COLLISIONS IN THE PRESENCE OF A LASER FIELD AND THE LASER AS A TOOL FOR STATE SELECTIVE PREPARATION OF MOLECULAR STATES IN COLLISIONS

HAL Id: jpa-00224473

https://hal.archives-ouvertes.fr/jpa-00224473

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

COLLISIONS IN THE PRESENCE OF A LASER FIELD AND THE LASER AS A TOOL FOR STATE

SELECTIVE PREPARATION OF MOLECULAR STATES IN COLLISIONS

I. Hertel

To cite this version:

I. Hertel. COLLISIONS IN THE PRESENCE OF A LASER FIELD AND THE LASER AS A TOOL

FOR STATE SELECTIVE PREPARATION OF MOLECULAR STATES IN COLLISIONS. Journal

de Physique Colloques, 1985, 46 (C1), pp.C1-37-C1-41. �10.1051/jphyscol:1985104�. �jpa-00224473�

COLLISIONS IN THE PRESENCE OF A LASER FIELD AND THE LASER AS A TOOL FOR STATE SELECTIVE PREPARATION OF MOLECULAR STATES IN COLLISIONS

I.V. Hertel

Institut fttr Molektilphysik, Freie Universitilt Berlin and Joint Institute for Laboratory Astrophysics*. University of Colorado and National Bureau of

Standards, Boulder, Colorado 80309, U.S.A.

Résumé - Dans l'étude d'événements collisionnels individuels, le rayonne- ment laser peut être utilisé pour modifier ou sonder le processus avant, pendant ou après 1'interaction binaire entre les particules. Nous discu-

tons certains problèmes et certaines possibilités particulièrement in- téressantes pour modifier le processus de collision dans un champ laser intense, mais pas trop intense. Nous discutons la possibilité de pré- parer sélectivement des états quasi-moléculaires Z et TT dans des col- lisions ion-atome, à partir d'états atomiques asymptotiques p pompés optiquement par laser.

Abstract - In the study of individual collision events laser light can be used to influence or probe the process prior to, during, or after the binary particle interaction. We discuss some problems and particularly challenging possibilities for modifying the colli- sion process in a high, but not too high, laser field. We discuss the possibilities of state selective preparation of quasimolecular I and II states in ion-atom collisions, with asymptotically laser optical pumped atomic p-states.

I. INTRODUCTION

The main subject of this workshop, collisions in the presence of a laser field, can be interpreted rather broadly: The laser may act on the system

a) while the colliding particles are still infinitely separated,

b) during the actual collision process, i.e., at intermiclear distances where the collisional interaction potential has become significant,

c) after the collision has occurred to probe the state of the system.

Going through the talks given at the workshop one finds that the majority of the contributions concentrate on aspect a) while one is inclined to find aspect b) and the possibilities of modifying the interaction itself perhaps more spectacular.

Obviously this topic is much more difficult to access experimentally than theo- retically due to the limitations on available laser power. A simple time scale argument illuminates this: The time of passage of an atomic beam through a laser beam may be 10~6 sec, the spontaneous lifetime of an excited atomic beam about 10- 8 sec, the time for induced transitions (i.e. the inverse Rabi frequency) around t^ ~ 1 0- 9 sec (at a conveniently available cw-laser intensity of 1 W/cm2),

*1983-1984 JILA Visiting Fellow.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985104

C 1-38 JOURNAL

DE

_PHYSIQUE

however, the collisional interaction time is tc

-

^{10-l2 to} sec depending on energy and type of particle interacting with the atom. Thus, we have in most practicable cases tc

<<

tR which implies that during an individual collision act the laser cannot modify the atomic states very much. Thus, in order to observe the influence of the laser on an individual collision event we have to either ob- serve very many collisions (typically in a bulk experiment thereby renouncing the degree of detailed information observable in a crossed beam experiment), or we have to increase the laser power drastically by a factor (tC/tR)', since the Rabi oscillation time scales with the square of the laser intensity. Thus this gives laser powers of the order of 10' to 10'' w/cm2, not impossible but difficult to use in a collision experiment. Then the observable effects are of great variety and some are genuine laser effects, i.e., effects that could not be observed with a weak photon source even if one were willing and able to accumulate data for a very long time. We will discuss one of these genuine laser effects which could open new paths for a detailed study of collisional scattering amplitudes and which so far has not achieved great attenti0n.l

11. LASER-INDUCED COHERENCE OF ELASTIC SCATTERING AMPLITUDES FOR DIFFERENT ELECTRONIC STATES

A typical differential cross section experiment involving laser excitation of an atomic resonance level usually cannot detect any interference between ground and excited state scattering amplitudes f and fe. Mostly, such studies2 have concen- trated on inelastic processes and the% amplitudes f e. However, one might be interested in exploiting the coherence between groun% and excited state which the laser introduces.

Let us consider a hypothetical two-level atom whose energy levels in a weak or strong near-resonant laser field are shown in Fi 1 . e> and Ig> indicate the original ground and excited states, le0>, (el>, fgl>: le2>, (g2> designate these states plus the photon field with n or n

+

1 or n

+

2 photons. The dressed states in the strong field are coherent superpositions of ground and excited states, the two states relating to the same energy level are split by haR where OR = h / t R is the Rabi frequency. Transitions between these dressed states have been observed spectroscopically in cell experiments by observing the re-emitted resonance fluo- rescence.3 In a crossed beam experiment one would have to observe the processes

1, 2

and

3

by appropriate energy analysis of the particles if one wants to avoid coincidence experiments with high optical resolution.

The differential cross sections measurable in crossed beam experiments would be related1 to the scattering amplitudes as shown in Table 1.

nhv

weak strong

laser field

collisions

Fig. 1. Energy levels of a two-level atom in a laser field and some possible collisional transitions.

Process Final kinetic energy Differential cross section

sum of 1,2,3

We see that interesting interference effects between ground and excited states could be observed, when the transitions among the (very closely spaced) dressed levels were observable individually in a differential scattering experiment.

These effects cancel if, as usual, one sums over all processes 1,2,3 in the ex- periment. The splitting of the levels at easily accessible 1 w/cm2 is typically

5

?( loe7 eV and at best one would be able to resolve some meV with state-of-the- art particle spectroscopy. S o , a factor of ~ ( 1 0 ~ ) ~ :

lo8

w/cm2 is needed to do the experiment

-

challenging and perhaps not impossible to do in the near future.

Also worthwhile considering is the possibility of using 1r/2 pulses for creating a coherent ground-excited state population.

111. PREPARATION OF QUASIMOLECULAR COLLISION STATES

BY

POLARIZED

LASER

LIGHT Many of the other processes, dealing with atom-atom, ion or molecule interactions which are the focus of this workshop can be schematically summarized as shown in Fig. 2.

Fig. 2. Schematic diagram of quasimolecular collision processes.

C1-40 JOURNAL

DE

PHYSIQUE

Figure 2(a) indicates asymptotic state selective preparation of atomic np' states by a polarized laser with subsequent superelastic collisions occurring at the curve crossing marked

'C.'

Figure 2(b) represents a prototype of laser assisted collision where the photon is tuned in resonance with the molecular states acces- sible only during the collision. Figure 2(c) shows the collisional redistribution of radiation experiment as reviewed by ~ u r n e t t ~ where the emphasis is (as in Fig.

(a)) on the population or repopulation of the C and

II

states in the circled area around RL. Finally, for comparison, in Fig. 2(d) a classical line shape experi- ment is illustrated; the asymptotically excited atom collides with B and the quasi- molecular system A*B re-emits radiation during the collision. Figure 2 illustrates the close relation of all these types of processes.

We discuss in more detail the particular aspect of whether, and how, it may be possible to prepare or detect the quasimolecular excited C and

II

states. Take the example of the process in Fi 2(a), which has been studied in detail, both experimentally and theoreticallyg:6 for the model case

in a center-of-mass energy range of

15

to 50 eV. The linearly p~larized laser prepares asymptotically the 3po or 3pr atomic states predominantly. The crucial question is, how do these atomic states correlate with the molecular X and II states.

From the potential energy diagram Fig. 2(a) we know that only preparation of the II state can lead to the nonadiabatic process via curve crossing ' C ' . Figure 3 shows the experimental result of the dependence of the differential cross section for pro- cess

(1)

on the laser polarization angle: For 0' one prepares asymptotically the 3po orbital, for 90' the 3pn. Obviously, the maximum is found near 90° and the asymptotic 3pr preparation thus leads into the

II

quasimolecular state. A closer look shows that the maximum of the cross section is found at an angle slightly less than 90". The intuitive interpretation of this phenomenon is shown in the lower part of Fig. 3. At large internuclear distances, the atomic charge cloud moves space fixed, at small internuclear distances it moves body fixed, i.e., rotates with the internuclear axis. The transition between the two types of be- havior occurs around RL in the circled region of Fig. 2(a). A semiclassical cal- culation6 shows that this intutive concept holds as long as the impact parameter

b

<<

RL but loses its meaning for b

>

RL. In the above case, RL is about 22 a.u.

Fig. 3. Upper part: Dependence of differ- ential cross section on polarization angle of state preparing linearly polarized laser light. Lower part: Schematic interpretation of the experimental result .5

p o l o r i s o f i o n a n g l e

l i g h t . I n p r o c e s s (1) one f i n d s a r e l a t i v e d i f f e r e n c e i n t h e s c a t t e r i n g s i g n a l of -30% a t 170 eVdegr, v a r y i n g o n l y s l i g h t l y w i t h c o l l i s i o n energy. Here a warning i s a p p r o p r i a t e : one s h o u l d n o t a t t e m p t t o u s e c o n c e p t s t h a t a r e t o o s i m p l e t o ex- p l a i n t h e r e s u l t . The s e m i c l a s s i c a l c a l c u l a t i o n 6 shows t h a t t h e a n g u l a r momentum t r a n s f e r a s s o c i a t e d w i t h t h e l e f t - r i g h t asymmetry o c c u r s a t v e r y l a r g e i n t e r n u c l e a r d i s t a n c e s R ) RL due t o d i f f e r e n t phase f a c t o r s f o r t h e s t a t e s e v o l v i n g on t h e long- r a n g e p a r t s of t h e m o l e c u l a r C and

It

s t a t e s .

I V . CONCLUSIONS

We have s e e n t h a t t h e l a s e r r a d i a t i o n used t o d i a g n o s e i n d i v i d u a l c o l l i s i o n pro- c e s s e s o f f e r s a v a r i e t y of s h a r p t o o l s t o probe t h e i n t e r a c t i o n . The outcome of t h e s e e x p e r i m e n t s can now be u n d e r s t o o d f o r some model c a s e s a s reviewed i n Ref.

6 . On t h e o t h e r hand, t h e l a s e r h a s , up t o now, n o t been f u l l y e x p l o i t e d i n modi- f y i n g c o l l i s i o n p r o c e s s e s d u r i n g t h e i n t e r a c t i o n . I n p a r t i c u l a r , c o h e r e n t s u p e r - p o s i t i o n of s c a t t e r i n g a m p l i t u d e s f o r d i f f e r e n t a t o m i c l e v e l s could be e n f o r c e d by a s t r o n g l a s e r f i e l d , l e a d i n g t o a new v a r i e t y of c o l l i s i o n s t u d i e s .

R e f e r e n c e s

1. L. Hahn and I. V. H e r t e l (19721, J. Phys. B

5,

1995.

2. I. V. H e r t e l and W. S t o l l (19781, Adv. Atom. Mol. Phys.

13,

113.

3. P. D. K l e i b e r , K. B u r n e t t and J. Cooper (1981), Phys. Rev. L e t t .

47,

1595.

4. K. B u r n e t t , t h i s volume.

5. A. BPhring, I. V. H e r t e l , E. Meyer and H. Schmidt ( 1 9 8 3 ) , 2. Phys. A=, 293.

6. I. V. H e r t e l , H. Schmidt, A. B I h r i n g and E. Meyer ( 1 9 8 4 ) , t o be p u b l i s h e d .