RADIATIVE COLLISIONS IN A STRONG FIELD REGIME

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RADIATIVE COLLISIONS IN A STRONG FIELD REGIME

P. Pillet, R. Kachru, N. Tran, W. Smith, T. Gallagher

To cite this version:

P. Pillet, R. Kachru, N. Tran, W. Smith, T. Gallagher. RADIATIVE COLLISIONS IN A STRONG FIELD REGIME. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-85-C1-95.

�10.1051/jphyscol:1985108�. �jpa-00224477�

JOURNAL DE PHYSIQUE

Colloque CI, supplement au n°l, Tome <f6, Janvier 1985 page Cl-85

RADIATIVE COLLISIONS IN A STRONG FIELD REGIME

P. Pillet , R. Kachru, N.H. Tran, W.W. Smith* and T.F. Gallagher

Chemical Physics Laboratory, SRI International, Menlo Park, California 94025, U.S.A.

Résumé - Le processus de transfert d'énergie résonnant,dans les collisions entre deux atomes de Rydberg, représente un point de départ idéal pour l'étude systématique des collisions assistées par photons. En utilisant une source micro- onde courante et de puissance modeste, on atteint sans difficulté le régime de champ fort dans de tels processus.

Abstract - The process of resonant collisional energy transfer between Rydberg atoms provides an ideal starting point for systematic studies of radiatively assisted collisions. In fact using modest, readily available microwave sources it is straightforward to enter the strong field regime for such processes.

INTRODUCTION

A collision of two atoms in which a photon is absorbed or emitted is frequently called a radiatively assisted collision, although it may also be viewed as emission or absorption of the transient molecule formed in the collision of the two atoms.

In either case the short duration of the collision implies that to drive such a transition, i.e. to either stimulate the emission or absorption of a photon, requires an intense radiation field. Thus it is not surprising that the study of such processes has awaited the development of the high power tunable dye laser. In recent years a variety of experimental studies has been undertaken, •> but in spite of the high power of pulsed tunable dye lasers the time of a collision is so short that nearly all the experiments are in the weak field regime in which the radiation field may be adequately treated by perturbation theory.

Only in one instance, in which power densities of 10y W/cm were used, was a less than linear power dependence observed. This saturation marks the onset of the strong field regime in which the radiation field may not be treated by perturbation theory. As it is unrealistic to expect increases of orders of magnitude in dye laser intensities the prospect of exploring the strong field regime for such systems does not appear to be very bright.

RESONANT COLLISIONS OF RYDBERG ATOMS

Often a phenomenon which is difficult or impossible to study in normal atoms is easily studied using Rydberg atoms, and the study of radiative collisions is an excellent example of this. Specifically, resonant Rydberg atom-Rydberg atom collisional energy transfer is an ideal system in which to study radiative colli-

v 12—15

sions. Although we have studied a variety of cases , the best case for the study of radiative collisions is the resonant process

(1) which occurs when the Na levels are tuned with an electric field so the ns level

lies exactly midway between the np and n-lp levels. An example of this is shown in Figure 1, a level diagram for the Na 17s, 16p and 17p states. When the electric

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985108

C 1-86 JOURNAL DE PHYSIQUE

field is at one of the four collisional resonances near 600 V/cm, two Na ns atoms can collide producing a 16p and a 17p atom.

This experiment is done using pulsed lasers to excite Na atoms in a thermal beam to the 17s state. Atoms of different velocities in the beam collide for l p s after the laser pulses at which time an electric field pulse is applied to analyze

FIG. 1. Energy-level diagram for the 16p-17s-17p states in a static electric field. The vertical lines are drawn at the four fields where the s state is midway between the two p states and the resonant

collisional transfer occurs.

by selective field ionization the products of the collisions which have

occurred.14 If the field ionizing pulse is set to detect the 17p states, we ohserve four collisional resonances corresponding to the splitting between the Iml=O and 1 levels of the p state as the dc electric field is scanned. An example of such a scan is shown in Figure 2 in which the four collisional resonances are quite evident. As might be anticipated from Eq. 1, this process is a resonant dipole- dipole collision process for which the interaction matrix element HI is given by13

where p is the electric dipole moment and r is the internuclear separation of the two atoms. As the dipole moments scale as n2, n being the principal quantum number, it is straightforward to show that the cross section a should scale as n4 and the collision time T as n2 (Equivalently the resonant collision linewidth scales as II-~). This is in agreement with the observed n scaling. Typical values, at n=20 are 0 = 1 0 ~ 8 ~ and ~=10-'s.l~ In sum this process is a textbook example of resonant energy transfer via the long range dipole-dipole interaction. As such, it forms an excellent starting point for more elaborate experiments.

FIG. 2. The observed 17p ion signal after population of the 17s state vs dc electric field, showing the sharp collisional reso- nances. The resonances are labeled by the ImR

1

values of the lower and upper p states.

RADIATIVE COLLISIONS

The long collision times of the resonant Rydberg atom collisions and the large dipole moments invite the consideration of radiative collisions using microwave radiation. For such collisions, the interaction matrix element has the form

HI = <ns 11.1 Inp><ns 11.1 In-lp><n-lp 1p In-ld> E

r3h ( 3

where A is the detuning of the virtual intermediate state from the real state n-lp and E is the magnitude of an applied microwave field. The levels are shown in Fig- ure 3. The expression of Eq. 3 differs from Eq. 2 by the factor <n-lp lp In-ld> E/A, and for such a radiatively assisted process to be observable, we require that this factor be

-

0.3. For typical values of A = 1 cm-I and p = 200 eao we find that E- 100 V/cm, a power of

-

1 w/cm2. The initial experiments verified these estimates, as shown by Figure 4, scans of the resonant collisions of Na 22s atoms with and without microwave f ields.16 As shown by Figure 4, with a microwave field present, an additional four resonances are observed at a field o f - 100 V/cm which correspond to the emission of one photon during the collision. The field separation of the two sets of four resonances corresponds to the 15 GHz microwave frequency.

In these experiments, the radiative collision signal scaled approximately linearly with the microwave power, although there was some evidence of saturation at the highest microwave powers used,

-

^{10 W.}

Cl-88 JOURNAL DE PHYSIQUE

As much h i g h e r microwave powers can b e r e a d i l y a t t a i n e d i t i s r e a s o n a b l e t o c o n s i d e r s t r o n g f i e l d e x p e r i m e n t s . The most s t r a i g h t f o r w a r d way t o d o s u c h

e x p e r i m e n t s i s t o u s e a microwave c a v i t y which m u l t i p l i e s t h e e f f e c t i v e power by t h e Q o f t h e c a v i t y . I n F i g u r e 5, we show t h e c a v i t y we have b u i l t f o r s u c h e x p e r i m e n t s which a l l o w s u s t o a p p l y t o t h e Rydberg atoms a s t a t i c t u n i n g f i e l d , a h i g h v o l t a g e

FIG. 3 . The e n e r g y l e v e l s f o r t h e r a d i a t i v e c o l l i s i o n p r o c e s s showing t h e r e a l and v i r t u a l l e v e l s .

100 120 140

DC F I E L D (V/cm)

SA-8702-73

FIG. 4. The o b s e r v e d 22p i o n s i g n a l a f t e r t h e p o p u l a t i o n o f 2 2 s s t a t e v s t h e d c f i e l d i n t h e p r e s e n c e o f a microwave f i e l d ( s o l i d t r a c e s ) o f f r e q u e n c y 1 5 GHz. The d o t t e d t r a c e s were o b s e r v e d w i t h n o microwave f i e l d , and t h e s h a r p r e s o n a n c e s i n t h e c e n t e r ( f o r b o t h s o l i d and d o t t e d t r a c e s ) r e s u l t from t h e r e s o n a n t c o l l i s i o n s w i t h t h e e m i s s i o n o f no p h o t o n s , w h i l e t h e d i s p l a c e d r e s o n a n c e s on t h e s i d e s ( s o l i d t r a c e ) a r e due t o m i c r o w a v e - a s s i s t e d c o l l i s i o n s .

f i e l d i o n i z a t i o n p u l s e , and a s t r o n g microwave f i e l d . 1 7 , 1 e We r e c a l l t h a t s i n c e t h e Na atoms a r e i n a t h e r m a l beam, t h e y d o n o t move a m a c r o s c o p i c d i s t a n c e d u r i n g t h e e x p e r i m e n t , and a l l t h r e e f i e l d s must be a p p l i e d i n t h e same p l a c e . Such a n a p p r o a c h works q u i t e w e l l . I n f a c t we can r e a d i l y o b s e r v e r a d i a t i v e l y a s s i s t e d c o l l i s i o n s w i t h 1 mW o f microwave power, a s shown by F i g u r e 6. S i n c e we h a v e t h e

7

Signal Out

Electron Multiplier

I I

_Source ^Atom

Pulsed

Dielectric

Microwave l nput

FIG. 5. Cut-away view o f t h e microwave c a v i t y ( n o t t o s c a l e ) . The c o p p e r septum b i s e c t s t h e h e i g h t o f t h e c a v i t y . Two h o l e s o f d i a - m e t e r 1 . 3 mm a r e d r i l l e d i n t h e s i d e w a l l s t o a d m i t t h e c o l l i n e a r l a s e r and Na a t o m i c beams, and 1 mm h o l e i n t h e t o p o f t h e c a v i t f a l l o w s ~ a + r e s u l t i n g from t h e f i e l d i o n i z a t i o n o f Na t o b e e x t r a c t e d .

22s ⁺ 21 p and 22p

No Microwaves

FIG. 6. The p r o c e s s Na 22s+Na 2 2 s + 21pl-22p w i t h and w i t h o u t 1 mw o f 1 4 GHz microwave r a d i a t i o n . As shown, t h e c r o s s s e c t i o n f o r t h e e m i s s i o n o f one photon d u r i n g t h e c o l l i s i o n i s a s l a r g e a s t h e c r o s s s e c t i o n f o r t h e e m i s s i o n o f no photons.

Cl-90 JOURNAL DE PHYSIQUE

c a p a b i l i t y o f p u t t i n g up t o 20 W i n t o o u r c a v i t y , which h a s a Q of

-

^{2000, i t i s}

e v i d e n t t h a t we s h o u l d be a b l e t o go w e l l i n t o t h e s t r o n g f i e l d regime.

Although we h a v e s t u d i e d s e v e r a l s t a t e s , we h e r e c o n c e n t r a t e on t h e 1 8 s

+

^{1 8 s +}

17p

+

18p s y s t e m shown i n F i g u r e 7. A s shown by F i g u r e 7 , i t i s p o s s i b l e f o r up t o t h r e e microwave photons t o b e e m i t t e d i n a c o l l i s i o n .

- 4 2 2 f

, , , , , ¹

0 100 200 300 400 500 600

ELECTRIC F I E L D (Vlcm)

SA-8702-81

FIG. 7. S t a r k e n e r g y - l e v e l diagram o f t h e 9 7 0 s t a t e s , r e l e v a n t t o t h e m u l t i p h o t o n - a s i s t e d r a d i a t i v e c o l l i s i o n s . The v e r t i c a l l i n e s i n d i c a t e t h e c o l l i s i o n a l t r a n s f e r and a r e drawn a t t h e f i e l d s where t h e y o c c u r . The t h i c k a r r o w s c o r r e s p o n d t o t h e e m i t t e d photons.

I n F i g u r e 8 we show t h e o b s e r v e d c o l l i s i o n a l r e s o n a n c e s when t h e Na 1 8 s s t a t e i s p o p u l a t e d and t h e 18p s t a t e i s d e t e c t e d f o r s e v e r a l microwave i n p u t powers a s t h e t u n i n g f i e l d i s scanned. The microwave f r e q u e n c y is 15.4 G H z .

There a r e s e v e r a l i n t e r e s t i n g p o i n t s t o n o t e r e g a r d i n g F i g u r e 2. F i r s t up t o t h r e e photon a s s i s t e d c o l l i s i o n s a r e o b s e r v e d , a t a n i n c i d e n t power of 1.2 W. Also a t t h e l o w e s t microwave power f o r which t h e m photon p r o c e s s i s o b s e r v e d t h e

c o l l i s i o n a l r e s o n a n c e i s b r o a d e r t h a n a t h i g h e r power. T h i s presumably r e f l e c t s t h e s m a l l e r i m p a c t p a r a m e t e r s and s h o r t e r t i m e s r e q u i r e d . I n some s e n s e one c a n a d j u s t t h e s t r e n g t h of t h e c o u p l i n g d u r i n g t h e c o l l i s i o n . F i n a l l y t h e z e r o and one photon p r o c e s s e s s a t u r a t e and a c t u a l l y d e c r e a s e a s t h e microwave power i s i n c r e a s e d , a n o b s e r v a t i o n t h a t i s o b v i o u s l y i m p o s s i b l e t o e x p l a i n u s i n g a p e r t u r b a t i o n t h e o r y approach.

To d e s c r i b e t h e s e d a t a , we have used t h e low f r e q u e n c y approach of A u t l e r and

~ o w n e s l ~ t o d e s c r i b e t h e a l t e r a t i o n of atoms i n t h e s t r o n g microwave f i e l d and t h e n we c o n s i d e r t h e r e s o n a n t d i p o l e - d i p o l e c o l l i s i o n s between t h e a l t e r e d atoms. The e s s e n c e o f t h e a p p r o a c h i s shown i n F i g u r e 9. At a s t a t i c f i e l d of Fs, a microwave

220 260 300 340 380 420 460 ELECTRIC FIELD (Vlcrn)

FIG. 8. The o b s e r v e d i o n s i g n a l a f t e r t h e p o p u l a t i o n o f t h e 1 8 s l e v e l v e r s u s t h e microwave f i e l d a t 15.42 G H z . T r a c e ( a )

c o r r e s p o n d s t o n o microwave power i n p u t t o t h e c a v i t y and shows t h e s e t o f f o u r z e r o photon c o l l i s i o n a l r e s o n a n c e s . T r a c e s ( b ) , ( c ) , ( d ) , and ( e ) c o r r e s p o n d r e s p e c t i v e l y t o 0.02, 0.30, 1.20, and 3.00 W o f i n p u t microwave power and show a d d i t i o n a l s e t s o f f o u r c o l l i s i o n a l r e s o n a n c e s c o r r e s p o n d i n g t o one, two and t h r e e photon r a d i a t i v e l y a s s i s t e d c o l l i s i o n s . The peaks l a b e l l e d 0 , 1, 2, and 3 c o r r e s p o n d t o t h e l o w e s t f i e l d member of t h e s e t o f f o u r r e s o n a n c e c o r r e s p o n d i n g t o 0, l., 2 , and 3 photon a s s i s t e d c o l l i s i o n s .

C 1-92 JOURNAL DE PHYSIQUE

f i e l d of amplitude Fmw produces a s i n u s o i d a l v a r i a t i o n i n t h e f i e l d and hence i n t h e energy a s shown by F i g u r e 9. Thus, t h e e n e r g i e s of t h e p s t a t e s vary approximately a s

Thus t h e e n e r g i e s a r e not s t a t i o n a r y , but o s c i l l a t e . The o s c i l l a t i o n of t h e e n e r g i e s may be expressed i n terms of a B e s s e l f u n c t i o n expansion. P h y s i c a l l y , t h e e f f e c t of t h e o s c i l l a t i n g microwave f i e l d i s t o produce sidebands on each of t h e 17p and 18p s t a t e s . The s s t a t e s a r e u n a f f e c t e d a s might be i n f e r r e d from F i g u r e 9.

E x p l i c i t l y t h e wave f u n c t i o n of t h e 17p s t a t e 117pmw>, f o r example, i s given by

=s

Here J, i s t h e Bessel f u n c t i o n , E is t h e energy of t h e 17p s t a t e , F i s t h e t o t a l e l e c t r i c f i e l d , FS and Fmw a r e t h e s t a t i c and microwave f i e l d s , w i s t h e a n g u l a r frequency of t h e microwave f i e l d ; and 117~) i s t h e wavefunction i n t h e absence of t h e microwave f i e l d . Note t h a t t h e s p a t i a l dependence i s not a l t e r e d . The

amplitude of t h e i t h sideband i s given by a Bessel f u n c t i o n which i s an o s c i l l a t i n g f u n c t i o n of t h e microwave f i e l d .

F,

FIELD -t

FIG. 9. S i m p l i f i e d energy l e v e l diagram of t h e 17p, 1 8 s , and 18p s t a t e s . A microwave f i e l d of amplitude F,, produces a s i n o s o i d a l v a r i a t i o n i n f i e l d and a p e r i o d i c v a r i a t i o n energy a s shown by t h e bold s e c t i o n of t h e energy l e v e l curves.

The energy l e v e l s of t h e s t a t e s and t h e f i r s t sidebands of t h e p s t a t e s a s a f u n c t i o n of t h e s t a t i c t u n i n g f i e l d a r e shown i n Figure 3 where t h e f i r s t sidebands of t h e p s t a t e s a r e shown. As shown by F i g u r e 10, p r o c e s s e s corresponding t o t h e n e t emission o r a b s o r p t i o n of d i f f e r e n t numbers of photons occur a t d i f f e r e n t f i e l d s , however s e v e r a l processes can l e a d t o t h e emission of t h e same number of photons. For example, one photon i s emitted when e i t h e r t h e 17p s t a t e and t h e upper 18p sideband o r t h e 18p s t a t e and upper 17p sideband a r e t h e f i n a l s t a t e .

To c a l c u l a t e t h e c r o s s s e c t i o n we assume t h a t i s p r o p o r t i o n a l t o t h e square of t h e dipole-dipole i n t e r a c t i o n m a t r i x element

From Eq. 6 it is apparent that the microwave power dependence is contained entirely in the product of the 17p and 18p Bessel function expansions given in Eq. 5. Using such a model we are able to reproduce quite accurately the experimental microwave power dependence of the cross section. This is shown in Figure 11 in which we show the observed and calculated power dependence for the various processes. One aspect of this treatment is worth noting. Consider the collisions in which one photon is emitted. It is clear from Figure 10 that three processes are possible, which are implicitly assumed to be coherent in Eq. 6. In fact if the coherence is neglected we find that the calculations do not agree with the experimental observations. For example if the coherence is neglected we would not expect to see the m photon emission collision cross section vanish.

FIG. 10. Schematic level diagram vs tuning field. The 17p and 18p levels are shown by solid lines with positive Stark shifts and their first upper and lower sideband by broken lines. The vertical lines show the possible resonant collision processes corresponding to the net number of photons emitted indicated at the top of the figure.

JOURNAL DE PHYSIQUE

MICROWAVE FIELD AMPLITUDE (Vlcm)

0 60 80 90 100 110 120 130 140 150 160 170

INPUT MICROWAVE POWER (W)

FIG. 11. Experimental cross sections for the m-photon-assisted collisions, as shown by the size of the (O,O)m resonance peaks, vs input microwave power; zero-photon- (open circle), one-photon- (closed circle), two-photon- (closed triangle), and three-photon- (closed square) assisted collisions. The cross section for a zero- photon collision at zero microwave power (not shown) is normalized to 1. Theoretical cross sections for zero-photon- (solid line), one-photon- (dashed line), two-photon- (long-dashed-short-dashed line), and three-photon- (dot-dashed line) assited collisions with the same normalization.

These and other recent experiments leave us convinced that radiative collisions and other phenomena involving strong radiation fields may best be studied with Rydberg atoms and microwaves. It is a pleasure to acknowledge stimulating conversations with D. C. Lorents and R. M. Hill In the course of this work. This work was supported by the Air Force Office of Scientific Research under contract F49620-79-(20212.

+ Permanent address: Laboratoire Aim6 Cotton C.N.R.S. I1 Ratiment 505, 91405 Orsay Cedex, France

*permanent address: Department of Physics, University of Connecticut, Storrs, Connecticut 06268

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