the corresponding intensities being ~3.2 x 1012 W/cm 2 and 1 x 1015 W/cm 2, respectively, which is equivalent to Keldysh parameters of 4.4 and 0.25 (or to ponderomotive potentials of 0.19 eV and 60 eV). For 5 ps pulses a "normal" bimodal mass spectrum is observed. In contrast, for high intensity 25 fs pulses, a series of multiply charged C~- ions is seen together with their large fragments (C2 evaporation). However, extremely little fragmentation is detected for singly charged C+0 - as illustrated by the insert with magnification x 200 - and only few small fragments if any. The peaks marked with asterisks (*) indicate metastable decay processes. The inserts on the right show the characteristic isotope distribution of C+0 with the isotopomer ratio [12C60 ] 9[12C59 13C]" [12C58 13C2] being 1"0.65" 0.21.
nq
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with 25 fs and 5 ps pulse duration, respectively. While the 5 ps pulse mass spectrum resembles very much the "standard" bimodal mass spectra, which we have seen before (Figs. 1 and 11) the 25 fs spectrum shows a rather different pattern, most striking perhaps the strong yield of multiple charged species, which have not been observed with laser pulses in the ns time regime even at the highest intensities. We mention, however, that in collision experiments involving fast electronic excitation similar mass spectra are observed, e.g., in high energy electron impact experiments (V61pel et al., 1993; Scheier et al., 1994, Itoh et al., 1999), in collision with singly and doubly charged high velocity ions (see, e.g., Schlath61ter et al., 1999; Reink6ster et al., 2001, 2003) in collision with highly charged ions with C60 (see, e.g., Schlath61ter et al., 1999; Jensen et al., 2004), and as illustrated in Figs. 13 and 14. 0.2 4+ C60
0.1
3-1-
060
v=0.24
/
0.0 C2+ 60-2m
v=0.32
[!
0.1 >., ...i-, m tO ..i-, c"-
0.0 -I-
Cn
v=0.45
0.1
0.0 v=0.6 0.1
0.0
0
20
40
60
nlr
FIG. 13. Mass spectra of the collision products from He2+-C60 collisions at different projectile energies given in atomic units from Schlath61ter et al. (1999). All spectra are normalized to the C~-0 signal.
244
[III
L V. Hertel et al.
L
+ ",,~.
C~1
1
3+ ~""60~2m]
,.,2+ ~60-2m
Ol t v`.,
Xe 28+, V -
b) 05+, v=0.25
?
~ C 2§
c) 9
p6+
c6;
7+ 060 "~
t c8; "1
i c +\l 5
\
10
15 nll
20
25
30
FIG. 14. Mass spectra of the collision products from (a) He+, (b) 0 5+, and (c) Xe 28+ collisions with C6o from Schlath61ter et al. (1999). The projectile velocity in atomic units is given in each plot. In all three plots the break on the intensity axis is at 33% of the strongest peak.
The common characteristics of these experiments is that the electronic system of C60 is excited on a time scale that is short compared to the electron-phonon coupling which is believed to be on the order of a few 100 fs. We also remark that in the 25 fs laser generated mass spectrum C~-0 shows almost no fragments (only about 0.5% as illustrated by the insert) at these relatively high intensities, the Keldysh parameter (Eq. 8) being 7 = 0.25. In contrast, multiply charged fragments are the strongly abundant. We note in passing, that the tail of the C~-0 peak seen in the 5 ps mass spectrum indicates the onset of delayed ionization of C60. The fraction of delayed C60 ions increases almost linearly with the pulse duration. No saturation has been found for pulses up to 5 ps, the longest pulse length available in these experiments (Campbell et al., 2001a). Further insight into mechanisms and time scales of the various energy transfer processes is gleaned from comparing mass spectra at different pulse
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duration but c o n s t a n t laser intensity (i.e., different pulse energy) (Campbell et al., 2000). Figure 15 shows three mass spectra at 4 • 1013 W/cm 2 (Keldysh parameter y = 2 . 5 ) - and for comparison again the 5 ps spectrum already shown in Fig. 12. At short pulse durations (25 fs and 110 fs) one observes mostly intact C~+ ions triply charged and only, little fragmentation. Obviously, with pulse duration between 25 and 500 fs the ratio C~-/C~of multiply to singly charged ions increases significantly. In addition, fragmentation also becomes more efficient. When using a 500 fs pulse the +
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abundance of doubly and triply charged ions and fragments C60_2 n and C+++ 60-2n is already larger than 1 It is difficult to compare the 5 ps laser pulse data directly, since the intensity is much smaller, but the multiply charged ions have completely disappeared and the mass spectrum is dominated by singly charged fragments- one possible reason being asymmetric fission and other processes discussed above (see Eq. (16)) which is supported by efficient heating of the system during the long pulse. Next we compare different laser intensities and wavelengths. The mass spectra in Fig. 16 show a characteristic dependence of charge states and fragment mass distribution on laser pulse intensity. While for both wavelengths, 395 and 790 nm, no fragmentation is seen at low intensities we note that at higher, but similar intensities fragmentation is more prominent at 395 nm. For 790 nm and 25 fs and intensities up to 1 x 1014 W / c m 2 o n e observes essentially intact Cg~- ions only (q < 3), while at 6 x 1014 W/cm 2 charge states up to q = 5 are discernable as well as a significant amount of multiply charged fragments with up to 6 C2 losses. Nevertheless, with 790 nm the signal from intact C~- is still larger than each +q of the respective C60_2 n fragment signals. In addition, small fragments with odd and even numbers of C atoms appear. In contrast, using 395 nm laser pulses we see massive fragmentation already at 8.9 x 1013 W/cm 2 while at 1.3 x 1014 W/cm 2 fragments dominate. The trends observed here become even more evident when near IR pulses are used for ionization as recently reported by Bhardwaj et al. (2003). They have investigated the ionization of C60 at 1800 nm with a pulse duration of 70 fs and intensities up to 1015 W/cm2-corresponding to a Keldysh parameter y=0.11. In contrast to the 400 or 800 nm experiments, the first optically allowed transitions of C60 are very far from 1 or 2 photon resonance with 1800 nm and ionization is supposed to occur either by tunneling, or "over-the-barrier" ionizationas one certainly expects for a Keldysh parameter )/<< 1. Figure 17 shows a mass spectrum from that work conducted with 1015 W/cm 2. Highly charged C~- ions with q < 12 are the dominant features of this mass spectrum and almost no fragments are observed. The highly charged intact C~- ions are explained by ultrafast ionization. Bhardwaj et al. (2003) also discuss the possibility of vibrational excitation due to induced dipole forcesone might call this impulsive Raman excitation- which is obviously only weak and hence the fragmentation rate is small. Apparently, in the context of fragmentation, the Keldysh parameter is not a relevant quantity to be discussed, a n d - as we shall discuss below (Sect. I I I . B ) - even for clean ionization without fragmentation the classical above barrier concept must be seriously questioned with such a large finite system and its many electronic degrees of freedom. The laser frequency enters obviously in a more specific manner into the process of
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FIG. 17. Highly charged cq~- cations, q < 12, by intense (1015 W/cm2), short (70 fs) infrared (1800 nm) laser pulses from Bhardwaj et al. (2003). The insets show the low m/q regions corresponding to C~-, q = 10 to 12, at increased magnification. Highly charged C6o ions are distinguished from possible interfering lower charged ions, e.g. , C + vs. ~10+ "~10 by their isotopomer distribution. Peak heights for z < 9 do not reflect mass abundances due to saturation.
fragmentation, so to say counterintuitive to what is expected from naively applying the "conventional" wisdom of atomic strong field physics. We believe that electronic resonances may be involved in heating the electronic system prior to ionization. We note that at 395 nm where most fragmentation is observed, the laser radiation is nearly resonant with the first small absorption maximum seen in Fig. 2. Recent theoretical calculations by Torralva et al. (2001) and Zhang et al. (2003) have shown that during a single femtosecond laser pulse even at moderate intensities (~1011 W/cm 2) more than one electron is excited. We emphasize that these multielectron processes involve sequential absorption of several photons - in contrast to multiphoton absorption of energy by a single electron as well-known from atomic physics. It is easily conceivable that several tens of eV can be deposited into the electronic system during a laser pulse at 1014 W/cm 2. This energy can then be redistributed in principle among all degrees of freedom. However, the coupling time between the electronic and vibrational degrees of freedom is on the order of a few 100 fs. Hence, for the shortest pulse durations discussed here, energy redistribution from electronic to nuclear system during the pulse is much less likely. Rather, the ionized electron(s) carry most of the energy and little fragmentation is observed (Shchatsinin et al., 2004). In contrast, for the longer pulses where energy can readily be transferred from the electronic to the nuclear
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system during the laser pulse, ionization occurs as an a f t e r t h o u g h t - and patterns as known from fragmentation with ns laser pulses are observed. Several reasons may be discussed for the particular puzzling lack of C+0 fragments from MPI with the shortest p u l s e s - even at high intensities. We first note that, again, similar trends are seen in the fast collision spectra, where in the experiments with highly charged Xe 28+ (Fig. 14) almost no q+ fragments are detected at all for any charge state of C60. Referring again to the single photoionization experiments (Fig. 7) we recall that the singly + charged C60_2m signals decrease significantly as the photon energy is 2+ 3+ increased while C60_2 m and C60_2 m are prominent and do not decrease at higher photon energy. Obviously, this somewhat mysterious higher abundance of multiply charged fragments cannot simply be attributed to the amount of energy deposited into the system. We recall in this context our earlier discussion (Sect. II.A) where we were led to relate multiply charged fragments to some kind of post-ionization effect with not too fast electrons emerging in a multiple ionization process. This is consistent with the missing fragmentation in collision with very highly charged ions (c.f. Fig. 14): in this case electrons are just extracted from C~-0 very rapidly by the strong Coulomb field so that no time for post-ionization interaction with C~remains. A similar situation appears to dominate the 1800 nm results shown in Fig. 17 where only very little fragmentation, if any, is seen: the above barrier process occurs at these wavelengths and intensities extremely fast. However, in a very recent MPI study of C60 at 1500 nm (70 fs) Bhardwaj 3+ et al. (2004) found a measurable, albeit small abundance of C60_2 m and 4+ 3+ 4+ 4+ 5+ C60_2 m. They observed the ratio of C60_2m/C60 and C60_2m/C60 to depend strongly on the ellipticity of the laser pulse. This clearly indicates that electrons which recollide during one laser oscillation cycle with the C~- ion contribute significantly to the fragmentation process (c.f. the discussion in Sect. II.C). Bhardwaj et al. (2004) calculated the distribution of return energies in the classical recollision model (Corkum, 1993) and found that the maximum energy in C~- recollision is significantly larger than the wellknown 3.2Up value for atoms. From this they were able to explain why in their experiment only fragments with q > 3 were observed. Hence, we conclude that such recollision processes may in part also be responsible for the high abundance of fragments in the mass spectra observed with shorter wavelength. A corresponding experiment is yet to be conducted. We summarize the observations and interpretations on the short pulse laser MPI of C60 as follows: for very short laser pulses (<70 fs), ionization occurs predominantly via direct multiphoton ionization with negligible vibrational heating. At intermediate pulse durations (a few hundred fs) we still observe essentially unfragmented, singly charged ions with only + some indication of C60_2m fragments and an increasing yield of higher
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charge states which also fragment, i.e., vibrational heating occurs during the laser pulse but does not lead to direct formation of singly charged fragments. Finally, for pulse durations beyond several hundred femtoseconds strong fragmentation is observed, multiply charged ions are no longer detected and the ionization process is followed by "thermionic" electron emission on a microsecond time scale. As one hypothesis, to e x p l a i n - at least p a r t i a l l y - the fragmentation behavior observed, we propose efficient postionization interaction of low energy photo-electrons with C~-0# vibrationally preheated during the excitation process. Additional evidence for this explanation is found in the observation that the fragmentation is strongly wavelength dependent, being nearly suppressed for 1800 nm. In these comparatively slowly oscillating laser fields, electrons are extracted most rapidly from ions and charge states up to q <_ 12 are detected. Furthermore, recollision processes may play a role in the fragmentation dynamics as documented for the weak fragmentation at 1500 nm. A careful analysis of the mass spectra taken with a RETOF mass spectrometer (illustrated in Fig. 12) revealed that fragments are always accompanied by metastable fragmentation on a time scale of 10 to 100 ~ts (Tchaplyguine et al., 2000; Campbell et al., 2001b). This is somewhat u n e x p e c t e d - at least at first t h o u g h t - and tells us that all these large fragments with several C2 units missing from C~- are generated in an essentially statistical process: once created they are still hot and can lose energy by C2 evaporation (and by thermal emission of electron or by radiation). The key question to which we have given some tentative answers is, how the energy >40 eV needed for fragmentation and ionization on the given time scale is initially deposited into the system. We feel that this cannot be explained in the familiar single active electron (SAE) picture. Rather, many active electrons (MAE) will be involved in the processes. Mass spectra give fingerprints of the final outcome of these energy deposition processes. We note, that the picture evoked here is more or less similar to that for describing femtosecond pulse excitation and electron relaxation on metal- or semiconductor-surfaces (see, e.g., Knoesel et al., 1996): C60 may be seen as an intermediate on the way to condensed matter and we can visualize its excitation as filling of the conduction band with electrons. We will come back to this notion in Sect. IV and V. B. INTENSITY DEPENDENCE AND POWER LAWS
At this point it is appropriate to look more quantitatively at the dependence of the ion yields on the laser intensity. Figure 18 (lower panels) summarizes the results of Tchaplyguine et al. (2000) at 795 and 400 nm.
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FIG. 18. C+0 (left) C~- (right) ion yield S as a function of the laser intensity I for 400 nm (circles) and 800 nm (squares). The lower panels give the standard log-log plot illustrating the power law S (x I n, where n corresponds to the order of the processes (the number of photons involved in one step). The top panel shows the same measurements in a lin-log plot as suggested by Hankin et al. (2001). The intercept of the fitted straight line with intensity axis defines the saturation intensity L,at.
By m e a s u r i n g the total ion yield as a function of incident laser intensity and assuming a power law (S o( I n) Tchaplyguine et al. (2000) found the C~-0 ion signal to rise with a power n - 5 • 1 at 795 nm. This corresponds to a direct m u l t i p h o t o n ionization process with five 795 n m p h o t o n s of 1.56 eV, as required to overcome the ionization potential of 7.6 eV. 3 The yield of C~- ion f o r m a t i o n follows a power law with n - 8 4- 1. The energy of eight red p h o t o n s ( 8 h v = 12.5 eV) gives clear evidence for a stepwise ionization m e c h a n i s m with the order of the process being that required to remove an extra electron from C~-0 (11.4 eV). At 400 n m ( h v - 3 . 1 2 eV) the slope i s - according to Fig. 18 (lower right panel) - n = 3-+- 1 and 6 + 1 for the yield of singly and doubly charged ions, respectively. To ionize C60 ~ C~-0 one needs indeed at least three blue p h o t o n s ( 2 h v 6.24 eV < E I = 7.58 eV < 3 h v - 9 . 3 6 eV), for ionization of C~-0 --+ C~four blue p h o t o n s (4hv = 12.48 eV) would suffice, rather than 6 as indicated by the slope. This p r o b a b l y illustrates the limitations of a strictly sequential ionization model for such a complex system. 3Earlier reports of a slope n - 13 by Hunsche et al. (1996) seemed to indicate the excitation of the plasmon resonance at 20-30 eV. This observation has never been reproduced and the discrepancy remains unresolved, possible explanations being connected with broad, low intensity prepulses or with the special manner in which the geometry was defined in these experiments.
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As seen in the lower panels of Fig. 18 the signals saturate for higher intensities, indicating that all available target molecules have reached a certain ionization stage as discussed in Sect. II.D. Determining and interpreting saturation intensities is an interesting, but yet not completely solved puzzle in the strong field, ultrafast photoionization of large molecules. The Ottawa group has analyzed the ionization rate in intense laser fields for many polyatomic, organic molecules (Hankin et al., 2000, 2001; Lezius et al., 2001, 2002) (see also, DeWitt and Levis, 1998; Markevitch et al., 2003, 2004) with the result that saturation intensities for molecules studied were generally much higher than predicted by the so called ADK tunneling theory (Ammosov et al., 1986), a well established model for strong field ionization of atoms. Also our own measurements for C60 show a large deviation of the calculated ADK ionization rates as reported by Campbell et al. (2001b). Shown in Fig. 18 (upper panels), we have replotted the data in a lin-log plot as suggested by Hankin et al. (2001) for better comparison. As discussed in Sect. II.D the linear rise of the signal at the high intensity limit essentially reflects the increase of the ion yield due to an increase of the volume in which saturation is reached. The intersection of the linear slope with the abscissa gives a pragmatic, experimental measure for the saturation intensity. The results of our own measurements as well as those from Bhardwaj et al. (2003) are shown in Fig. 19 as a function of final charge state along with two slightly different approaches to compare these results with the classical "over the barrier" model in an SAE picture. Bhardwaj et al. r in the laser field (2003) have described the ionization process C~- --+ ~60 by using a q fold charged, conducting and polarizable sphere for the interaction of the active electron with C~-. Saturation is assumed to occur when the thus derived barrier falls below the ionization energy for C~-. We compare this conducting sphere model with the very well tested potential Vo(r) for an electron in the field of C~-0 Eq. (5). 4 We need to add the laser field (c.f. see Sect. II.A), the field induced dipole and the centrifugal barrier of the C60 ground state electron in a spherical approximation (Boyle et al., 2001), i.e., we use the overall interaction potential (in atomic units) o/
V(r) - Vo(r) + Eo(r c o s O - }5) +
2r 2
(17)
with E0 the laser field amplitude, ot the polarizability of C60 and g = 5. The comparison shown in Fig. 19 between the conducting sphere model of Bharadwaj et al. (2003), our present model potential, and the 4Lacking any better approximation we replace the terms 1/(r-R) in Eq. (5) by (q + 1/(r-R) for the higher charge states.
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FIG. 19. Saturation intensities Isa ' for C60 ----->cq~- ionization with short laser pulses as a function of the final charge state q of the ion. Experimental results for 1800 nm, 70 fs (triangles) and estimates for over the barrier ionization using the conducting sphere model (dashed line) are taken from Bhardwaj et al. (2003). The data for 395 nm, 45 fs (circles) and 790 nm, 25 fs (squares) pulses are derived from Campbell et al. (2001b). We compare this also with an estimate from the model potential Eqs. (5) and (17) with polarization screening in the field and centrifugal barrier for ~ = 5 (full line). For comparison, the latter is also used without centrifugal barrier (dotted line).
experimental points is not entirely satisfactory. While the model potential fits the 1800 nm data for q = 1 nicely, it fails completely for higher charge states. The opposite is true for the conducting sphere model, with a general tendency that the experimental data are higher than both theoretical p r e d i c t i o n s - except for the 395 nm data which may be influenced by the llTlu resonance (Fig. 2). We note that the model potential Eq. (5) was designed for singly charged C~-0 ions only and the scaling used for higher charge states is probably not adequate. On the other hand, the charged sphere model of Bharadwaj e t al. (2003) is missing the centrifugal potential. Clearly, as indicated by the dotted line in Fig. 19 for low charge states the centrifugal potential is essential. As documented by the experimental points in Fig. 19 the saturation intensities also depend on the w a v e l e n g t h a notion which is not directly compatible with the classical "over the barrier" or A D K models. In a more rigorous approach one would have to consider dynamical polarization screening which might be particularly important for the 790 nm data. In general it is probably fair to give a warning not to take these classical models too literal. Figure 20 illustrates the e - - C ~ - 0 potentials in a laser
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FIG. 20. 2-D plot of the potential energy of a hypothetical atom with EI= 7.6 eV (left) and the screened model potential for C60 at different field intensities: 1.3 • 1013 W/cm2, 5.5 x 1012 W/cm2, and 1.8 x 1014 W/cm2 in the left, middle, and right graph, respectively. The white planes indicate the energetic position of the ground state energy and the possibilities for electrons to undergo above barrier ionization.
field at two different intensities in c o m p a r i s o n with an fictitious a t o m with a 1/r potential and 7.6 eV ionization potential. 5 It is evident from these graphs that with a complex structure as C60 one c a n n o t expect that m a x i m u m ionization probability and saturation really coincide with the intensity at which the barrier equals to the binding energy of the electron. Recently, more realistic theoretical approaches for the interaction of C60 with intense, short laser pulses have been reported in the literature (Torralva and Allen, 1999; Torralva et al., 2001; Bauer et al., 2001; Bauer, 2002; Z h a n g et al., 2003; Z h a n g and George, 2004). Directly c o m p a r a b l e with the experimental results is at present only the elaborate T D D F T calculation of Bauer et al. (2001) which is extended in Bauer (2002). Starting point is a jellium like potential, very similar to the one described in Eq. (5), which is then used to calculate K o h n - S h a m orbitals for all relevant n and a electrons. The specific route of nonlinear T D D F T used allows one to distinguish between ionization, single particle transitions, or plasmons, and also accounts for higher order processes beyond single particle hole excitations. In Fig. 21 results from this theory are shown, clearly illustrating the validity of the experimentally observed n - 5 power law for C~-0 ionization (Tchaplyguine et al., 2000) 6.
5For these plots, it was assumed that the external field cannot penetrate inside the C60. While this assumption is true for a conducting sphere calculations of Delaney and Greer (2004) show that such screening indeed exists but is by no means complete as assumed here. 6Very recently Uiterwaal et al. (2004) reported a new, rather simple and surprising approach to intense field photonization, assuming that in photons of energy mEph arriving within a typical electronic response time are effictively equivalent to a single photon of energy in Eph by which they were able to estimate saturation intensities for a whole variety of molecules, including C60.
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IV. Above Threshold Ionization Kinetic energy spectra of photoelectrons give valuable complementary information for a deeper understanding of the excitation and ionization mechanisms of C60 in strong laser fields. We have studied photoelectron spectra under many different excitation conditions. The spectra given in this section originate from all electrons collected by the detector regardless of the ion from which they are ejected (singly and multiply charged cq~- as well as all fragments). Figure 22 shows photoelectron spectra taken at 790 nm with 25 fs pulse duration (Campbell et al., 2001b). The intensity increases from top to bottom. At the lowest intensity of 3.7 x 1013 W/cm 2 one clearly observes an above threshold ionization (ATI) peak structure with an energy difference of 1.57 eV corresponding to the laser wavelength. This ATI structure is a convincing proof of the multiphoton character of the ionization under these conditions. At increasing intensities up to 7.5 x 1013 W/cm 2 the ATI structure is still visible but the peaks become broader and the relative amplitudes decrease. At the highest intensity a smooth unstructured electron spectrum is detected. Also given in Fig. 22 is the Keldysh parameter
256
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according to Eq. (8). It is interesting to note that the disappearance of the ATI structure roughly coincides indeed with ?, ~ 1 - separating the multiphoton regime ( 7 > 1) from the above barrier/tunneling region (9/<< 1). As discussed in the previous section, the underlying classical models should be taken with a grain of salt when describing such a complex system as C60. These approximation work reasonably well for atoms, but appear to substantially overestimate 9/for polyatomic, aromatic molecules, as it has, for example, been shown by DeWitt and Levis (1998) and Lezius et al. (2002). It is hence very instructive to compare the T D D F T results of
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FIG. 23. Photoelectron ATI spectra calculated by Bauer (2002) from the most ionizing Kohn-Sham (KS) orbital after a 10 cycles 800 nm laser pulse for three different peak intensities (5.5 x 1012, 1.8 • 1013, and 2.0 x 1013 W / c m 2 f r o m top to bottom). The vertical, dotted lines indicate the expected peak positions including the ponderomotive shift. Left panels: All KS orbitals were propagated in time (MAE picture). At lowest laser intensity (top) a clear ATI structure is visible. At an intermediate intensity (middle) the ATI peaks appear splitted and are completely washed out at even higher intensity (bottom). Right panels: Only the outermost KS orbital was propagated in time (SAE picture) while all others were kept "frozen". Peak splittings are visible for the two higher intensities. The lines remain narrow. Ionization is higher than in the MAE case where energy may be distributed among the electrons. B a u e r (2002) w h o has calculated A T I spectra by the T D D F T m e t h o d as s h o w n in Fig. 23. T h e e x p e r i m e n t a l l y o b s e r v e d A T I s t r u c t u r e o f C60 on a b r o a d backg r o u n d is b o r n o u t very clearly. T o a first a p p r o x i m a t i o n one expects the A T I peaks to occur at
Eet = n h v - E I -
Ut,
(is)
as i n d i c a t e d by the d a s h e d vertical lines in the figure, the p o n d e r o m o t i v e p o t e n t i a l being U p = 0 . 3 3 , 1.1 a n d 1.2 eV for the intensities e m p l o y e d in the t h e o r y (top to b o t t o m p a n e l in Fig. 23, respectively). T h e p o n d e r o m o t i v e shifts derived in the s i m u l a t i o n are smaller w h i c h is a t t r i b u t e d to the fact t h a t the initial state also has a S t a r k shift. I n d e e d , in the e x p e r i m e n t too, only a small shift o f the A T I peaks if a n y d u e
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to changing Up was observed. Generally speaking, the full MAE treatment shown in the left panels in Fig. 23 reproduce the trends observed experimentally very well, although several differences warrant discussion. Following Bauer (2002) we note firstly, that the peaks in the calculated ATI spectra are narrower. Bauer (2002) attributes this to the facts that in the theoretical simulation there is no "blurring" due to laser focus effects (where different electrons "see" different laser intensities) and that the trapezoidal model pulses have a well defined peak intensity over cycles, minimizing ponderomotive sweeping which also leads to a broadening of ATI peaks. Secondly, the jellium model is slightly easier to ionize than real C60. This together with the Gaussian profile is the reason why the disappearance of ATI peaks occurs in the model already around 2 • 1013 W/cm 2 whereas in the experiment this occurs at about 1014 W/cm 2. Thirdly, the electron temperatures derived by Campbell et al. (2000, 200 lb) are lower than those obtained from the model (--~40000 K). As a fourth point, we note that the theoretical ATI peaks are split while such a splitting cannot be observed experimentally due to the peak broadening. Bauer (2002) attributes this to Autler-Townes splitting caused by intermediate resonances as discussed in Sect. II.C. When a resonant coupling of two bound states leads to almost complete Rabi flops, the ATI peaks not only show a substructure but split in two equally strong peaks, separated by the Rabi frequency (see e.g., La Gattuta, 1993). One nice possibility of theoretical simulations is that one can switch on and off certain interactions. The photoelectron spectra shown in the right panels of Fig. 23 have been calculated by freezing all KS orbitals except for the outermost one, i.e., by suppressing all MAE effects and following the SAE dynamics exclusively. We see that the lines are much narrower in the SAE picture. Moreover, in the SAE model the ionization degree is higher because energy cannot be transferred to the other electrons. Moreover, the population of a levels is suppressed. And clearly the damping at higher intensities is not reproduced. Hence, the disappearance of ATI peaks in laser C60 interaction appears to originate from multiple peak splittings (a SAE effect) in combination with line broadening due to electron-electron interaction. For a realistic description of the dynamics we need the full MAE picture. In Sect. III (Fig. 15) we have presented mass spectra taken at different laser pulse durations and gave a rough classification of the time scales of the different energy relaxation processes. We can refine this picture now by looking at photoelectron spectra taken with the same laser parameters as Fig. 15. Figure 24 shows this series. The laser intensities for Fig. 24 (a) to (d) was kept almost constant at about 4 • 1013 W/cm 2 while Fig. 24 (e) was obtained with an intensity of 4 • 1012 W/cm 2 . The shortest pulse width of 25 fs gives the reference for a clear ATI structure as just discussed. As the
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(a)
15 10 5 0
(b)
150 100 50
0
(c)
150 110fs
"--" 100 .m
u~
50
._E
0
t(D
(d)
15 10 5 0
r ,
40
I
(e)
20 0
0
5
10
15
20
electron e n e r g y [eV]
FIG. 24. Photoelectron spectra as a function of laser pulse duration. The laser intensity was kept constant at 4 x 1013 W/cm2 (a)-(d), and 4 x 1012W/cm2 (e). The loss of the ATI structure with increasing pulse duration is indicative for recoupling of the electronic energy. Reproduced from Campbell et al. (2000) laser pulse gets longer, this ATI structure becomes less pronounced already for 70 fs while at 110 fs a broad structureless background signal begins to dominate, which becomes dominant at 500 fs pulse duration. W h a t has already been indicated in the mass spectra is now brought out very clearly in the photoelectron spectra. The results have been interpreted by Campbell e t al. (2000, 2001b) in terms of a two step relaxation process: electronelectron coupling occurs on a time scale of 100 fs or even less and electrons thermalize if the interaction with the laser field persists that long, hence the A T I peaks are lost. F r o m the T D D F T point of view (Bauer, 2002) the wobbling electrons give rise to a quasi stochastic time-dependent effective
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potential with not precisely defined energy levels. However, well-defined energy levels are a prerequisite to predict the position of the ATI peaks. Therefore, the rapidly time-dependent effective potential "washes out" the ATI structure. On a time scale of several 100 fs the hot electron gas in turn interacts with the nuclear core (electron-phonon interaction), electrons cool even more while the nuclear vibrational modes are heated so that fragmentation may eventually occur on a long (many ps, ns, gs) time scale. These hot ~c,q+# 60 are then, as already discussed, particularly by susceptible to secondary processes, such as multiple ionization by not too fast ejected electrons.
V. Multielectron Excitation, Energy Redistribution, and Coupling to Nuclear Motion As we have discussed in Sect. III and IV, one of the fascinating, but difficult to analyze, facets of intense laser field interaction with Buckminster fullerenes is the broad scope of potential responses of C60, ranging from atomic to solid-like behavior such as above-threshold ionization on one side and thermionic electron emission on the other, or from single photon absorption to plasmon excitation- depending on how we interrogate this large finite molecular system. This raises quite a general question of lasermatter interaction: if many electrons are present in a laser field, how do they interact with each other to generate the finally observed outcome? Which of them are most strongly affected and how do they contribute to the overall response of the systems? Or more specifically, when does the single active electron (SAE) dynamics which dominate the strong field response of atoms, give way to a richer multielectron response expected in large finite systems? Using theoretical modelling this aspect can be worked out as we have already seen in the analysis of the ATI peaks (see Fig. 23). A particular illustrative view from the time dependent calculation of Kohn-Sham (KS) orbitals by Bauer et al. (2001) is shown in Fig. 25. The 2D intensity plot of dipole responses of individual KS orbitals after a delta kick to the system shows that all orbitals contribute in a broad spectral range while the individual action cannot be extracted from the overall response of the system shown on top of Fig. 25. While such detailed information can never be extracted from experiments, we may possibly try to identify specific aspects of the response of C60 to strong field interaction as being attributable to one or the other of these "two faces". One example is the observation of Rydberg states: while the population mechanism of these states is clearly driven by multielectron excitation processes (MAE), the binding energies of the Rydberg states
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FIG. 25. Spectrum of Kohn-Sham (KS) orbital resolved dipole response from TDDFT calculation of Bauer et al. (2001) for C60. Shown is the response of 70 KS orbitals as a function of frequency after a delta kick to the system. Also shown is the total dipole response. themselves can be derived in a very simple SAE approach describing the almost atom-like single Rydberg electron on its orbital far away from the C60 core. Consequently, this is an ideal observable to address these questions. From a detailed understanding of the underlying excitation processes one may, in principle, glean deep insight into the photodynamics of large molecular systems with delocalized ~ electrons in strong laser fields. This will be discussed in the following Sect. V.A with the focus on multielectron excitation by absorption of many photons, followed by energy redistribution within the " h o t " electron cloud and accompanied coupling to nuclear motion. As we have already seen, the efficient excitation of the electronic and the subsequent heating of the nuclear system lead to extensive fragmentation depending on the laser parameters. Many aspects of this process such as the high excitation threshold for fragmentation (kinetic shift) and the bimodal fragment distribution at high excitation energies can be explained
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very well in terms of statistical theory, essentially on the basis of knowing the energetics of the system as described, for example, by Campbell and Levine (2000). However, recent experiments give evidence also to direct, non-statistical processes driven by bond-softening and/or repulsive state crossings induced by the strong laser field. This leads back to a more molecular description of dissociation, where the system "surfs" on potential energy surfaces rather than being exclusively controlled by statistics. This coexistence will be discussed in Sect. V.B underlying the complexity of fullerenes, which are full of surprises.
A. POPULATIONOF C60 RYDBERG STATES- BEYOND THE SINGLE ACTIVE ELECTRON PICTURE
One fascinating recent experimental finding in short laser pulse interaction with C60 was the observation of very pronounced sharp structures in the photoelectron spectra on top of the ATI-peaks or a broad thermal electron background distribution by Boyle et al. (2001) as shown in Fig. 26 for several laser intensities. The structure is most clearly observed with a laser pulse duration of 1.5 ps at 800 nm wavelength with intensities on the order of 1012 W/cm 2. The left panels in Fig. 26 illustrate the photoelectron signal on a log-lin scale over a wide range of energies as essentially already seen in Fig. 22, illustrating the thermal nature of the background electron distribution. At the lowest intensity, the ATI peaks are just barely visible. The right panels show a rich structure of the photoelectron yield on a linear scale, blown up for the energy of the first ATI peak. With increasing laser intensity the structure becomes blurred as documented in Fig. 26, obviously not only due to the dramatically enhanced background signal but also due to an effective broadening of the peaks. This might be expected from the respective ponderomotive shift - if it were fully active on the observed energy levels and the ionization potential would not change correspondingly. However, as the discussion of the ATI peaks has shown (see Fig. 23), this broadening in the more intense field may also be due to electronelectron interactions. The series of peaks is seen most clearly in the lower right panel of Fig. 26 and has been studied extensively since its discovery. The observed kinetic electron energies Let were found to converge towards the photon energy hoJ. A numerical analysis based on fitting the spectra with Lorentzian line profiles gives
Eel = h v -
E B ( n i ) -~ h c o -
(19) (ni - 8i) 2
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FIG. 26. Photoelectron spectra of C60 for 800 nm, 1.5 ps laser excitation at different laser intensities. The left panels on a log-lin scale show the signal over a wide range of electron energies. For the lowest intensity, the ATI structure is just barely visible. On the right a blow up with linear yield scale show pronounced structures on top of the ATI peaks.
with Ry being the Rydberg constant, ni a quantum number of the states with binding energy Ee(ni), and 5; an almost constant quantum defect for at least two series. This allows the conclusion that the observed structures arise from single-photon ionization of high lying Rydberg states of the neutral C60 fullerene, defined by one active electron. The same series was found when using 400 and 660 nm laser radiation for excitation and detection, again converging towards the respective photon energies (Boyle et al., 2004a). By solving the Schr6dinger equation for one active electron in the jellium-like model potential Eq. (5)) adapted from Puska and Nieminen (1993), the peaks could be assigned quantitatively to the several Rydberg series (Boyle et al., 2001). These Rydberg states are assumed to be excited by a multiphoton process - whose nature warrants further discussion - and
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V(r)/E o
0 0 _
5 ~
10 I
15 I
.~ydberg levelss , ~
20 I
25 I
r/a o I
14 12
t- ground state
-0.5
10 n
8 6
-1
l=3 -1.5
o0,
l=7 i
,
,
(binding energy / eV) -1/2
FIG. 27. Left: Model potential for C60 according to Eq. (5) with ground state energy (heavy line) and some Rydberg levels (light lines). Right: Comparison of peak positions from experimental fits (open symbols) and calculated binding energies (filled symbols and lines) for = 3 (triangles), 5 (circles), and 7 (squares).
subsequently ionized by one additional photon from the same laser pulse (an assumption confirmed by independent experimental tests). As a result, one obtains binding energies of the Rydberg states involved, which are in excellent agreement with the measured kinetic energy distribution of photoelectrons as shown in Fig. 27 (right). It is quite surprising that this highly simplified model works so well, keeping in mind that the large number of delocalized valence electrons responds "simultaneously" to the external laser field. However, as illustrated by the model potential reproduced in Fig. 27 (left), together with energies of some of the observed Rydberg states, one easily verifies that once a Rydberg state is populated, its characteristic radius is significantly larger than the fullerene radius of approximately 5 A. Hence, the effective one particle treatment (SAE) of the energetic problem is a very valid approximation, the active electron interaction with the C~-0 ion core being sufficiently well described by a phase shift which in turn determines the quantum defect. The calculation shows that the observed electronically excited states correspond mainly to the Rydberg series with angular momentum quantum numbers ~ = 3 (f), 5 (h), and (j). Since in the spherical model used here the highest occupied molecular orbital of C60 (HOMO) has an angular momentum of ~ = 5 ( h ) the observed spectra result from the absorption of an effective even number of photons. At first glance, this may seem to indicate a direct excitation process of the Rydberg states. However, some important aspects warrant further discussion, mostly the observed energy mismatch E B ( n i ) - E I - n h c o between the excitation energy of the Rydberg states EB(ni) -- E1 and the n number of exciting photons. Simply speaking, it is not possible to be in resonance with all the Rydberg states at once with n photons of a given energy at these low intensities. The bandwidth of the laser (Fourier limited) is much too narrow to allow for the excitation of
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Rydberg states covering an energetic range of 1 - 2 eV depending on the photon energy. And since the spectra can be observed at very weak intensities also, broadening and energy sweeping by the ponderomotive potential (< 100 meV) as first identified as a key mechanism for atomic systems in strong fields (Freeman et al., 1987) cannot explain the Rydberg excitation process in the present case. To explain this energy mismatch and to understand the excitation mechanism, several scenarios have to be discussed and to date no finally conclusive scheme has been ascertained. At first sight, one plausible explanation might be that energy is drawn from the nuclear motion of the system. As we have already discussed in Sect. II.A, several eV of energy are stored in the 3 n - 6-- 174 vibrational modes of C60 after preparation in an effusive beam at a temperature of ~ 770 K. However, such concerted energy transfer from many nuclear degrees of freedom into the electronic system is very unlikely to happen in a direct multiphoton process. As already discussed in Sect. IIA and illustrated in Fig. 4, Franck-Condon factors are expected to be prohibitive for such a mechanism, the geometry of neutral C60 being very similar to the singly charged C+0 to which the Rydberg states converge. Thus, we expect a strong propensity for ionization without change of any vibrational quantum numbers (Av-= 0) as illustrated in Fig. 4 (right). Consequently, the probability to excite the Rydberg state manifold directly from the molecular ground state is low even when including nuclear vibrations into the p i c t u r e - as typically done in the so-called inverse Born-Oppenheimer approximation as described by Remacle and Levine (2001): in this approximation each vibrational degree of freedom (considered slow in comparison with the Rydberg orbiting time) carries its series of Rydberg levels. While this picture explains why we observe sharp Rydberg series at all, it does not give us a genuine clue as to how they may be excited in the first place. However, the situation can be rather different if we invoke excitation of intermediate electronic states during the laser pulse by single- or multi-photon processes, possibly with subsequent internal conversion (IC) or even transitions induced by the strong laser field itself through a "doorway state". Such processes have recently received great attention in the literature and a number of theoretical models have been discussed, including excitation from the ground state to an excited doorway state (Lezius et al., 2002; Markevitch et al., 2004), nonadiabatic multielectron dynamics (NMED) (Lezius et al., 2001, 2002) and field induced, time dependent potential energy crossings (Kono et al., 2003, 2004). N M E D has been used successfully to describe the dissociative ionization dynamics of different aromatic molecules as a function of their characteristic length and the extension of the re-electron delocalization (Markevitch et al., 2003,
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2004). From time-of-flight mass spectroscopy supported by results of numerical simulation, the authors developed a model of the fs-laser interaction consisting of three key elements: (i) nonadiabatic excitation from the ground state to the excited-state quasi-continuum via a "doorway" state, (ii) dynamic polarization of the entire electronic system which leads to an exponential enhancement of this transition, and (iii) sequential energy deposition in the neutral molecule and the molecular ion before undergoing fragmentation. The concept of doorway electronic states originates from the fact that the initial rate-limiting step in the nonadiabatic excitation can be regarded as a kind of bottleneck for the energy coupling into the electronic system. Recent theoretical calculations on laser-induced ultrafast dynamics in isolated C60 using time-dependent density-functional (Torralva et al., 2001) and matrix formalisms (Zhang et al., 2003; Zhang and George, 2004) reveal that even at relatively low laser intensities of 101~ ~1 W/cm 2 many electrons are excited during a typical fs-laser pulse. Note that such processes where many electrons (MAE) are sequentially excited (possibly into the same set of unoccupied levels) involve absorption of a corresponding number of photons. However, in contrast to genuine multiphoton processes, in this case we cannot glean information on the number of photons involved from the intensity dependence. Rapid thermalization of the excited electrons may then follow, first by electron interaction and on a slower time scale by electron-phonon coupling. In a classical molecular picture one would typically invoke doubly excited states and internal conversion to describe such processes. We note here in passing that similar Rydberg structures have been reported for several organic molecules (see, for example, Schick and Weber, 2001; Kuthirummal and Weber, 2003). The excitation mechanism is explained there by "superexcited" states. In the context of the finite system C60 MAE/NMED processes may be seen as the multielectron equivalent to such superexcited states. In the model calculations by Zhang et al. (2003) multielectron excitation of the LUMO + 1 level of C60 is accompanied by strong vibrational excitation and massive energy exchange with the ag(1) breathing mode. Excitation of this mode has been reported from ultrafast excitation of undoped (Dexheimer et al., 1993) and doped (Fleischer et al., 1997) C60-thinfilms. However, intuitively, in a strong oscillating electric field one would expect the hg(1) prolate-oblate mode to be excited (Bhardwaj et al., 2003) rather then the total symmetric ag modes. Nevertheless, one may envisage this mode to become active if several electrons are excited into an antibonding electronic state in which electron repulsion would tend to inflate the Buckyball. More recently, the model calculations of Zhang and George (2004) have shown that such excitation depends strongly on pulse duration
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and intensity. Although an experimental proof of such oscillating energy exchange of several eV between electronic and vibrational motion is still missing, the picture appears attractive to explain the observed nonresonant Rydberg excitation. The left panel of Fig. 28 reproduces essentially the orbital energy diagram introduced in Fig. 2 - adding the Rydberg levels at their respective binding energies as observed experimentally. Two possible scenarios, a and b, for Rydberg excitation with 800 nm photons are indicated (scenario c refers to the pump probe experiment discussed below). As seen, the (LUMO + 1)tg level is 2-photon resonant and we assume it to be the "doorway state". In the strong field its excitation is possible as documented in the right panel of Fig. 28 which reproduces the dipole response calculated in TDDFT approximation with a strong second harmonic component (Bauer et al., 2001). In addition to the already broad response which originates from electron-electron coupling the interaction with the nuclear motion (not included in the TDDFT model) may lead to a significant broadening of the excited level and to nonadiabatic, field induced coupling with other excited levels (e.g., with the LUMO tu) as indicated by thick double arrows. This may eventually also lead to internal conversion with irreversible exchange of energy between electronic and vibrational motion. Scenario (a) illustrates how we can thus picture the excitation of a lower Rydberg state from the thus populated doorway state(s) by two or three red photons. Scenario (b) indicates how high lying Rydberg states are excited. In both cases a further red photon is used for finally ionizing the system as detected by the emission of an electron (downward arrows labeled e-). We mention here, that these population mechanisms appear to be rather fast, since even when using pulses as short as 30 fs, some traces of Rydberg excitation can still be o b s e r v e d - albeit unresolved due to a spectral broadening which corresponds to the Fourier limited bandwidth. A recent pump probe study gives additional experimental evidence that N M E D may indeed be the key mechanism to understand the energetics and ultrafast dynamics of C60 in optical fs-laser fields (Boyle et al., 2004a). In these experiments a blue pump pulse of comparatively low intensity which is quasi resonant to the dipole-allowed HOMO hu ~ (LUMO + 1)tg transition deposits energy very efficiently into the electronic system. The dynamics of the energy redistribution within the excited electron cloud and accompanied coupling to the nuclear motion is then probed by a timedelayed red probe pulse. The polarization of the two pulses is perpendicular, pointing into the detector direction for the red pulse. The photoelectron spectra recorded as a function of the time-delay between 400 nm pump (1 • 1011 W/cm 2) and 800 nm probe-pulse (2 • l012 W/cm 2) are shown by the contour plot in Fig. 29(a). A cut through this contour plot for zero time-delay along the vertical dotted line is given in Fig. 29(b). It corresponds
enerqy
bindina 2-
UI
=
P z
-
.-B -1
ItiUI,lC)-l
9,
-
-0 'Iq
a
102 100 1@ 10-4 10-6 1D-'
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0
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15 20 25 Harmonic order
10
30
35
FIG.28. Left: Schematic orbital energy level diagram of C6,,(see also Fig. 2) including here the Rydberg states observed by Boyle et al. (2001) and some intermediate states (Dresselhaus et al., 1996) following the terminology applied in Zhang et al. (2003), in order to illustrate the excitation cascade. Occupied HOMO and HOMO-I states (black boxes), unoccupied LUMO and LUMO 1 states (shaded boxes), fast thermalization within the excited electrons and coupling to the nuclear vibrations (double arrow) visualized nonadiabatic multielectron effects. Three scenarios ( a x ) indicate potential excitation steps. Right: Excitation by an 800 nm 26 fs pulse calculated in the TDDFT approximation by Bauer et al. (2001) at two different intensities. The dark lines give the dipole strength during, and the gray lines after, the pulse. For details see text.
+
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FIG. 29. (a) Contour plot of the photoelectron signal as a function of the time-delaybetween 400 nm pump 1 x 1011 W/cm 2 and 800 nm probe pulse 2 x 1012 W/cm 2. (b) Kinetic energy distribution of photoelectrons for zero delay time, which corresponds to a vertical cut in (a) along the dotted line. Reproduced from Boyle et al. (2004a).
to a photoelectron spectrum which essentially reproduces the features obtained in the one color (800 nm) experiments (Fig. 2 6 ) - except for the poorer spectral widths of the peaks due to the enhanced temporal resolution. One can immediately see that in order to observe a signature of populated Rydberg states, the resonant pre-excitation of the ( L U M O + 1)tg state by the weak blue laser pulse is essential. In contrast, if the red pulse leads the blue pulse (negative time delay) almost no photoemission signal from excited Rydberg states is observed. The photoelectron yield changes dramatically once pump and probe pulse overlap, with a maximum population of the Rydberg series 50-100 fs above zero time delay. The population of the L U M O + 1 state is clearly identified as the bottleneck in the excitation cascade. It acts as a doorway to the Rydberg state population followed by single-photon ionization from the excited states. At time delays > 400 fs the signal remains nearly constant for several picoseconds. In Fig. 30 this is shown more quantitatively as recorded by the photoelectron yield from the 4g Rydberg state. The spectrum results from a cut through the contour plot along the At axis at an electron binding energy corresponding to the 4g Rydberg state. Two different blue pump intensities are compared in the left panels of Fig. 30.
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1.6 1.0 "0
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9
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FIG. 30. Left: Photoelectron signal for a kinetic energy corresponding to the 4g Rydberg state as a function of short delay times between blue and red laser pulses. Zero intensity has been set at the (low) level for negative delay times and At =0 to the turning point of the error function. Right: same on a longer time scale for 3 Rydberg levels with blue at 1 x 1011W/cm2. Red (probe pulse) is always at 2 x 1012W/cm2. Fits indicate a range of decay times for accessible excitation in the doorway state. Reproduced from Boyle et al. (2004a)
The interpretation of these experimental data has benefited from recent theoretical work by Zhang et al. (2003) already mentioned. In these simulations the laser frequency is tuned to the first dipole allowed transition H O M O h , ~ ( L U M O + 1)tg state. Hence, although their pulse duration of 10 fs and the laser intensity of 3 x 10 l~ W/cm 2 used do not exactly match the experimental conditions of the time-resolved two-color experiment, some interesting general trends described in the theoretical work are highly pertinent for the present discussion. The simulations predict, that the initial configuration of the C60 lattice and all the 60 ~ electrons occupying the 30 lowest energy levels change significantly upon laser irradiation. At the beginning of the excitation, the energy is exclusively absorbed by the electronic subsystem. The time evolution of the electron density in the excited state increases approximately linearly with increasing pump intensity. At the end of the 10 fs short laser pulse even at these low intensities about 2 electrons are excited to the ( L U M O + 1) orbital. The total absorbed energy indicates that the excited electron cloud has become slightly overheated with respect to the H O M O / L U M O + 1 band
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gap energy. As already discussed, this is followed by a very efficient coupling of electronic excitation to nuclear vibrations. Scenario (c) indicated in Fig. 28 illustrates the excitation of a lowlying Rydberg state. The main difference to the single color experiments with 795 nm is the very efficient pre-excitation with the blue pulse. Guided by these theoretical predictions it is assumed that the time-dependent electron signal in the two-color experiments shown in Fig. 30 results from the combined effect of the doorway state population due to multielectron excitation, plus an additional fast relaxing channel indicated by the hump in the photoelectron yield. The fast relaxation is attributed tentatively to a thermalization of the multiple excited electrons in the LUMO + 1 state. A relaxation time within the electronic degrees of freedom of about 95 fs is derived from a detailed analysis of the data by Boyle et al. (2004a). This value is comparable to the characteristic time for thermalization due to electron-electron scattering below ca. 100 fs, previously concluded from single pulse experiments (Campbell et al., 2000; Hansen et al., 2003). At lower blue intensity the hump disappears, indicating possibly that less electrons are injected into the excited state bands. Note that the life time of the doorway state after the pulse is over is surprisingly long as derived from the decay of the pump probe signal monitored in different exit channels. We have to bear in mind that the population of the doorway state is probed here via the population of the Rydberg states which are excited resonantly from the doorway states by two or three red p h o t o n s - as indicated by scenario (c) in Fig. 28. The extended time scale shown in the right panel of Fig. 30 show that this lifetime may be several ps up to ns, increasing with the energy stored in the doorway state. At this point, one is tempted to question again the role of initial vibrational excitation of the C60. Although that energy cannot be accessed in a direct multiphoton excitation or ionization process, energy exchange between electronic and vibrational system in the doorway state(s) as just described may significantly profit from the thermal energy stored in the system. Also, a change of the excited state geometry will change the Franck-Condon region for subsequent excitation of the Rydberg states, thus giving access to at least some of the vibrational energy content. Hence, experiments have been performed comparing "hot" (770 K) and "cold" (80 K) C60 target molecules (Boyle et al., 2004a). This may allow one to control the strength of vibrational coupling in the excitation cascade. Note, that in the "hot" C60 about 23% and 8% of the molecules are in the vibrationally excited v = 1 and v = 2 states of the hg(1) mode, respectively, while at 80 K the molecule is predominantly in its vibrational ground state with the population of the lowest vibrationally excited state being as low as 0.6%. The data have been taken in a one-color experiment with a
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FIG. 31. Comparison of photoelectron signal as a function of kinetic energy from hot (770 K) and cold (80 K) C60. Red photons of 100 fs (2 x 1012 W/cm 2) were used for Rydberg excitation and detection. The two curves are normalized to each other at an electron energy of 2 eV where only a thermal electron distribution is detected. Reproduced from Boyle et al. (2004a).
single pulse of 800 nm photons and 100 fs duration. The result is shown in Fig. 31. The photoelectron spectra recorded for hot fullerenes exhibit the rich structure of Rydberg states discussed above. In contrast, the structure has completely disappeared in the photoelectron spectrum from cold C60. Following the above discussion this may be understood in terms of the much higher population of vibrationally excited states for the hot molecule which increases the effective phonon density and consequently enhances electron-phonon coupling. Similar effects have been observed, for instance, in 2-photon photoelectron spectroscopy on silver surfaces (Knoesel et al., 1996). The coupling of electronic excitation to vibrational modes of the molecule may be viewed as giving rise to a relatively broad energy band. As seen in case of hot C60, this broadening is essential for accessing the manifold of excited Rydberg states. Without coupling, electron emission is mainly statistical. Summarizing our discussion on the population dynamics of Rydberg states in fullerenes we refer again to the energy level diagram of C60 in Fig. 28. It illustrates the main excitation steps for the one-color as well as for the two-color pump probe experiment. We must be aware of the limitations of the commonly used single-active electron picture when dealing with at least the 60 most weakly bound ~ electrons and their responses to the laser field. Multielectron excitation, electron-electron and electron-phonon
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coupling and thermalization have to be considered when describing any excitation process. As shown by T D D F T calculations, the SAE p i c t u r e although it may describe some observations for low intensity and particularly short pulses rather c l e a r l y - is not sufficient to describe the details of just the electronic response. If the nuclear degrees of freedom enter also into the p i c t u r e - which is obviously the case for Rydberg excitation as shown by comparing hot and cold target molecules- one needs to study the full picture, involving all couplings and degrees of freedom. Such a rigorous theoretical treatment would be highly desirable and one may look forward to some serious approaches which are presently undertaken by several theory groups. In the end it may turn out that a lot of the notions used p r e s e n t l y - such as NMED, time-dependent potential surfaces, field induced crossings and Autler-Townes splitting can be combined into one uniform, rigorous approach.
B. ULTRAFAST FRAGMENTATION OF C6o - BEYOND A PURELY STATISTICAL DESCRIPTION
Photoffagmentation of C60 has been studied soon after the discovery of fullerenes using nanosecond laser excitation in combination with mass spectroscopy (O'Brien et al., 1988). The characteristic bimodal distribution of heavy and light fragments was observed as mentioned in Sects. II.A and III. The large fragments C2+mobserved are formed mostly by sequential evaporation of C2 units on a time scale of nano- to microseconds. With laser pulse durations below 100 femtoseconds one observes significantly less fragments but a large amount of multiply charged ions instead, as discussed in detail in Sect. III. Here too, the large fragments observed are believed to arise from evaporative cooling of the hot C~0 ions which are formed and excited during the C60 interaction with the laser pulse. The observed metastable fragmentation on a time scale of several microseconds gives evidence for further evaporative cooling of still hot parent fragment ions with a temperature of a few thousand Kelvin. Since this is similar to the value derived after ns-irradiation of C60 one assumes that the fragmentation patterns of C60 after short pulse laser interaction are also to a large extent, of statistical origin (Campbell et al., 2001b), the major difference being a strong contribution of multiply charged species. On the other hand, small carbon cluster ions Cn+ with odd and even numbers of carbon atoms must be formed in a different manner, possibly by asymmetric fission as discussed by Rentenier et al. (2004) for fast collisional processes or by postionization of fast neutral fragments during the laser pulse. We note, however, that the abundance of such small fragment
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ions after short pulse interaction with C60 is much smaller than in the case of longer pulses (see, for example, Fig. 12). In this context, we would like to recall that using single pulse excitation in combination with "standard" time-of-flight techniques allow to detect only charged interaction products and information on neutral fragmentation can only be derived indirectly. Little is known therefore about neutral fragments which may nevertheless be byproducts of the formation of (multiply) charged large fragments C q+ 2m" Since the majority of fragmentation channels results in at least one neutral fragment (typically the smaller fragment), the pump-probe postionization method is a useful technique to study directly their formation dynamics. And from detecting initial kinetic energies one may even glean some information on the distances from the parent ion in which these fragments are ionized. In such a pump-probe experiment the first pulse initiates a (multielectron) dynamics which is then probed by a delayed pulse. The latter further excites and ionizes the C60 parent by a multiphoton process. Alternatively it ionizes already formed neutral fragments. The respective ion-yield as a function of the time delay between pump and probe, can give information on the characteristic time scales for the formation of neutrals. This technique has been previously employed by Lykke and Wurz (1992) and Lykke (1995) using ns laser pulses. They detected the interaction products C +, C +, C~-, and C +. The appearance of C + and C + was unexpected, since the fragmentation pattern of larger + + fullerenes results only peaks of C60_2n. However, C and C~- could not be necessarily assigned to the fragmentation of fullerenes, or successive fragmentation of already dissociated fragments. Furthermore, the ns time scale is quite long compared to typical times for energy redistribution. Recently, the observation of fast fragmentation of C60 using the pumpprobe postionization technique has been reported applying bandwidth limited 800 nm pulses of 120 fs duration (Boyle et al., 2004b). The shorter pulse duration compared to the pioneering work by Lykke and Wurz allows for enhanced time resolution beyond the characteristic time scales for a fully statistically driven fragmentation process. These experimental results are discussed below. Time-of-flight mass spectrometry has been used to detect the post-ionized neutral fragments. In these experiments a pump pulse at an intensity of 5 x 1013 W/cm 2 deposits energy into the electronic system by exciting one or more electrons into higher lying states (see Sect. V.A). The multielectron dynamics initiated is probed by a weaker probe pulse of 1.8 x 1013 W/cm 2, which further excites and ionizes by a multiphoton process. Figure 32 shows the formation of C +, C~-, C~-, and C~-. For negative time delays, the weak pulse leads the strong pulse and a constant signal for each fragment is observed. When the strong pulse initiates the multielectron dynamics, a dramatic increase in the C +-C~- ion
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FIG. 32. Time dependent C +, C+, C+, and C+ ion signals formed by short pulse laser (800 nm, 100 fs) interaction of C60 at 5 x 1013W/cm 2 (pump) and ionization at 1.8 x 1012 W/ cm2 (probe). For positive delay times, the stronger pulse leads the weaker pulse.
yields is observed as the separation of the pulses is changed, whereas C + exhibits nearly no dynamic behavior. At time delays > 50 ps the signal remains almost constant up to the longest time scales studied in these experiments (~100 ps). It is possible to fit the dynamics using single exponential curves with time constants of 11 ps (C +), 12 ps (C~-), and 18 ps (C~-). The time constants are found to be almost independent of the weak probe pulse energy, which indicates that the weak probe pulse is not active in the formation process of small neutral fragments (Boyle et al., 2004b). Furthermore, the absence of small fragments in single pulse experiments indicates that the small fragments are initially uncharged. The addition of the second pulse excites and ionizes these neutral fragments by multiphoton absorption. It is important to note that although a rapid formation of small neutral fragments is observed, it cannot be distinguished whether they come directly from a fullerene-like fragment or from another fragment that has dissociated before, for example, Cs. Future fs-laser experiments, using the postionization method in combination with the photoion-photoion coincidence technique with a position sensitive detector will clarify this aspect. Pioneering coincidence experiments have been performed by Vandenbosch et al. (1998), in order to study fragmentation partners using collisional dissociation of 75-keV C60 with H2 gas. They have shown that odd-n as well as even-n light fragments are fragmentation partners to even-n heavy fragments, indicating a sequential decay. The combination
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of the coincidence information with the time resolution of the pumpprobe technique will allow one to obtain an almost complete picture of the ultrafast fragmentation dynamics. Unfortunately, the time resolution in the above discussed one-color experiments was limited by interference fringes once pump and probe pulses overlap in time. Consequently, it was not possible to reach the limit given by the laser pulse duration of 120 fs. Nevertheless, even with the present resolution of 2-3 ps we can conclude that fast fragmentation processes of C60 happen at a time when its internal energy is not completely equilibrated among all degrees of freedom and thus fragmentation is not purely statistically driven. However, the measured time scale for the formation of small neutral fragments in the ps-range suggests that electronic energy has already been transferred to some extend into nuclear vibrations via electron phonon coupling. For isolated fullerenes, Hansen et al. (2003) have recently determined this coupling time to be ~240 fs by modeling experimental Penning ionization data. The Penning ionization yield depends on electron emission and coupling to the nuclear degrees of freedom. The electronic density of states of C60 and the Penning ionization yields was used by Hansen et al. (2003) in order to determine a single fitting parameter, the electron-vibration coupling time constant. This model, however, is again purely statistical and does not provide insight to systems not in equilibrium. On the theoretical side, ultrafast fragmentation of C60 after fs-laser pulse excitation has been simulated by Torralva et al. (2001) and Jeschke et al. (2002). It was found that the laser field efficiently excites the ag(1) breathing mode accompanied by fragmentation on a subpicosecond time scale. Torralva et al. (2001) used a combination of tight-binding electron dynamics and density-functional theory to simulate the ultrafast response of C60 exposed to fs-laser fields. With a 10-fs laser pulse of 2.0 eV photon energy, they predict the excitation of the ag(1) and the ag(2) vibrational modes for low fluences (0.006 J/cm2). As the fluence increases, fragmentation occurs. The lowest fluence producing fragmentation within 1 ps derived from these calculations is 0.117 J/cm 2, which corresponds to an intensity of "-~1013 W/cm 2. A different theoretical model was used by Jeschke et al. (2002). They considered tight binding energy levels with a time-dependent fractional occupation number. For a laser pulse of 80 fs duration, which deposits 3.5 eV per atom into the system, they found that the cage is torn open 90 fs after the pulse maximum and begins to fragment at 140 fs. These calculations indicate that nonadiabatic multielectron effects discussed in Sect. V.A in the context of the Rydberg population mechanism are also active in the fragmentation processes of the molecule.
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The pump-probe postionization experiments on small neutral fragments seem to be able to access this new regime of ultrafast fragmentation dynamics predicted by theory. To investigate the formation in more detail, analog time-resolved two-color pump-probe measurements are currently on the way. These will allow one to look into the sub-ps time regime and resolve the influence of electron-phonon coupling.
VI. Conclusion and Outlook It is hoped that this report gives a useful introduction to the present status of ultra fast laser interaction with C60 as a model case for a large finite system with many active electrons and vibrational degrees of freedom. Since we have summarized the results of the different aspects touched in this review at the end of each individual chapter we may refrain here from repeating this effort. We remind the reader that most of the observations and insights discussed here have emerged during the last few years. A variety of new phenomena has emerged from these studies and much has been learned about this ever fascinating object C60 exposed to hitherto unused conditions in strong, (but not too strong) laser fields. We are, nevertheless, still far from fully understanding the intricacies of intense field interaction with such a relatively complex system. The directions to continue this research have been indicated as far as obvious. On one hand, rigorous theoretical efforts are needed to quantitatively explain the key aspects of the experimental observations presented here and those to emerge in the near future: the nature of the ionization processes beyond the simple above barrier ionization model, the fragmentation mechanisms which produce predominantly multiply charged fragments, the excitation dynamics for the population of Rydberg states, mechanisms for ultrafast fragmentation, the long lifetimes observed in the doorway state. On the other hand, further experimental work is desirable (Boyle et al. 2004b) - preferentially with even shorter pulses (Shchatsinin et al. 2004) and better tunability of the fs light sources to perform sophisticated and direct multi color pump probe experiments. Experimental detection schemes need to become more sophisticated, e.g., the full exploitation of state-of-the-art techniques for dynamical imaging promises a whole new multi dimensional view into the dynamics discussed here. One other fascinating aspect of this type of pertinent subject might be quantum or optimal c o n t r o l - presently an extremely active and fascinating field of research applicable to a broad range of topics (see, for example, Levis and Rabitz, 2002; Rabitz, 2003). Assume we would like to do more than just study the fragmentation patterns of C60 after interaction with an intense laser pulse as documented by the mass spectra we have discussed.
2
a
FIG.33. First results from a fragmentation experiment with temporally shaped pulses. The lower left panel shows a “standard” C60 mass spectrum after interaction with a 50 fs 800 nm laser pulse. Its temporal and spectral profile is shown in the lower right panel as obtained from an X-FROG analysis. The mass spectrum in the top left panel documents a mass spectrum after 100 generations of iterative trial to maximize the C l fragment. The temporal and spectral characteristics of the pulse responsible for this mass spectrum is given in the top right panel.
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Could we try to modify these fingerprints of the interaction at will? We just show one of the first examples of such studies presently emerging from our laboratory (Schulz et al., 2004). Using temporally shaped laser pulses one may try to amplify specific fragmentation reactions rather than just compare short and long laser pulses as shown in Fig. 12. Figure 33 shows how one may with such shaping techniques optimize the fragment C~- ion. A signal enhancement of about 10 is found when C60 is exposed to the structured multiple pulse characterized by the pattern in the upper right panel as opposed to a short 50 fs pulse of equal total fluence. Presently there is not even a clue of how to understand this observation in terms of the fullerence dynamics in strong fields discussed in this report. We are, however, confident that with detailed analysis and strong theoretical support such patterns will help us to reveal a much more detailed insight into these processes in the near future.
VII. Acknowledgments Financial support from the Deutsche Forschungsgemeinschafl through Sonderforschungsbereich 450 is gratefully acknowledged, as well as support from the BMBF through VDI programme GILCULT, FKZ: 13N7958.
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Index ab initio calculations, 33 Above threshold ionization (ATI), 222-3, 234-6, 255-60, 262 Absorption, 117 Absorption spectroscopy, 19 Adiabatic potential curves, 35 ADK ionization rates, 252 ADK model, 253 Aharanov-Bohm effect, 75 Aharanov-Casher effect, 75 Allan standard deviation, 80 Altitude variation of isotopic composition of oxygen in stratospheric CO2, 49 Anderson experiment, 25 Angular isotope effect, 27 Anisotropic medium, atom interaction with, 106 Anisotropy effects in vW shift, 136 Annihilation, 206-7 detection, 183 imaging, 175 Antihydrogen, 156 ls-2s transition frequencies, 165 beyond counting, 185-95 chaotic trajectories, 191 cold antiprotons, 168-70 comparing production methods, 200 energies involved in production, slowing and trapping, 167 future directions, 200-8 ground state, 200 ingredients, 168-75 low-temperature, 160 methods of production, 158 number of atoms detected is linear, 181
number of atoms surviving ionization field, 189 production of, 180 required properties, 159 Antimatter, atoms entirely of, 155-217 Antiprotons, 156-7, 208 accumulation with deceleration, 170-1 axial energy loss, 179 driven eS + s cooling, 180 losses from nested Penning trap, 182 lost while being driven from one side of nested Penning trap, 181 magnetic moment, 162 numbers that can be accumulated, 169 positron cooling, 160, 175-80 stacking techniques, 157-8 Antiproton Decelerator (AD), 170-1, 176 Antiproton-to-proton charge-to-mass ratio, 163 Antiquark, 164 Anti-Rydberg constant, 165 ASACUSA collaboration, 171 Asymmetric fission, 241,273 Asymmetric ozone molecules, 21 ATHENA, 158, 160-1, 168, 172-3, 175, 180, 182-4, 194, 209 rate of production as function of elevated, 193 Atmospheric ozone photoanalysis, 21 Atom chips, 82-3 Atom guides, 60 Atom holography, 56, 59 Atom interaction with anisotropic medium, 106 with nanobodies, 144-6 287
288
Index
Atom interferometry, 55-89 foundations of, 74-5 state-of-the-art, 73-82 tests of quantum mechanics, 73-4 Atom mirror, 67 Atom optical tools, 56-8 Atom optics, 55-89 with evanescent waves, 56 Atom-atom interaction in tightly confined medium, 140 long-range, 93 Atom-by-atom implantation, 93 Atom-surface distances, 144-5 Atom-surface distance, ranges, 96 Atom-surface interaction, 94, 140 in resonant situations, 133-4 long-range, 93 principles and near-field limit, 94-106 near-field, 94 probing of, 107-25 vW, 140 Atom-surface problem, 93 ATOMICS, 59 Atomic beam, surface-induced inelastic transfer in, 142-4 Atomic diffraction, 108-9 Atomic Hamiltonian, 95 Atomic lifetime, 93 Atomic matter control at quantum level, 56 wave properties, 55 Atomic oxygen concentration, 18 Atomic quantum states, 63-4 Atomic relaxation rate, 104 Atomic resonance, 57 Atomic Sagnac effect, 75, 78 Atomic Sagnac interferometers, 76 Atomic structure, 93 Atomic symmetry, 99 Atomic-wall interaction, long-range regime, 91-154 Atoms in intense laser fields, 233-6 Atoms, entirely antimatter, 155-217
ATRAP, 158-9, 161, 172-6, 179-80, 182-3, 185-6, 191, 194, 196, 198, 203-4, 207, 209 Attenuated Total Reflection (ATR), 122-3 Attractive behavior, 145 Autler-Townes splitting, 258 Auto-charge transfer (ACT), 241 Autocorrelation function, 237-8 Auto-ionizing levels, 101 Average dipole fluctuations, 98 Average trajectory lifetime, 37 Axial well depth, 178 Axiomatic quantum field theory, 163
Baryon (antibaryon), 163-5 Beam splitters, 60 BEC, 56, 58, 66, 68, 71, 73, 83 and optical dipole potentials, 67-9 Bragg diffraction of, 71-2 coherence, 69, 72 continuous, 67 density modulations, 70 expansion of, 68-9 experimental work, 66-7 in highly elongated magnetic potentials, 69-71 macroscopic coherent transport, 67 multi-component, 67 nature of, 66 non-equilibruim, 70 optical realization, 67 phase-fluctuating, 69 reflection and guiding, 67-9 transition temperature, 69 Binding energies, 189, 197 Binding energy, 242, 260-1,263-4, 276 Blue detuning, 57, 67 Bonding techniques, 60 Born-Oppenheimer approximation, 265 Born-Oppenheimer potentials, 206 Bose-Einstein condensation see BEC Bragg diffraction, 71-2, 76
Index Bragg pulses, applications of, 71-2 Bragg spectroscopy, 70 Branching ratio, 19
C3 coefficient, 128-31, 141 comparing experimental values with theoretical predictions, 130-1 consistency of vW determination, 129-30 fitting method, 128-9 C60, 219-86 degrees of freedom, 221 dynamics, 222 energetics, kinetics and properties, 223-40 experimental and theoretical studies, 221 experimental aspects, 236-40 ionization, charge states and fragmentation, 240-54 isolation, 220 outlook, 277-9 potential responses, 260 resilience of, 241 simple model potential, 232-3 Casimir attraction, 92 Casimir effect, 147 Casimir-Polder expansion, 108-9 Casimir-Polder limit, 97 Cavity QED, 93-4 CERN Antiproton Decelerator (AD), 156 CERN PS-200 Collaboration, 168 Chapman-reactions, 4-5 Chappuis bands, 9 Charge conjugation transformation, 163 Charge-to-mass ratios, 157 Circular guiding center, polarized and ionized by electric field, 187-8 Clusters in intense laser fields, 233-6
289
C02, 43-4 isotopic equilibration, 47 stratospheric, 46 CO2 laser, 200 Coherence length, 70, 111-12 Coherent atom optics, 66-72 Coherent beam splitting, 76 Cold and ultracold collisions, 56, 64 Cold antiprotons for slow antihydrogen experiments, 168-70 Cold atom Sagnac interferometer, 77 Cold atom technology, 109-10 Cold free-falling atoms, 75 Cold positrons, accumulation methods, 171-3 Collisions cooling via with He atoms, 206 with hydrogen, 205 Collision energy, 37 Collision products, 243-4 Collisions, annihilation and vacuum, 206-7 Collisions with matter, 205 Collisional dissociation, 275 Collisional processes, 273 Complete basis set (CBS), 32 Cooling mechanisms, 221 Cooling via collisions with He atoms, 206 with hydrogen, 205 Cosmological constant, 92 Coulomb field, 249 Coulomb force, 190, 200 Counting techniques, 182-5 Coupling to nuclear motion, 260-77 CPT invariance, 163-4 testing, 162-6 CPT violations, 166 Cs atom, 101
Debye length, 180 Debye screening length, 203 Deexcitation, 191, 194-6
290 Delayed ionization, 241,244 Density of states, 39 Depletions, 4, 16-17 Desorption processes, 93 Detection techniques, 184-5 Diagonal interaction, 142 Dick-effect, 82 Dielectric image coefficient, tunability, 107 Dielectric medium index, 104 Dielectric medium, interaction with, 101-3 Dielectric permittivity, 106 Dielectric reflection coefficients, 102 Dielectric resonances, 102 Dielectric solid bodies, interaction between, 101-2 Dipole atomic fluctuations, 98 Dipole fluctuations, 140 Dipole force, 57 Dipole orientation, 103 Dipole potential, 57 Dipole traps, 63-4 Dispersive Voigt profile, 112-13 Dissociation energy, 28 Dissociation methods, 8 Dissociative lifetime, 38 Doppler broadening, 114-15, 124 Doppler cooling, 81 Doppler shift, 119-20 Doughnut beams, 68 Doughnut waveguide, 69 Dual trap collector system, 43-4 Dynamical imaging, 277 Dynamical processes, 221
Earth's atmosphere, ozone isotope effect, 40-8 ECR ion source, 230 Elastic scattering channel, 205 Electric discharge, 8 Electrode cross sections, 177 Electromagnetic field, 233 Electromagnetic field fluctuations, 92
Index Electromagnetic interaction between two metal plates, 96 Electromagnetic oscillation, vacuum wavelength of, 97 Electron-electron coupling, 272-3 Electron-electron interaction, 258 Electron impact ionization, 228 Electron magnetic moment, 166 Electron plasma, 172 Electron-phonon coupling, 244, 266, 272-3, 277 Electron-vibration coupling time constant, 276 Electronic damping, 172 Electronic ground state, 29 Electronic resonances, 248 Electrostatic image induced in reflector by charged dipole system, 95 Electrostatic interaction, 96 Electrostatic model, 101 Electrostatic quadrupole, 202, 204 Electrostatic quadrupole potential, 174 Endothermic processes, 6 Energetic threshold, 227-8 Energy level scheme, 139 Energy mismatch, 265 Energy redistribution, 260-77 Energy shift, 93, 95, 103 Energy spectra antiprotons trapped from single pulse from AD, 169 hot protons and cooled protons, 176 Energy transfer processes, 244-5 Enhancement, 161 Enrichments, 4, 9-10, 16-17, 21, 40, 44-8 reliable measurements, 49 stratosphere, 50 troposphere, 41, 50 Entanglement of atoms, 64 Evanescent wave (EV) spectroscopy, 122-4 Evaporation, 221,229 Evaporative cooling, 58
Index Exchange reactions, 6, 10, 14, 17, 21, 32-6 cross sections, 33 isotope dependence, 34-6 rate coefficients, 33-4 temperature dependence, 33-4 Excitation mechanism, 265 Excited atom, 93 in front of reflector, radiative and ZS-3s near-field behaviors, 97 near-field modification of lifetime, 103-5 Excited state, 102 Exothermic exchange reactions, 24 Exothermic processes, 6 Extra-decay channels, 103 Extremely Thin Vapor Cells (ETC), 136-9
F6rster-like energy transfer induced by near-field coupling to surface, 134-5 Fabry-Perot behavior, 137 Far-field effects, 97 Field-assisted formation, 161 Field ionization detection, 159, 161, 183-5, 209 Field ionization method, 209 Field ionization spectrum, 186-9, 196 Fractionation, 17, 44 temperature dependence, 10 Fractionation factor, 48 Fractionation ratio, 21 Fragmentation, 227, 229-31,240-50 experiment with temporally shaped pulses, 278 mechanisms, 277 patterns, 277-8 Franck-Condon factors, 227 Franck-Condon region, 271 Frequency-dependent dielectric permittivity, 102 Fresnel formulae, 110
291
Fullerenes, 219 FWHM, 238
Gas mixtures, 10, 13 Gas-phase process, 50 Gas slowing method, 173 Gaussian beams, 238-40 Gravitational properties, 167 Gravity tests, 166-8 Ground state atom and perfect reflector: from London-van der Waals interaction to retarded Casimir-Polder limit, 95-7 Ground-state PES, 30-1 Guided atoms, 55-89 interferometer-type structures, 61 splitting process, 62 Guiding center approximation, 197, 202 Guiding center atoms (GCA), 186, 189-91, 196-7, 204-5
Half-Maxwellian, 114 Hartley bands, 8, 31 Heavyside function, 102 Helium gas cooling, 206 Heterogeneous process, 10 High harmonic generation (HHG), 235 High-lying states, 101 Hollow laser beams, 56 Hybrid trap, 67 Hydrogen l s-2p resonances, 208 spectroscopy, 166, 201 HYPER, 78 Hyperfine-dependent broadening, 101
Illumination with UV light, 8 Image coefficient, 101-2 Image factor, 102 Inertial atomic quantum sensors, 76-8 Instantaneous (near-field) approximation, 96
292
Index
Integrated atom optics, 56, 58-66 Integrated magneto-optical trap (MOT), 65-6 Integration, future prospects, 64-6 Intense laser fields, 233-6 Intense laser pulses, 222, 277-8 Interaction Hamiltonian, 106 Interaction potential, 95 Interatomic potential, 93 Interferometer for atomic clouds released from optical waveguide, 72 Interferometer-type structures for guided atoms, 61 Internal atomic structure, 62 Internal energy content, 225 Internal oscillation, 175 Intramolecular coupling, 38 Intramolecular energy redistribution, 26 Ioffe trap, 157 Ionization potential, 186, 233 Ionization processes, 277 Ionization threshold, 225-7 Ionization well, 183 IQ (Institut ffir Quantenoptik), 77 IR spectra, 225 Isotope dependence, exchange reaction, 34-6 Isotope-specific channels, 6 Isotope-specific ozone formation rate coefficients, 49 Isotopically-enriched oxygen mixtures, 2 Isotopologues, 2-6, 9-10, 14, 16, 21, 23, 39, 45, 47
K mesons, 164 Keldysh parameter, 235, 244, 246-7, 256 Kinetic isotope effect in ozone formation, 17 Kohn-Sham (KS) orbital, 254, 257, 261
Laboratory experiments, 3 Laser-controlled production, 158, 161, 198-200, 209 Laser cooled magnesium atoms, 79 Laser cooling and trapping, 56, 59 Laser-induced ultrafast dynamics, 266 Laser intensity, 245, 247, 251,256, 263 and wavelength, 246 Laser intensity dependence, 250-4 Laser pulse duration, 245, 259 Laser pulse interaction studies, 236 Laser pulse profile, 239 LDA, 225-6 LEAR, 170, 176 Lense-Thirring effect, 78 Leptons, 164-6 Level crossing induced by surface resonance, 138-9 Lindemann-Hinshelwood mechanism, 26 Liquid-crystal displays, 65 Long-range electromagnetic coupling, 146 Lorentz invariance, 166 Lorentzian line profiles, 262 Lorentzian resonance, 112 Lorentzian response, 114 Lyman alpha photons, 167 Lyman alpha radiation, 207-8
Mach-Zehnder type geometry, 75 Mach-Zehnder-type interferometer, 74, 76-7 Mach-Zehnder-type structures, 62 Magnetic manipulation, 58 Magnetic trapping, 58, 68, 70 Magneto-optical trap (MOT), 65, 77 Magnetron motion, 203 Magnetron orbits, 202 Malmberg-Penning trap, 203 Malmberg trap, 202 Many active electrons (MAE), 223, 250, 257-8, 266
Index Mass independence, ozone isotope effect, 3 Mass spectra, 219-21,231,240-50, 277-8 Mass spectrometer beam system (MSBS), 14, 18 Mass spectrometry, 43 Mass-dependent fractionation, 10, 41 Mass-dependent relationship of symmetric molecules, 16-17 Matsubara frequencies, 141 Medium anisotropy, 106 Mesons, 164-5 Metastable atoms, 143 monokinetic incident beam of, 144 Metastable beam transmission, 109 Michelson-type structures, 62 Micro-fabricated magnetic or current carrying structures, 59 Micro-fabricated mechanical systems, 59 Micro-fabricated optical elements, 60 Micro-fabricated optical systems, 59 Micro-fabrication technologies, 65 Micro-lenses, 61 Micro-optical components, 60, 64-5 Micro-optical elements, 59-60, 82 Micro-optics, overviews, 60 Micro-opto-electro-mechanical systems (MEMS), 65 Microwave discharge, 8 Mie resonance, 226 Miniaturized magnetic trapping and guiding structures, 58 Miniaturized sources of ultracold atoms, 65 Molecular dynamics, 26 Molecular oxygen, 19, 50 Molecular symmetry, 2, 20 Molecules in intense laser fields, 233-6 Monokinetic incident beam of metastable atoms, 144 Multi-level atoms, 57
293
Multielectron excitation processes (MAE), 260-1,266, 272-3 Multiphoton experiments, 222 Multiphoton ionization (MPI), 242, 249, 251
Na BEC, 67 Nanobodies, atom interaction with, 144-6 Nanocell spectroscopy, 136-40 Nanogratings, 108 Nanotechnologies, 93 Narrow-line cooling, 81 Nd:YVO4 82 Near-field effects, 97 Near-field electrostatic approximation, 98 Near-field modification of lifetime of excited atom, 103-5 Nested Penning trap, 158, 160, 175-86, 197, 208-9 Neutral atoms, 63-4 Neutral particle trap, 161 Neutron interferometers, 74 NIST, 172 Nonadiabatic multielectron dynamics (NMED), 222, 265, 267, 273 Nonlinear selective reflection, 120-2 Nonlinear spectroscopy, 120-2 Nuclear fusion, 222
One-electron quantum cyclotron, 166 Optical absorption spectra, 223-4 Optical clocks, 75, 79-82 Optical dipole force, 57 Optical dipole potentials, 60, 67-9 Optical frequency, 79 Optical lattices, 56 Optical methods, 59 Optical micro-structures, 58-66 Optoelectronic devices, 65 Orbital energy level diagram, 268
294 "Over the barrier" model, 252-3 Overall interaction potential, 252 Oxygen, stable isotopes, 5 Oxygen isotope distribution, 48 Oxygen isotope exchange reaction, 3 Oxygen isotope mixtures, 15 Oxygen mixtures, temperature dependence, 7 Oxygen-ozone system, 2 photochemistry, 4-8 Ozone complex, 28 formation, 26 formed in O and O2 collisions, 36-40 lifetime of, 36-40 Ozone condensation, 44 Ozone formation, 26 classical trajectory study, 27 in isotopically enriched oxygen mixtures, 10-17 kinetic isotope effect in, 17 Ozone formation channels, 17-18 Ozone formation rate equation, 5 Ozone isotope, 4 distributions, 13 formation, 2 measurements, 6 produced in natural oxygen, 8-10 research, 50 signature, 8 transfer to stratospheric CO2, 46-8 Ozone isotope analysis, 40 Ozone isotope anomaly, 2, 21 Ozone isotope effect assessment of, 1-54 Earth's atmosphere, 40-8 mass independence, 3 model development, 26 overview, 1-4 roots in molecular symmetry, 17 state-of-the-art description, 2 stratosphere, 42-5 theoretical perspectives, 26-40 troposphere, 41-2 use of term, 9
Index
Ozone isotope studies, results and discussion, 9-10 Ozone isotopomer quantification, 19 Ozone loss process, 7 Ozone photolysis, 7 Ozone production, 10 Ozone production, pressure, and temperature effects, 8-9 Ozone-specific enhancement, 11 Ozone-specific isotope effect, magnitude of, 10 Ozone studies, results and discussion, 15-17
Parity transformation, 162 Particle-wave dualism, 73 Penning-Ioffe trap, 201,203 Penning ionizaton data, 276 Penning trap, 161, 173-6, 198, 204 electrodes, 201 with radial Ioffe magnetic field, 202 Permittivity coefficients, 106 Phase factor, 111 Phase modulation factor, 111 Phase-space theory (PST), 35 Photoelectron spectra, 255-7, 259, 263, 269, 272 Photofragmentation, 240, 273 Photoion yield in single photon ionization, 226 Photolysis-recycling, 8-10, 14 Photon energy, 161,249 ~r-electron delocalization, 265 Photon ionization experiment, 229-30 Photon scattering, 57 Photonic device, periodicity of, 145 Planar optics, 65 Plasma diagnostics, 173-5 Plasma temperature, 175 Plasmon resonance, 251 Polarization correction to cyclotron frequency of molecular ion, 162
Index Ponderomotive potential, 234 Population dynamics, 272 Position dependent laser intensity, 57 Positrons, 156, 179 Positron cooling of antiprotons, 160, 175-80 production method, 209 Positron-electron CPT test, 166 Positronium method, 172 Postionization, 273 Potential energy surface (PES), 26-7, 29-33, 51 two-dimensional representations, 30 Power laws, 250-4 PPKTP, 82 Precision atom interferometry, 74-5 Pressure dependence of ozone isotope enhancement in natural oxygen, 12 Pressure dependence of ozone isotope fractionation, 12 Probing internal orbits, 185-6 Proton (antiproton), 157, 163-4 Pulse durations, 248, 250 Pump-probe postionization, 274, 277 Pump-probe study, 267 Pump-probe technique, 276
Quantum chaos, 56 Quantum chemical methods, 232 Quantum control, 59 Quantum electrodynamics (QED), 92 Quantum gate operations, 64 Quantum information processing, 56, 58-66, 83 Quantum mechanical calculation, 33, 38 resonance lifetimes, 37-40 Quantum mechanical dynamics calculations, 40 Quantum mechanical effects, 34 Quantum mechanical resonance calculations, 51 Quantum mechanical study, 39 Quantum mechanics, 103
295
Quantum mechanics, atominterferometric tests, 73-4 Quantum optical techniques, 58-9 Quarks, 164 Quasicondensates, physics of, 70 Quench cooling, 81 Quench MOT, 81-2
Radiofrequency quadrupole decelerator (RFQ), 171 Raman interaction, 74 Raman interferometer, 76 Raman spectra, 225 Raman transitions, 74 Ramsey-Bord6 interferometry, 74-5, 79-82 Ramsey-type interferometers, 74 85Rb, 62-3 87Rb, 67 Rate coefficient, 2, 17-26, 27, 39, 50 concepts and experiments, 17-20 dependence on temperature, pressure, and third body, 22-6 exchange reactions, 33-4 pressure dependent, 49-50 results of measurements, 20-2 temperature dependent, 49-50 Rate coefficient ratios, 3 Rate equations, 18 Rayleigh length, 238 Recollision, 235, 249 Reflection coefficient, 110 Reliable measurements, enrichments, 49 Remote sensing, 43 Repulsive behavior, 145 Resonance lifetimes, 51 quantum mechanical calculation, 37-40 Resonance spectrum, 38 Resonant atom-surface coupling, prediction of, 132-3 Resonant atomic response, 112-14
296
Index
Resonant coupling, measurement of vW surface interaction, 133-4 Resonant long-range coupling between surface mode and excited atomic level, 132-4 Resonant near-field atom-surface coupling, 134 Resonant reflected field, 111 Resonant reflectivity change, 110 RETOF mass spectrometer, 250 RRKM, 229 RRKM model, 29, 32, 35 RRKM theory, 28, 50 Rydberg atoms, binding energies of, 200 Rydberg constant, 165 Rydberg electron, 261 Rydberg excitation, 267 Rydberg levels, 108 Rydberg population, 276 Rydberg state, 198-9, 223, 227, 232, 260-73, 277 Sagnac phase, 77 Sapphire, 104 Saturation intensities, 237, 252-3 Schr6dinger equation, 263 Selective Reflection (SR) spectroscopy 120-2, 145 atomic response and atomic motion, 112-15 atomic trajectories, spectroscopy vs. mechanical effects, 119-20 basic principle, 110-12 de-excitation at arrival onto surface, 118-19 diagnostics tool of atom-surface interaction, 125-35 finite Doppler width, 119 frequency-modulated lineshapes, 114-18 linear, 126-8 lineshapes, 114 beyond several simplifying approximations, 117
in presence of atom-surface interaction potential, 115-17 multiple nonlinear spectroscopy beam, 121-2 normal and oblique incidence, 119 pseudo-thermal pumping in excited state, 122 saturation with single irradiating beam, 121 symmetry of velocity distribution, 118 theoretical lineshape, 113 thin vapor film, micro- and nano-cells, 124-5 under normal incidence, 123 vW interaction, 126-8 Shake processes, 231-2 Short pulse lasers, 221-2, 237 Signal-to-noise ratio (S/N), 80 Single active electron (SAE), 223, 250, 252, 257, 260-73 Single electron energy level diagram, 224 Single photon absorption, 223 Single photon ionization, 225 photoion yield in, 226 Slow antihydrogen atoms, speed measurement, 191-4 SMOW (Standard Mean Ocean Water), 47-8 Spatial correlation function, 70 Spatial light modulators (SLM), 65 Spectroscopic analysis, 19 Spectroscopic data, 51 Spectroscopy, 166 Spontaneous absorption, 140 Spontaneous scattering process, 57 Stabilization process, 26, 29, 51 Stark effect, 236 State-selective guided-atom beam splitter, 62 State-selective optical potential, 62 Storage ring for antihydrogen experients, 170
Index Stratosphere enrichments, 50 ozone isotope effects, 42-5 Strong field regime, 234 Sub-Doppler logarithmic singularity, 114 Superimposed hollow laser beam, 68 Superposition principle, 73 Surface-induced effects, 137-8 Surface-induced inelastic transfer in atomic beam, 142-4 Surface-induced matastability transfer, 143 Surface interaction potential, 96 Surface resonance, 103 level crossing induced by, 138-9 Surface response, change in, 145 Surface vicinity probing, 110-20 Symmetry effects, 27 SYRTE (Syst6mes de R&6rence Temps-Espaces), 77
TDDFT, 254-7, 259, 261,267, 273 Temperature dependence exchange reactions, 33-4 heavy ozone enhancement in natural oxygen, 11 isotope fractionation, 10 kinetics, 2 Theoretical concepts and models, 3 Thermal beam method, 107-9 Thermal effects, 140-2 Thermal gas-phase decomposition, 7 Thermionic emission, 224, 241 Three body formation, 194 and related experiments, 195-7 Time-dependent fractional occupation number, 276 Time-dependent ion signals, 275 Time-of-flight mass spectrometry, 274 Time-of-flight mass spectroscopy, 266 Time reversal transformations, 163 Total angular momentum, 37
297
Transition frequency, 102 Transition state (TS), 28-9, 32-3 Transmission grating, 109 Transparent dielectric medium, 103-4 TRAP, 168, 209 Trapped electrons, 174 Trapped ions, 174 Trapped plasma, density and spatial distribution, 174 Trapping, 157, 200-5 excited states, 204 proposed trapping alternatives, 204 Triatomic molecules, 28 Troposphere enrichments, 50 ozone isotope effect, 41-2 water contamination, 47 Tunable diode laser (TDL), 19 Tunable laser source, 139 Tunneling, 34
Ultracold atoms, minaturized sources of, 65 Ultrafast fragmentation, 273-7 UV photo-dissociation, 19
Vacuum ultra-violet (VUV) range, 101 Vacuum wavelength of electromagnetic oscillation, 97 van der Waals (vW) anisotropy and surface-induced inelastic transfer in atomic beam, 142-4 van der Waals (vW) atom-surface interaction, 125 observation through mechanical effects, 107-10 van der Waals (vW) attraction, 92 van der Waals (vW) Hamiltonian, 98-9 van der Waals (vW) interaction, 100, 102 anisotropy in, 135 between two solids, 147 in linear SR spectroscopy, 126-8
298 van der Waals (vW) interaction potential, 100 van der Waals (vW) repulsion, 103 van der Waals (vW) shift, 97-101, 102 anisotropy effects in, 136 Vibrational excitation, 271 Vibrational modes, 265 Virtual couplings, 99-100 Virtual emission, 103
Index Virtual transitions, 97-101 Volume resonances, 138 Wave properties of atomic matter, 55 YAG, 104 Zeeman components, 135, 142 Zeeman structure, 136 Zero-point energies (ZPE), 6, 21-2, 27-8, 34-7
Contents of Volumes in This Serial
Volume 1
Molecular Orbital Theory of the Spin Properties of Conjugated Molecules, G. G. Hall and A. T. Amos
Electron Affinities of Atoms and Molecules, B.L. Moiseiwitsch Atomic Rearrangement Collisions,
Experimental Studies of Excitation in Collisions between Atomic and Ionic Systems, F.J. de Heer Mass Spectrometry of Free Radicals, S.N. Foner
Volume 3
B.H. Bransden
The Production of Rotational and Vibrational Transitions in Encounters between Molecules, K. Takayanagi
The Study of Intermolecular Potentials with Molecular Beams at Thermal Energies, H. Pauly and J.P. Toennies High-Intensity and High-Energy Molecular Beams, J.B. Anderson,
The Quantal Calculation of Photoionization Cross Sections, A.L. Stewart
Radiofrequency Spectroscopy of Stored Ions I: Storage, H.G. Dehmelt Optical Pumping Methods in Atomic Spectroscopy, B. Budick Energy Transfer in Organic Molecular Crystals: A Survey of Experiments, H. C. Wolf
R.P. Andres and J.B. Fen
Volume 2
The Calculation of van der Waals Interactions, A. Dalgarno and W.D. Davison
Thermal Diffusion in Gases,
Atomic and Molecular Scattering from Solid Surfaces, Robert E. Stickney Quantum, Mechanics in Gas CrystalSurface van der Waals Scattering, E. Chanoch Beder
Reactive Collisions between Gas and Surface Atoms, Henry Wise and Bernard J. Wood
E.A. Mason, R.J. Munn and Francis J. Smith
Spectroscopy in the Vacuum Ultraviolet, W.R.S. Garton
The Measurement of the Photoionization Cross Sections of the Atomic Gases, James A.R. Samson The Theory of Electron-Atom Collisions, R. Peterkop and V. Veldre
Volume 4
H.S.W Massey- A Sixtieth Birthday Tribute, E.H.S. Burhop Electronic Eigenenergies of the Hydrogen Molecular Ion, D.R. Bates and R.H.G. Reid
299
300
C O N T E N T S OF V O L U M E S IN THIS SERIAL
Applications of Quantum Theory to the Viscosity of Dilute Gases, R.A. Buckingham and E. Gal Positrons and Positronium in Gases, P.A. Fraser Classical Theory of Atomic Scattering, A. Burgess and L C. Percival Born Expansions, A.R. Holt and B.L. Moiseiwitsch Resonances in Electron Scattering by Atoms and Molecules, P.G. Burke Relativistic Inner Shell Ionizations, C.B.O. Mohr Recent Measurements on Charge Transfer, J.B. Hasted Measurements of Electron Excitation Functions, D.W.O. Heddle and R.G. W. Keesing Some New Experimental Methods in Collision Physics, R.F. Stebbings Atomic Collision Processes in Gaseous Nebulae, M.J. Seaton Collisions in the Ionosphere, A. Dalgarno The Direct Study of Ionization in Space, R.L.F. Boyd
Tables of One- and Two-Particle Coefficients of Fractional Parentage for Configurations sZslUpq, C.D.H. Chisholm, A. Dalgarno and F.R. Innes Relativistic Z-Dependent Corrections to Atomic Energy Levels, Holly Thomis Doyle
Volume 6
Dissociative Recombination, J.N. Bardsley and M.A. Biondi Analysis of the Velocity Field in Plasmas from the Doppler Broadening of Spectral Emission Lines, A.S. Kaufman The Rotational Excitation of Molecules by Slow Electrons, Kazuo Takayanagi and Yukikazu Itikawa The Diffusion of Atoms and Molecules, E.A. Mason and T.R. Marrero Theory and Application of Sturmian Functions, Manuel Rotenberg Use of Classical Mechanics in the Treatment of Collisions between Massive Systems, D.R. Bates and A.E. Kingston
Volume 5
Flowing Afterglow Measurements of Ion-Neutral Reactions, E.E. Ferguson, F.C. Fehsenfeld and A.L. Schmeltekopf Experiments with Merging Beams, Roy H. Neynaber Radiofrequency Spectroscopy of Stored Ions II: Spectroscopy, H.G. Dehmelt The Spectra of Molecular Solids, O. Schnepp The Meaning of Collision Broadening of Spectral Lines: The Classical Oscillator Analog, A. Ben-Reuven The Calculation of Atomic Transition Probabilities, R.J.S. Crossley
Volume 7
Physics of the Hydrogen Maser, C. Audoin, J.P. Schermann and P. Grivet Molecular Wave Functions: Calculations and Use in Atomic and Molecular Processes, J.C. Browne Localized Molecular Orbitals, Harel Weinstein, Ruben Pauncz and Maurice Cohen General Theory of Spin-Coupled Wave Functions for Atoms and Molecules, J. Gerratt
C O N T E N T S OF V O L U M E S IN THIS S E R I A L Diabatic States of MoleculesQuasi-Stationary Electronic States, Thomas F. O'Malley
Selection Rules within Atomic Shells, B.R. Judd
Green's Function Technique in Atomic and Molecular Physics, Gy. Csanak,
301
Molecular Beam Electric Resonance Spectroscopy, Jens C. Zorn and Thomas C. English
Atomic and Molecular Processes in the Martian Atmosphere, Michael B. McElroy
H.S. Taylor and Robert Yaris
A Review of Pseudo-Potentials with Emphasis on Their Application to Liquid Metals, Nathan Wiser and A.J. Greenfield
Volume 10
Relativistic Effects in the Many-Electron Atom, Lloyd Armstrong Jr. and Serge Feneuille
The First Born Approximation, Volume 8
Interstellar Molecules: Their Formation and Destruction, D. McNally Monte Carlo Trajectory Calculations of Atomic and Molecular Excitation in Thermal Systems, James C. Keck
Nonrelativistic Off-Shell Two-Body Coulomb Amplitudes, Joseph C.Y.
K.L. Bell and A.E. Kingston
Photoelectron Spectroscopy, W.C. Price Dye Lasers in Atomic Spectroscopy, W. Lange, J. Luther and A. Steudel
Recent Progress in the Classification of the Spectra of Highly Ionized Atoms, B. C. Fawcett
A Review of Jovian Ionospheric Chemistry, Wesley T. Huntress Jr.
Chen and Augustine C. Chen
Photoionization with Molecular Beams, R.B. Cairns, Halstead Harrison and R.L Schoen The Auger Effect, E.H.S. Burhop and W.N. Asaad
Volume 11
The Theory of Collisions between Charged Particles and Highly Excited Atoms, L C. Percival and D. Richards
Volume 9
Correlation in Excited States of Atoms, A. W. Weiss
The Calculation of Electron-Atom Excitation Cross Sections, M.R.H. Rudge
Collision-Induced Transitions between Rotational Levels, Takeshi Oka
The Differential Cross Section of Low-Energy Electron-Atom Collisions, D. Andrick
Electron Impact Excitation of Positive Ions, M.J. Seaton The R-Matrix Theory of Atomic Process, P.G. Burke and W.D. Robb Role of Energy in Reactive Molecular Scattering: An Information-Theoretic Approach, R.B. Bernstein and R.D. Levine
Inner Shell Ionization by Incident Nuclei, Johannes M. Hansteen Stark Broadening, Hans R. Griem Chemiluminescence in Gases, M.F. Golde and B.A. Thrush
302
C O N T E N T S OF V O L U M E S IN THIS SERIAL
V o l u m e 12
Nonadiabatic Transitions between Ionic and Covalent States, R.K. Janev Recent Progress in the Theory of Atomic Isotope Shift, J. Bauche and R.-J. Champeau
Topics on Multiphoton Processes in Atoms, P. Lambropoulos Optical Pumping of Molecules, M. Broyer, G. Goudedard, J.C. Lehmann and J. Vigud
Highly Ionized Ions, Ivans A. Sellin Time-of-Flight Scattering Spectroscopy, Wilhelm Raith
Ion Chemistry in the D Region, George C. Reid
The Accurate Calculation of Atomic Properties by Numerical Methods, Brian C. Webster, Michael J. Jamieson and Ronald F. Stewart
(e, 2e) Collisions, Erich Weigold and Ian E. McCarthy
Forbidden Transitions in One- and Two-Electron Atoms, Richard Marrus and Peter J. Mohr
Semiclassical Effects in Heavy-Particle Collisions, M.S. Child Atomic Physics Tests of the Basic Concepts in Quantum Mechanics, Francis M. Pipkin
Quasi-Molecular Interference Effects in Ion-Atom Collisions, S.V. Bobashev Rydberg Atoms, S.A. Edelstein and T.F. Gallagher
V o l u m e 13
Atomic and Molecular Polarizabilities - Review of Recent Advances, Thomas M. Miller and Benjamin Bederson
Study of Collisions by Laser Spectroscopy, Paul R. Berman Collision Experiments with LaserExcited Atoms in Crossed Beams, I.V. Hertel and W. Stoll
Scattering Studies of Rotational and Vibrational Excitation of Molecules, Manfred Faubel and J. Peter Toennies
Low-Energy Electron Scattering by Complex Atoms: Theory and Calculations, R.K. Nesbet Microwave Transitions of Interstellar Atoms and Molecules, W.B. Somerville
V o l u m e 14
Resonances in Electron Atom and Molecule Scattering, D.E. Golden
UV and X-Ray Spectroscopy in Astrophysics, A.K. Dupree Volume
15
Negative Ions, H.S.W. Massey Atomic Physics from Atmospheric and Astrophysical Studies, A. Dalgarno Collisions of Highly Excited Atoms, R.F. Stebbings
Theoretical Aspects of Positron Collisions in Gases, J.W. Humberston Experimental Aspects of Positron Collisions in Gases, T.C. Griffith Reactive Scattering: Recent Advances in Theory and Experiment, Richard B. Bernstein
Ion-Atom Charge Transfer Collisions at Low Energies, J.B. Hasted Aspects of Recombination, D.R. Bates The Theory of Fast Heavy Particle Collisions, B.H. Bransden Atomic Collision Processes in Controlled Thermonuclear Fusion Research, H.B. Gilbody
C O N T E N T S OF V O L U M E S IN THIS SERIAL Inner-Shell Ionization, E.H.S. Burhop Excitation of Atoms by Electron Impact, D. W. O. Heddle
Coherence and Correlation in Atomic Collisions, H. Kleinpoppen Theory of Low Energy ElectronMolecule Collisions, P.G. Burke Volume 16
Atomic Hartree-Fock Theory, M. Cohen and R.P. McEachran
Experiments and Model Calculations to Determine Interatomic Potentials, R. Dfiren
Sources of Polarized Electrons, R.J. Celotta and D.T. Pierce
Theory of Atomic Processes in Strong Resonant Electromagnetic Fields, S. Swain
Spectroscopy of Laser-Produced Plasmas, M.H. Key and R.J. Hutcheon Relativistic Effects in Atomic Collisions Theory, B.L. Moiseiwitsch Parity Nonconservation in Atoms: Status of Theory and Experiment, E.N. Fortson and L Wilets
Volume 17
Collective Effects in Photoionization of Atoms, M. Ya. Amus& Nonadiabatic Charge Transfer, D.S.F. Crothers
303
Inner-Shell Vacancy Production in Ion-Atom Collisions, C.D. Lin and Patrick Richard
Atomic Processes in the Sun, P.L. Dufton and A.E. Kingston
Volume 18
Theory of Electron-Atom Scattering in a Radiation Field, Leonard Rosenberg Positron-Gas Scattering Experiments, Talbert S. Stein and Walter E. Kauppila
Nonresonant Multiphoton Ionization of Atoms, J. Morellec, D. Normand and G. Petite
Classical and Semiclassical Methods in Inelastic Heavy-Particle Collisions, A.S. Dickinson and D. Richards
Recent Computational Developments in the Use of Complex Scaling in Resonance Phenomena, B.R. Junker Direct Excitation in Atomic Collisions: Studies of Quasi-One-Electron Systems, N. Andersen and S.E. Nielsen Model Potentials in Atomic Structure, A. Hibbert
Recent Developments in the Theory of Electron Scattering by Highly Polar Molecules, D.W. Norcross and L.A. Collins
Quantum Electrodynamic Effects in Few-Electron Atomic Systems, G. W.F. Drake
Atomic Rydberg States, Serge Feneuille and Pierre Jacquinot
Superfluorescence, M.F.H. Schuurmans, Q.H.F. Vrehen, D. Polder and H.M. Gibbs
Applications of Resonance Ionization Spectroscopy in Atomic and Molecular Physics, M.G. Payne, C.H. Chen, G.S. Hurst and G.W. Foltz
Volume 19
Electron Capture in Collisions of Hydrogen Atoms with Fully Stripped Ions, B.H. Bransden and R.K. Janev
Interactions of Simple Ion Atom Systems, J. T. Park
304
C O N T E N T S OF V O L U M E S IN THIS SERIAL
High-Resolution Spectroscopy of Stored Ions, D.J. Wineland, Wayne M. Itano and R.S. Van Dyck Jr. Spin-Dependent Phenomena in Inelastic Electron-Atom Collisions, K. Blum and H. Kleinpoppen The Reduced Potential Curve Method for Diatomic Molecules and Its Applications, F. Jend The Vibrational Excitation of Molecules by Electron Impact, D.G. Thompson Vibrational and Rotational Excitation in Molecular Collisions, Manfred Faubel Spin Polarization of Atomic and Molecular Photoelectrons, N.A. Cherepkov Volume 20
Ion-Ion Recombination in an Ambient Gas, D.R. Bates Atomic Charges within Molecules, G.G. Hall Experimental Studies on Cluster Ions, T.D. Mark and A.W. Castlemen Jr. Nuclear Reaction Effects on Atomic Inner-Shell Ionization, IF.E. Meyerhof and J.-F. Chemin Numerical Calculations on Electron-Impact Ionization, Christopher Bottcher Electron and Ion Mobilities, Gordon R. Freeman and David A. Armstrong On the Problem of Extreme UV and X-Ray Lasers, I.I. Sobel'man and A.V. l/'inogradov Radiative Properties of Rydberg States in Resonant Cavities, S. Haroche and J.M. Raimond Rydberg Atoms: High-Resolution Spectroscopy and Radiation Interaction-Rydberg Molecules,
J.A.C. Gallas, G. Leuchs, H. Walther, and H. Figger Volume 21
Subnatural Linewidths in Atomic Spectroscopy, Dennis P. O'Brien, Pierre Meystre and Herbert Walther Molecular Applications of Quantum Defect Theory, Chris H. Greene and Ch. Jungen Theory of Dielectronic Recombination, Yukap Hahn Recent Developments in Semiclassical Floquet Theories for Intense-Field Multiphoton Processes, Shih'I Chu Scattering in Strong Magnetic Fields, M.R.C. McDowell and M. Zarcone Pressure Ionization, Resonances and the Continuity of Bound and Free States, R.M. More Volume 22
Positronium- Its Formation and Interaction with Simple Systems, J. IF. Humberston Experimental Aspects of Positron and Positronium Physics, T.C. Griffith Doubly Excited States, Including New Classification Schemes, C.D. Lin Measurements of Charge Transfer and Ionization in Collisions Involving Hydrogen Atoms, H.B. Gilbody Electron Ion and Ion-Ion Collisions with Intersecting Beams, K. Dolder and B. Peart Electron Capture by Simple Ions, Edward Pollack and Yukap Hahn Relativistic Heavy-Ion-Atom Collisions, R. Anholt and Harvey Gould Continued-Fraction Methods in Atomic Physics, S. Swain
C O N T E N T S OF V O L U M E S IN THIS SERIAL Volume 23
Vacuum Ultraviolet Laser Spectroscopy of Small Molecules, C.R. Vidal Foundations of the Relativistic Theory of Atomic and Molecular Structure, Ian P. Grant and Harry M. Quiney
Point-Charge Models for Molecules Derived from Least-Squares Fitting of the Electric Potential, D.E. Williams and Ji-Min Yan
Transition Arrays in the Spectra of Ionized Atoms, J. Bauche, C. Bauche-Arnoult and M. Klapisch
Photoionization and Collisional Ionization of Excited Atoms Using Synchroton and Laser Radiation, F.J. Wuilleumier, D.L. Ederer and J.L. Picqud
305
Alexander Dalgarno: Contributions to Aeronomy, Michael B. McElroy Alexander Dalgarno: Contributions to Astrophysics, David A. Williams Dipole Polarizability Measurements, Thomas M. Miller and Benjamin Bederson
Flow Tube Studies of Ion-Molecule Reactions, Eldon Ferguson Differential Scattering in He-He and He +-He Collisions at keV Energies, R.F. Stebbings
Atomic Excitation in Dense Plasmas, Jon C. Weisheit
Pressure Broadening and Laser-induced Spectral Line Shapes, Kenneth M. Sando and Shih-I Chu
Model-Potential Methods, C. Laughlin and G.A. Victor
Volume, 24
The Selected Ion Flow Tube (SIDT): Studies of Ion-Neutral Reactions, D. Smith and N.G. Adams
Near-Threshold Electron-Molecule Scattering, Michael A. Morrison Angular Correlation in Multiphoton Ionization of Atoms, S.J. Smith and G. Leuchs
Optical Pumping and Spin Exchange in Gas Cells, R.J. Knize, Z. Wu and W. Happer
Correlations in Electron-Atom Scattering, A. Crowe Volume 25
Alexander Dalgarno: Life and Personality, David R. Bates and George A. Victor
Alexander Dalgarno: Contributions to Atomic and Molecular Physics, Neal Lane
Z-Expansion Methods, M. Cohen Schwinger Variational Methods, Deborah Kay Watson
Fine-Structure Transitions in Proton-Ion Collisions, R.H.G. Reid Electron Impact Excitation, R.J.W. Henry and A.E. Kingston
Recent Advances in the Numerical Calculation of Ionization Amplitudes, Christopher Bottcher
The Numerical Solution of the Equations of Molecular Scattering, A.C. Allison
High Energy Charge Transfer, B.H. Bransden and D.P. Dewangan
Relativistic Random-Phase Approximation, W.R. Johnson Relativistic Sturmian and Finite Basis Set Methods in Atomic Physics, G.W.F. Drake and S.P. Goldman
Dissociation Dynamics of Polyatomic Molecules, T. Uzer
306
C O N T E N T S OF V O L U M E S IN THIS SERIAL
Photodissociation Processes in Diatomic Molecules of Astrophysical Interest, Kate P. Kirby and Ewine F. van Dishoeck The Abundances and Excitation of Interstellar Molecules, John H. Black
Volume 26
Comparisons of Positrons and Electron Scattering by Gases, Walter E. Kauppila and Talbert S. Stein Electron Capture at Relativistic Energies, B.L. Moiseiwitsch The Low-Energy, Heavy Particle Collisions - A Close-Coupling Treatment, Mineo Kimura and Neal F. Lane Vibronic Phenomena in Collisions of Atomic and Molecular Species, V. Sidis Associative Ionization: Experiments, Potentials and Dynamics, John Weiner, Fran.coise Masnou-Seeuws and Annick Giusti-Suzor On the 13Decay of 187Re: An Interface of Atomic and Nuclear Physics and Cosmochronology, Zonghau Chen, Leonard Rosenbery and Larry Spruch Progress in Low Pressure Mercury-Rare Gas Discharge Research, J. Maya and R. Lagushenko
Volume 27
Negative Ions: Structure and Spectra, David R. Bates Electron Polarization Phenomena in Electron-Atom Collisions, Joachim Kessler Electron-Atom Scattering, I.E. McCarthy and E. Weigold
Electron-Atom Ionization, I.E. McCarthy and E. Weigold Role of Autoionizing States in Multiphoton Ionization of Complex Atoms, V.I. Lengyel and M.L Haysak Multiphoton Ionization of Atomic Hydrogen Using Perturbation Theory, E. Karule Volume 28
The Theory of Fast Ion-Atom Collisions, J.S. Briggs and J.H. Macek Some Recent Developments in the Fundamental Theory of Light, Peter W. Milonni and Surendra Singh Squeezed States of the Radiation Field, Khalid Zaheer and M. Suhail Zubairy Cavity Quantum Electrodynamics, E.A. Hinds Volume 29
Studies of Electron Excitation of Rare-Gas Atoms into and out of Metastable Levels Using Optical and Laser Techniques, Chun C. Lin and L. W. Anderson Cross Sections for Direct Multiphoton Ionionization of Atoms, M.V. Ammosov, N.B. Delone, M.Yu. Ivanov, LL Bondar and A.V. Masalov Collision-Induced Coherences in Optical Physics, G.S. Agarwal Muon-Catalyzed Fusion, Johann Rafelski and Helga E. Rafelski Cooperative Effects in Atomic Physics, J.P. Connerade Multiple Electron Excitation, Ionization, and Transfer in High-Velocity Atomic and Molecular Collisions, J.H. McGuire
C O N T E N T S OF V O L U M E S IN THIS S E R I A L Volume 30
Differential Cross Sections for Excitation of Helium Atoms and Helium-Like Ions by Electron Impact, Shinobu Nakazaki
Cross-Section Measurements for Electron Impact on Excited Atomic Species, S. Trajmar and J.C. Nickel The Dissociative Ionization of Simple Molecules by Fast Ions, Colin J. Latimer
Theory of Collisions between Laser Cooled Atoms, P.S. Julienne, A.M. Smith and K. Burnett
Light-Induced Drift, E.R. Eliel Continuum Distorted Wave Methods in Ion-Atom Collisions, Derrick S.F. Crothers and Louis J. Dub~ Volume 31
Energies and Asymptotic Analysis for Helium Rydberg States, G. W.F. Drake
Spectroscopy of Trapped Ions, R. C. Thompson
Phase Transitions of Stored Laser-Cooled Ions, H. Walther Selection of Electronic States in Atomic Beams with Lasers, Jacques Baudon, Rudolf Dfiren and Jacques Robert
Atomic Physics and Non-Maxwellian Plasmas, Mich~le Lamoureux Volume 32
Photoionization of Atomic Oxygen and Atomic Nitrogen, K.L. Bell and A.E. Kingston
Positronium Formation by Positron Impact on Atoms at Intermediate Energies, B.H. Bransden and C.J. Noble
307
Electron-Atom Scattering Theory and Calculations, P.G. Burke Terrestrial and Extraterrestrial H~-, Alexander Dalgarno
Indirect Ionization of Positive Atomic Ions, K. Dolder Quantum Defect Theory and Analysis of High-Precision Helium Term Energies, G. W.F. Drake Electron-Ion and Ion-Ion Recombination Processes, M.R. Flannery
Studies of State-Selective Electron Capture in Atomic-Hydrogen by Translational Energy Spectroscopy, H.B. Gilbody
Relativistic Electronic Structure of Atoms and Molecules, I.P. Grant The Chemistry of Stellar Environments, D.A. Howe, J.M.C. Rawlings and D.A. Williams
Positron and Positronium Scattering at Low Energies, J.W. Humberston How Perfect are Complete Atomic Collision Experiments?, H. Kleinpoppen and H. Handy
Adiabatic Expansions and Nonadiabatic Effects, R. McCarroll and D.S.F. Crothers
Electron Capture to the Continuum, B.L. Moiseiwitsch
How Opaque Is a Star?, M.J. Seaton Studies of Electron Attachment at Thermal Energies Using the Flowing Afterglow-Langmuir Technique, David Smith and Patrik Span6l
Exact and Approximate Rate Equations in Atom-Field Interactions, S. Swain Atoms in Cavities and Traps, H. Walther
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Some Recent Advances in ElectronImpact Excitation of n--3 States of Atomic Hydrogen and Helium, J.F. Williams and J.B. Wang
Atomic Collisions, E.W. McDaniel and E.J. Mansky
Volume 34
Volume 33
Principles and Methods for Measurement of Electron Impact Excitation Cross Sections for Atoms and Molecules by Optical Techniques, A.R. Filippelli, Chun C. Lin, L.W. Andersen and J.W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Analysis of Scattered Electrons, S. Trajmar and J.W. McConkey Benchmark Measurements of Cross Sections for Electron Collisions: Electron Swarm Methods, R. W. Crompton Some Benchmark Measurements of Cross Sections for Collisions of Simple Heavy Particles, H.B. Gilbody The Role of Theory in the Evaluation and Interpretation of Cross-Section Data, Barry L Schneider Analytic Representation of CrossSection Data, Mitio Inokuti, Mineo Kimura, M.A. Dillon and Isao Shimamura Electron Collisions with N2, O2 and O: What We Do and Do Not Know, Yukikazu Itikawa Need for Cross Sections in Fusion Plasma Research, Hugh P. Summers Need for Cross Sections in Plasma Chemistry, M. Capitelli, R. Celiberto and M. Cacciatore Guide for Users of Data Resources, Jean W. Gallagher Guide to Bibliographies, Books, Reviews and Compendia of Data on
Atom Interferometry, C.S. Adams, O. Carnal and J. Mlynek Optical Tests of Quantum Mechanics, R.Y. Chiao, P.G. Kwiat and A.M. Steinberg Classical and Quantum Chaos in Atomic Systems, Dominique Delande and Andreas Buchleitner Measurements of Collisions between Laser-Cooled Atoms, Thad Walker and Paul Feng The Measurement and Analysis of Electric Fields in Glow Discharge Plasmas, J.E. Lawler and D.A. Doughty Polarization and Orientation Phenomena in Photoionization of Molecules, N.A. Cherepkov Role of Two-Center ElectronElectron Interaction in Projectile Electron Excitation and Loss, E.C. Montenegro, W.E. Meyerhof and J.H. McGuire Indirect Processes in Electron Impact Ionization of Positive Ions, D.L. Moores and K.J. Reed Dissociative Recombination: Crossing and Tunneling Modes, David R. Bates
Volume 35
Laser Manipulation of Atoms, K. Sengstock and W. Ertmer Advances in Ultracold Collisions: Experiment and Theory, J. Weiner Ionization Dynamics in Strong Laser Fields, L.F. DiMauro and P. Agostini
C O N T E N T S OF V O L U M E S IN THIS SERIAL Infrared Spectroscopy of Size Selected Molecular Clusters, U. Buck Fermosecond Spectroscopy of Molecules and Clusters, T. Baumer and G. Gerber
Calculation of Electron Scattering on Hydrogenic Targets, L Bray and A.T. Stelbovics
Relativistic Calculations of Transition Amplitudes in the Helium Isoelectronic Sequence, W.R. Johnson,
309
Channeling Heavy Ions through Crystalline Lattices, Herbert F. Krause and Sheldon Datz
Evaporative Cooling of Trapped Atoms, Wolfgang Ketterle and N.J. van Druten
Nonclassical States of Motion in Ion Traps, J.I. Cirac, A.S Parkins, R. Blatt and P. Zoller
The Physics of Highly-Charged Heavy Ions Revealed by Storage/Cooler Rings, P.H. Mokler and Th. St6hlker
D.R. Plante and J. Sapirstein
Rotational Energy Transfer in Small Polyatomic Molecules, H.O. Everitt and F.C. De Lucia
Volume 38
Electronic Wavepackets, Robert R. Jones and L.D. Noordam
Volume 36
Complete Experiments in ElectronAtom Collisions, Nils Overgaard Andersen and Klaus Bartschat
Stimulated Rayleigh Resonances and Recoil-induced Effects, J.-Y Courtois and G. Grynberg
Precision Laser Spectroscopy Using Acousto-Optic Modulators, W.A. van Wijngaarden
Highly Parallel Computational Techniques for Electron-Molecule Collisions, Carl Winstead and Vincent McKoy
Quantum Field Theory of Atoms and Photons, Maciej Lewenstein
Chiral Effects in Electron Scattering by Molecules, K. Blum and D.G. Thompson
Optical and Magneto-Optical Spectroscopy of Point Defects in Condensed Helium, Serguei L Kanorsky and Antoine Weis
Rydberg Ionization: From Field to Photon, G.M. Lankhuijzen and L.D. Noordam
Studies of Negative Ions in Storage Rings, L.H. Andersen, T. Andersen and P. Hvelplund
Single-Molecule Spectroscopy and Quantum Optics in Solids, W.E. Moerner, R.M. Dickson and D.J Norris
and Li You
Volume 37
Volume 39
Evanescent Light-Wave Atom Mirrors, Resonators, Waveguides, and Traps,
Author and Subject Cumulative Index Volumes 1-38 Author Index Subject Index Appendix: Tables of Contents of Volumes 1-38 and Supplements
Jonathan P. Dowling and Julio Gea-Banacloche
Optical Lattices, P.S. Jessen and LH. Deutsch
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Volume 40
Electric Dipole Moments of Leptons, Eugene D. Commins
High-Precision Calculations for the Ground and Excited States of the Lithium Atom, Frederick W. King Storage Ring Laser Spectroscopy, Thomas U. K~ihl
Laser Cooling of Solids, Carl E. Mungan and Timothy R. Gosnell
Optical Pattern Formation, L.A. Lug&to, M. Brambilla and A. Gatti
Optical Dipole Traps for Neutral Atoms, Rudolf Grimm, Matthias Weidemfiller and Yurii B. Ovchinnikov
Formation of Cold (T < 1 K) Molecules, J.T. Bahns, P.L. Gould and W. C. Stwalley
High-Intensity Laser-Atom Physics, C.J. Joachain, M. Dorr and N.J. Kylstra
Coherent Control of Atomic, Molecular and Electronic Processes, Moshe Shapiro and Paul Brumer
Resonant Nonlinear Optics in Phase Coherent Media, M.D. Lukin, P. Hemmer and M.O. Scully
Volume 41
Two-Photon Entanglement and Quantum Reality, Yanhua Shih Quantum Chaos with Cold Atoms, Mark G. Raizen
Study of the Spatial and Temporal Coherence of High-Order Harmonics, Pascal Salidres, Ann L'Huillier, Philippe Antoine and Maciej Lewenstein
Atom Optics in Quantized Light Fields, Matthias Freyburger, Alois M. Herkommer, Daniel S. Krdhmer, Erwin Mayr and Wolfgang P. Schleich Atom Waveguides, Victor I. Balykin
Atomic Matter Wave Amplification by Optical Pumping, Ulf Janicke and Martin Wilkens Volume 42
Fundamental Tests of Quantum Mechanics, Edward S. Fry and Thomas Walther
Wave-Particle Duality in an Atom Interferometer, Stephan D~irr and Gerhard Rempe
Atom Holography, Fujio Shimizu
The Characterization of Liquid and Solid Surfaces with Metastable Helium Atoms, H. Morgner Quantum Communication with Entangled Photons, Harald Weinfurter Volume 43
Plasma Processing of Materials and Atomic, Molecular, and Optical Physics: An Introduction, Hiroshi Tanaka and Mitio Inokuti
The Boltzmann Equation and Transport Coefficients of Electrons in Weakly Ionized Plasmas, R. Winkler Electron Collision Data for Plasma Chemistry Modeling, W.L. Morgan Electron-Molecule Collisions in LowTemperature Plasmas: The Role of Theory, Carl Winstead and Vincent McKoy
Electron Impact Ionization of Organic Silicon Compounds, Ralf Basner, Kurt Becker, Hans Deutsch and Martin Schmidt
Kinetic Energy Dependence of Ion-Molecule Reactions Related to Plasma Chemistry, P.B. Armentrout
C O N T E N T S OF V O L U M E S IN THIS SERIAL Physicochemical Aspects of Atomic and Molecular Processes in Reactive Plasmas, Yoshihiko Hatano Ion-Molecule Reactions, Werner
311
Electron Interactions with Excited Atoms and Molecules, Loucas G. Christophorou and James K. Olthoff
Lindinger, Armin Hansel and Zdenek Herman
Uses of High-Sensitivity White-Light Absorption Spectroscopy in Chemical Vapor Deposition and Plasma Processing, L. W. Anderson, A.N. Goyette and J.E. Lawler
Fundamental Processes of Plasma-Surface Interactions, Rainer Hippler
Recent Applications of Gaseous Discharges: Dusty Plasmas and Upward-Directed Lightning, Ara Chutjian
Opportunities and Challenges for Atomic, Molecular and Optical Physics in Plasma Chemistry, Kurl Becker, Hans Deutsch and Mitio Inokuti
Volume 45
Comparing the Antiproton and Proton, and Opening the Way to Cold Antihydrogen, G. Gabrielse Medical Imaging with Laser-Polarized Noble Gases, Timothy Chupp and Scott Swanson
Polarization and Coherence Analysis of the Optical Two-Photon Radiation from the Metastable 22S1/2 State of Atomic Hydrogen, Alan J. Duncan, Hans Kleinpoppen and Marian O. Scully
Laser Spectroscopy of Small Molecules, W. Demtr6der, M. Keil and H. Wenz
Coulomb Explosion Imaging of Molecules, Z. Vager
Volume 44
Volume 46
Mechanisms of Electron Transport in Electrical Discharges and Electron Collision Cross Sections,
Femtosecond Quantum Control,
Hiroshi Tanaka and Osamu Sueoka
Theoretical Consideration of Plasma-Processing Processes, Mineo Kimura
Electron Collision Data for Plasma-Processing Gases, Loucas G. Christophorou and James K. Olthoff
Radial Measurements in Plasma Processing, Toshio Goto Radio-Frequency Plasma Modeling for Low-Temperature Processing, Toshiaki Makabe
T. Brixner, N.H. Damrauer and G. Gerber
Coherent Manipulation of Atoms and Molecules by Sequential Laser Pulses, N. V. Vitanov, M. Fleischhauer, B.W. Shore and K. Bergmann
Slow, Ultraslow, Stored, and Frozen Light, Andrey B. Matsko, Olga Kocharovskaya, Yuri Rostovtsev, George R. Welch, Alexander S. Zibrov and Marlan O. Scully
Longitudinal Interferometry with Atomic Beams, S. Gupta, D.A. Kokorowski, R.A. Rubenstein, and IV. IV. Smith
312
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Volume 47
Nonlinear Optics of de Broglie Waves, P. Meystre Formation ,of Ul~W~td Molecules (T < 200 ~tK) via Photoassociation in a Gas of laser-Cooled Atoms, Franl:oise Masnou-Seeuws and Pierre Pillet Molecular Emissions from the Atmospheres of Giant Planets and Comets: Needs for Spectroscopic and Collision Data, Yukikazu Itikawa, Sang ,loon Kim, Yong Ha Kim, and Y.C. Mirth Studies of Electron-Excited Targets Using Recoil Momentum Spectroscopy with Laser Probing of the Excited State, Andrew James Murray and Peter Hammond Quantum Noise of Small Lasers, J.P. Woerdman, N.J. van Druten and M.P. van Exter
Volume 48
Multiple Ionization in Strong Laser Fields, R. D6rner, Th. Weber, M. Weckenbrock, A. Staudte, M. Hattass, R. Moshammer, J. Ullrich, H. Schmidt-B6cking Above-Threshold Ionization: From Classical Features to Quantum Effects, W. Becker, F. Grasbon, R. Kopold, D.B. Milogevi6, G.G. Paulus and H. Walther Dark Optical Traps for Cold Atoms, Nir Friedman, Ariel Kaplan and Nir Davidson Manipulation of Cold Atoms in Hollow Laser Beams, Heung-Ryoul Nob, Xinye Xu and Wonho Jhe Continuous Stern-Gerlach Effect on Atomic Ions, Gfinther Werth,
Hartmut H~tffner and Wolfgang Quint The Chirality of Biomolecules, Robert N. Compton and Richard M. Pagni Microscopic Atom Optics: From Wires to an Atom Chip, Ron Folman, Peter Krfiger, J6rg Schmiedmayer, Johannes Denschlag and Carsten Henkel
Methods of Measuring Electron-Atom Collision Cross Sections with an Atom Trap, R.S. Schappe, M.L. Keeler, T.A. Zimmerman, M. Larsen, P. Feng, R.C. Nesnidal, J.B. Boffard, T.G. Walker, L.W. Anderson and C.C. Lin Volume 49
Applications of Optical Cavities in Modern Atomic, Molecular, and Optical Physics, Jun Ye and Theresa W. Lynn Resonance and Threshold Phenomena in Low-Energy Electron Collisions with Molecules and Clusters, H. Hotop, M.-W. Ruf, M. Allan, LL Fabrikant Coherence Analysis and Tensor Polarizaiton Parameters of (y, ey) Photoionization Processes in Atomic Coincidence Measurements, B. Lohmann, B. Zimmermann, H. Kleinpoppen and U. Becker Quantum Measurements and New Conceptsfor Experiments with Trapped Ions, Ch. Wunderlich and Ch. Balzer Scattering and Reaction Processes in Powerful Laser Fields, Dejan B. MiloYevi( and Fritz Ehlotzky Hot Atoms in the Terrestrial Atmosphere, Vijay Kumar and E. Krishnakumar
