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LASER INDUCED COLLISIONAL ENERGY TRANSFER : HIGH RESOLUTION STUDIES AND
COHERENCE EFFECTS IN DIPOLE-DIPOLE INTERACTION
C. Bréchignac, Ph. Cahuzac, A. Débarre
To cite this version:
C. Bréchignac, Ph. Cahuzac, A. Débarre. LASER INDUCED COLLISIONAL ENERGY TRANSFER : HIGH RESOLUTION STUDIES AND COHERENCE EFFECTS IN DIPOLE- DIPOLE INTERACTION. Journal de Physique Colloques, 1985, 46 (C1), pp.C1-107-C1-111.
�10.1051/jphyscol:1985110�. �jpa-00224480�
JOURNAL DE PHYSIQUE
Colloque C I , supplement au n ° l , Tome 46, Janvier 1985 page C l - 1 0 7
LASER INDUCED COLLISIONAL ENERGY TRANSFER : HIGH RESOLUTION STUDIES AND COHERENCE EFFECTS IN DIPOLE-DIPOLE INTERACTION
C. B r e c h i g n a c , Ph. Cahuzac and A. D e b a r r e
Laboratoire Aimé Cotton , C.N.R.S. II, Bâtiment 505, 91405 Orsay Cedex, France
Résumé - Deux méthodes complémentaires ont été utilisées pour étudier des transferts collisionnels d'énergie induits par laser dans le cas d'une inter- action dipole-dipole. Une étude de profil spectral à haute résolution dans un mélange Na-Ca a confirmé l'existence d'un profil universel pour une in- teraction donnée, la mesure de taux de polarisation dans un mélange Eu-Sr a confirmé l'hypothèse que de tels processus préservaient partiellement les cohérences induites par un champ extérieur polarisé.
A b s t r a c t - Two complementary methods have been used t o i n v e s t i g a t e l i g h t i n - duced c o l l i s i o n a l energy t r a n s f e r s f o r a d i p o l e - d i p o l e i n t e r a c t i o n . A high r e s o l u t i o n s p e c t r a l p r o f i l e study i n a Na-Ca m i x t u r e has confirmed the as- sumption of a universal p r o f i l e f o r a given i n t e r a c t i o n , the measurement of p o l a r i z a t i o n r a t i o s i n a Eu-Sr mixture has confirmed the assumption t h a t such processes may p a r t i a l l y preserve the coherences induced by an external p o l a r i z e d f i e l d .
L i g h t - i n d u c e d c o l l i s i o n a l e x c i t a t i o n t r a n s f e r (LICET) process opens new e x c i t a t i o n channels which are otherwise a d i a b a t i c a l l y f o r b i d d e n / 1 , 2 / . Two atoms A and B undergo a c o l l i s i o n and simultaneously absorb a photon from an e x t e r n a l f i e l d which frequency matches the energy t o e x c i t e the atoms from the i n i t i a l s t a t e A ( i ) , B ( i ' ) t o the f i n a l s t a t e A ( f ) , B ( f ' ) :
(1) The r e a c t i o n
i s assumed e n e r g i c a l l y f o r b i d d e n . The i n f o r m a t i o n on the i n t e r a t o m i c p o t e n t i a l s which are r e l e v a n t i n the process(1)can be gained e i t h e r by the study o f the high r e s o l u t i o n s p e c t r a l p r o f i l e of the process, i . e . the v a r i a t i o n s of the cross sec- t i o n versus thelaser frequency u>, or by the study of the coherence p r o p e r t i e s of the f i n a l B s t a t e , induced by a p o l a r i z e d f i e l d .
These two d i f f e r e n t methods have been used i n the case of a d i p o l e - d i p o l e i n t e r a c - t i o n between d i s c r e t e l e v e l s : an high r e s o l u t i o n s p e c t r a l p r o f i l e study has been performed i n a Na-Ca m i x t u r e i n v o l v i n g an o r i g i n a l e x c i t a t i o n s c h e m e / 3 / , p o l a r i z a - t i o n r a t i o s have been measured i n a Eu-Sr r a d i a t i v e c o l l i s i o n process / 4 / .
In the case of a m u l t i p o l a r c o l l i s i o n a l i n t e r a c t i o n , the cross section of the p r o f i - l e i s maximum v/hen the energy of the photon e x a c t l y matches the i n t e r a t o m i c energy d i f f e r e n c e E [ B ( f ' ) ] - E [ A ( i ' ) ] . When the i n t e r e s t time 1 / A U , where AID i s the s h i f t between the photon frequency u and the i n t e r a t o m i c frequency u i s l a r g e r than the
-12 ° c o l l i s i o n time T ( = 10 s ) , the LICET process can be described as a two-photon
t r a n s i t i o n in the atom B, one v i r t u a l photon i s provided by the c o l l i s i o n a l t r a n s f e r Laboratoire associe a l'Universite Paris-Sud
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985110
C1-108 JOURNAL DE PHYSIQUE
and t h e o t h e r i s t h e l a s e r photon, corresponding t o t h e t ~ o e x c i t a t i o n channels 1 and 2 (Fig. 1 ) . The arocess i s enhanced by t h e presence of a real level in atom 6 c l o s e t o t h e v i r t u a l l e v e l , when i t e x i s t s the-channel f o r which A i s t h e smaller i s predominant.
i ,
I
'vj
r ' 42---- --. .--
e 'f
A 1 6 2
Fig. 1
-
E x c i t a t i o n schemefor a LICET process.The wavy arrows stand f o r t h e c o l l i s i o n a l energy t r a n s f e r . The s t r a i g h t arrows stand f o r t h e l a s e r photon a b s o r p t i o n .
For smaller i n t e r e s t t i n e s , A u ~ ~ > > l , t h e process i s more conveniently described by a molecular p i c t u r e and corresponds t o a p h o t o t r a n s i t i o n between t h e entrance ABi (R) and e x i t ABf(R) channels of t h e t r a n s i e n t molecule AS(R). In t h e q u a s i s t a t i c ap- proximation, t h e frequency of t h e absorbed photon w i s r e l a t e d t o t h e i n t e r n u c l e a r d i s t a n c e by t h e Franck Condon p r i n c i p l e and depends on t h e m u l t i p o l a r i t y of t h e i n t e r a c t i o n n , which a s s i g n e s t h e shape of t h e r e l a t i v e p o t e n t i a l curves ABi and AB,.
The s p e c t r a l p r o f i l e of t h e c r o s s - s e c t i o n o versus w i s deduced from a ~ a n d a u - ~ e n e r ' model. Thus, t h e power law of t h e q u a s i s t a t i c wing which corresponds t o t h e c r o s s i n g region of t h e dressed 1 eve1 s of t h e t r a n s i e n t mol ecul e i s f o r a 1 ong-range dipole-dipole i n t e r a c t i o n of t h e form
c ~ R - ~ .
This p i c t u r e i s v a l i d f o r both channels I and 2 andan universal p r o f i l e is expected f o r a given i n t e r a c t i o n , whatever t h e e x c i t a t i o n scheme i s .1 . Na-Ca LICET experiment
The s p e c i f i c e x c i t a t i o n scheme of t h e channel 1 has been a l r e a d y involved i n a high r e s o l u t i o n study of LICET i n a Eu-Sr mixture f o r a dipole-dipole i n t e r a c t i o n /5/, 1eaZing t o an experimental power law AN-
"'
f o r t h e q u a s i s t a t i c wing. The Na-Ca energy diagram i s s u i t a b l e t o study t h e channel 2 e x c i t a t i o n scheme ( F i g . 2 ) . Two dye l a s e r s pumped by a N2 pulsed l a s e r copropagate in a c e l l which c o n t a i n s t h e va- pours of Na and Ca a t p a r t i a l p r e s s u r e s of about 2 and 1 t o r r and a b u f f e r gas. One of them, a t a f i x e d frequency, d r i v e s t h e atoms of Na t o t h e 3p 2 ~ 3 / 2 l e v e l while t h e o t h e r i s tuned a c r o s s t h e interatomic t r a n s i t i o n 3p 2F3h -
4 p2ID^
and d r i v e s-
1t h e Ca atoms t o a v i r t u a l l e v e l 94.2 cm away from t h e resonant 4 s 4p
IP,
l e v e l . The collisional t r a n s f e r completes t h e e x c i t a t i o n of Ca t o t h e f i n a l 4p2 ID,. TheL
r a d i a t i v e c o l l i s i o n process i s monitored by t h e measurement of t h e i n t e n s i t y of t h e f l u o r e s c e n c e emitted from this l e v e l t o t h e resonant 4s 4p P I l e v e l when t h e l a s e r 1 frequency is varied.
The o t h e r r e a l l e v e l s of Ca l i e f a r from t h e v i r t u a l l e v e l . Furtherniore,the c o n t r i - bution of t h e channel 1 t o t h e f i n a l c r o s s s e c t i o n can be neglected because in Ca t h e r e i s no t r a n s i t i o n i n quasi-coincidence with t h e D l i n e s of Na. The doniinant c o l l i s i o n a l i n t e r a c t i o n i s then dipole-dipole Na (3s-3p)
-
Ca ( 4 s 4p-
4p 2 ) .F i g . 2
-
Energy l e v e l diagram f o r Na-Ca experiment. The two v i r t u a l l e v e l s94.2 cm-I and 1 1 1.4 cm-I away f r o m t h e 4s 4p I p 1 l e v e l c o r r e s p o n d t o t h e two p o s s i - b l e LICET processes f r o m t h e i n i t i a l 3p 2~ 3/2,
i2
Na l e v e l s .To a v o i d d i r e c t two-photon e x c i t a t i o n i n Ca, t h e t r a n s f e r l a s e r i s d e l a y e d a g a i n s t t h e f i x e d o n e a n d an e f f i c i e n t t r a n s f e r between t h e 3p l e v e l s o f Na o c c u r s b e f o r e t h e t r a n s f e r process.
The LICET process i s d e s c r i b e d by t h e f o l l o w i n g r e a c t i o n :
J stands f o r 312 o r 1/2.
Thus, t h e p r o f i l e r e s u l t s o f t h e s u p e r p o s i t i o n o f two s i g n a l s , and t h e q u a s i s t a t i c wing extends f o r t h e p o s i t i v e d e t u n i n g s i n agreement w i t h t h e m o l e c u l a r scheme
( F i g . 3 ) .
h1 = 4209.9 A b I
Fig. 3
-
Experimental spectrum o f Na-Ca LICETuexperiment.The two peaks p o i n t a t 1 = 4209.9 and 4206.9 A correspond t o i n t e r a t o m i c t r a n s i - t i o n s f r o m t h e 3p P3/2,1,2 2 Na l e v e l s . The p a r t i a l c o n t r i b u t i o n s a r e r e p r e s e n t e d by t h e c u r v e s 1 and 2 c o r r e s p o n d i n g i n t h e q u a s i s t a t i c wings t o t h e e x p e r i m e n t a l power l a w 6 0 - " ~ where 80 i s t h e l a s e r d e t u n i n g i n wavenumbers. The sum o f t h e two s i g n a l s i s reproduced on t h e t o t a l p r o f i l e by t r i a n g l e s .
L i n e a : s t e p e x c i t a t i o n t o t h e 4p2 ' D ~ l e v e l o f Ca,
L i n e b,c : s t e p e x c i t a t i o n t o t h e 14s 2 ~ 1 / 2 l e v e l o f Na v i a t h e 3p 2 P
3/2,1/2 '
C1-110 JOURNAL DE PHYSIQUE
The b e s t f i t o f t h e t o t a l c r o s s s e c t i o n r e s u l t s o f t h e sum o two independant s i - gnals, f o r which t h e experimental q u a s i s t a t i c law i s
.
For t h e process i n - volv$g t h e i n i t i a l 2 ~ ~ ~ ~ le v e l t h e cross s e c t i o n a t c e n t r a l t u n i n g i s170 A / ~ ~ . c m - ~ 2 o f t h e same order o f magnitude than i n t h e case Eu-Sr. These r e s u l t s c o n f i r m t h e assumption o f an u n i v e r s a l p r o f i l e f o r a given i n t e r a c t i o n as f o r t h e two e x c i t a t i o n channels (Eu-Sr channel 1, Na-Ca channel 2) t h e same behaviour i s observed. The discrepancy w i t h the expected law suggests t h a t a more r e a l i s t i c po- t e n t i a l i n v o l v i n g s h o r t range i n t e r a c t i o n s should be necessary t o f i t t h e p r o f i l e s . 2. Eu-Sr LICET experiment
Recently, i t has been p o i n t e d o u t t h a t t h e coherences induced i n a r a d i a t i v e c o l l i- s i o n process by a p o l a r i z e d e x t e r n a l f i e l d may be p a r t i a l l y p r e s e r ~ e d ~ r e f l e c t i n g t h e n a t u r e o f the c o l l i s i o n a l i n t e r a c t i o n /6/. F o l l o w i n g Berman, we can g i v e a s i a - p l e p i c t u r e o f t h e coherences p r o p e r t i e s o f t h e f i n a l B s t a t e e x c i t e d by a LICET reaction. I n t h e case o f a m u l t i p o l a r i n t e r a c t i o n , t a k i n g i n t o account t h e average over a l l parameters and p o s s i b l e o r i e n t a t i o n s , t h e LICET process reduces t o t h e combined a c t i o n o f t h r e e f i e l d s : two u n p o l a r i z e d m u l t i p o l a r f i e l d s o r i g i n a t i n g from a l l d i r e c t i o n s a c t i n g separately on A and B b u t c o r r e l a t e d by c o u p l i n g constants, which represent t h e c o l l i s i o n a l energy t r a n s f e r and t h e e x t e r n a l p o l a r i z e d f i e l d a c t i n g on B. This p i c t u r e i s r e c t r i c t e d t o t h e impact core o f t h e p r o f i l e and t o t h e case where a l l t h e i n v o l v e d l e v e l s arequasi-degenerate (the energy s p l i t t i n g w i t h i n each m a n i f o l d i s l e s s than t h e r e c i p r o c a l c o l l i s i o n time). I n t h e case o f t h e channel 1, i f t h e i n i t i a l l e v e l i s unpolarized, so i s t h e v i r t u a l l e v e l and t h e coherences o f t h e f i n a l s t a t e B ( f l ) r e f l e c t t h e l i g h t p o l a r i z a t i o n . I n t h e case o f t h e channel 2, t h e v i r t u a l l e v e l i s p o l a r i z e d and s e l e c t i o n r u l e s a r e a p p l i e d t o t h e atom A by t h e i n t e r m e d i a t e o f t h e c o u p l i n g constants. The f i n a l coherences e x p l i c i t l y depend on t h e mu1 t i p o l a r i t y o f t h e c o l l i s i o n a l i n t e r a c t i o n . These coherences can be ~ o n i t o - r e d by p o l a r i z a t i o n measurenents. I f the e x t e r n a l f i e l d i s 1 in e a r l y p o l a r i z e d i n t h e z d i r e c t i o n , one can define t h e p o l a r i z a t i o n r a t i o o f t h e fluorescence propagating i n t h e y d i r e c t i o n and p o l a r i z e d e i t h e r i n t h e z o r x d i r e c t i o n as
S Z
-
Sx p = ---+ Sx
where S i s the fluorescence s i g n a l . I n t e r e s t i n g f e a t u r e s o f the method can be poin- t e d o u t : t h e measurement o f P o n l y i m p l i e s r e l a t i v e measurements o f c r o s s sections i n t h e core o f t h e p r o f i l e w h e r e t h e s i g n a l i s maximum. The i n f o r m a t i o n on t h e c o l l i - sional i n t e r a c t i o n i s obtained w i t h o u t t u n i n g t h e l a s e r frequency on t h e c o n t r a r y o f s p e c t r a l p r o f i l e a n a l y s i s .
As a t e s t o f t h e t h e o r e t i c a l p r e d i c t i o n s , t h i s method has been used t o measure t h e p o l a r i z a t i o n r a t i o o f the fluorescence e n i t t e d from t h e f i n a l degenerate Zeeman s t a - t e s 5p2 o f Sr i n a r a d i a t i v e c o l l i s i o n process w i t h Eu, i n an e x t e r n a l II p o l a r i - zed f i e l d . The l e v e l scheme i s of t h e type 1 o f F i g . 1. The Eu atoms a r e i n i t i a l l y d r i v e n t o t h e 6s 6p 8 Pgl2 l e v e l which i s unpolarized. They t r a n s f e r t h e i r energy t o t h e S r a t o m which a r e d r i v e n t o a v i r t u a l l e v e l 63 cm-' away from t h e resonant 5s 5p Ipl l e v e l . The a b s o r p t i o n o f a
n
p o l a r i z e d e x t e r n a l photon completes t h e e x c i - t a t i o n t o t h e 5p2 Ib2. An e x p l i c i t c a l c u l a t i o n o f t h e p o l a r i z a t i o n r a t i o o f t h e2 1 fluorescence e m i t t e d from t h e 5p2 'p2 e x c i t e d by t h e LICET process i s then in. I n t h i s s p e c i f i c case, t h e v i r t u a l s t a t e i s unpolarized and d e s p i t e t h e d i f f e r e n t nature o f t h e processes, the same value should be obtained i n a two-step e x c i t a t i o n from t h e 5s2
I s o
t o t h e 5p2ID^
v i a t h e r e a l 5s 5p PI leve1,provided t h a t the f i r s t 1 photon i s unpolarized. The r e l a t i v e t r a n s i t i o n p r o b a b i l i t i e s between t h e Zeeman suble-1 21
v e l s o f t h e 5s 5p PI and 5p2 '13~ l e v e l s l e a d t o t h e sane r a t i o T .
The t r a n s f e r l a s e r i s
n
p o l a r i z e d , t h e backward fluorescence i s c o l l e c t e d through an analyser which a l l o w s p o l a r i z a t i o n measurements. A weak magnetic f i e l d i s used to. d e f i n e p r e c i s e l y t h e q u a n t i f i c a t i o n a x i s . We have measured t h e p o l a r i z a t i o n r a t i ob o t h i n t h e c o r e and i n t h e q u a s i s t a t i c wing o f t h e p r o f i l e as shown on t h e F i g . 4.
F i g . 4
-
a ) a n a l y s i s i n t h e z p o l a r i z a t i o n d i r e c t i o n ; b ) a n a l y s i s a t r i g h t a n g l e ; X ) e x p e r i m e n t a l power l a w (60)-Oe8 ; A ) comparison between Sz p r o f i l e and renormal i- zed Sx p r o f i l e .E i t h e r f o r t h e f l u o r e s c e n c e s i g n a l a l o n g t h e p o l a r i z a t i o n a x i s (upper t r a c e ) o r a t r i g h t a n g l e ( l o w e r t r a c e ) t h e power l a w i n t h e wing i s ( A L O ) - ~ ' ~ d e m o n s t r a t i n g t h a t i n t h i s s p e c i a l case where t h e v i r t u a l l e v e l i s unpolarized, t h e p o l a r i z a t i o n r a t i o i s independant o f t h e s h i f t o f t h e l a s e r Aw. The experimental v a l u e P = 0.43 (0.C5) i s i n v e r y good agreement w i t h t h e p r e d i c t e d value. F o r an u n p o l a r i z e d l i g h t , t h e p o l a r i z a t i o n f a l l s t o z e r o w i t h i n t h e u n c e r t a i n t y .
The good agreement observed i n t h i s s i m p l e case between experimental and t h e o r e t i - c a l r e s u l t s demonstrates t h a t t h i s txethod can r e v e a l an u s e f u l t o o l f o r f u r t h e r i n - v e s t i g a t i o n s o f LICET processes e s p e c i a l l y i n t h e case o f weak c r o s s s e c t i o n s . REFERENCES
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