LEVEL-CROSSING OPTOGALVANIC SPECTROSCOPY

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LEVEL-CROSSING OPTOGALVANIC SPECTROSCOPY

P. Hannaford, D. Gough, G. Series

To cite this version:

P. Hannaford, D. Gough, G. Series. LEVEL-CROSSING OPTOGALVANIC SPECTROSCOPY.

Journal de Physique Colloques, 1983, 44 (C7), pp.C7-107-C7-115. �10.1051/jphyscol:1983709�. �jpa-

00223266�

JOURNAL DE PHYSIQUE

Colloque C7, suppl6ment au n o l l , Tome 44, novembre 1983 page C7-107

L E V E L - C R O S S I N G O P T O G A L V A N I C SPECTROSCOPY P. Hannaf ord, D. S. Gough and G.W. s e r i e s r

CSIRO D i v i s i o n o f Chemical Physics, P.O. Box 260, CZayton 3168, A u s t r a l i a r ~ l a r e n d o n Laboratory, Parks Road, Oxford OX2 3PU, U. K.

Resume - La s p e c t r o s c o p i e o p t o g a l v a n i q u e e s t u t i l i s e e p o u r l a d g t e c t i o n d e c r o i s e m e n t s d e n i v e a u x e n champ r n a g n e t i q u e n u 1 o u d e v a l e u r f i n i e . C e t t e me- t h o d e o f f r e u n e t e c h n i q u e s e n s i b l e , s a n s e f f e t D o p p l e r , p o u r d e t e r m i n e r l a s t r u c t u r e h y p e r f i n e d e s n i v e a u x p r o f o n d s e t 6 l e v 6 s i r n p l i q u k s d a n s l e s t r a n - s i t i o n s a t o r n i q u e s .

A b s t r a c t - O p t o g a l v a n i c spectroscopy i s a p p l i e d t o t h e d e t e c t i o n o f l e v e l - c r o s s i n g s a t z e r o and f i n i t e magnetic f i e l d s . The method p r o v i d e s a sens- i t i v e , D o p p l e r - f r e e t e c h n i q u e f o r d e t e r m i n i n g h y p e r f i n e s t r u c t u r e s i n b o t h l o w e r and upper l e v e l s o f a t o m i c t r a n s i t i o n s .

I

-

INTRODUCTION

The d e t e c t i o n o f changes i n t h e p o l a r i z a t i o n p r o p e r t i e s o f f l u o r e s c e n t l i g h t when two s u b l e v e l s become degenerate, e i t h e r a t z e r o o r f i n i t e magnetic f i e l d , has become a w e l l - e s t a b l i s h e d t e c h n i q u e f o r d e t e r m i n i n g s p e c t r o s c o p i c q u a n t i t i e s such as h y p e r f i n e s t r u c t u r e f a c t o r s , S t a r k s h i f t s , r a d i a t i v e l i f e t i m e s and c o l l i s i o n a l d i s a l i g n m e n t c r o s s s e c t i o n s o f e x c i t e d a t o m i c l e v e l s /l/. The r e s o l u t i o n o f t h e t e c h n i q u e i s determined b y t h e homogeneous w i d t h o f t h e c r o s s i n g s u b l e v e l s

( t y p i c a l l y 1-10 MHz) and t h u s a l l o w s v e r y s m a l l s p l i t t i n g s t o be determined w i t h a h i g h degree o f p r e c i s i o n .

I n t h i s paper we d e s c r i b e t h e a p p l i c a t i o n o f o p t o g a l v a n i c spectroscopy t o t h e d e t e c t i o n of l e v e l - c r o s s i n g s . The mechanism f o r d e t e c t i n g t h e c r o s s i n g s d i f f e r s from t h a t n o r m a l l y employed i n f l u o r e s c e n c e experiments. The o p t o g a l v a n i c c u r r e n t i n a gas d i s c h a r g e a t p r e s s u r e s o f t h e o r d e r o f 1 t o r r tends t o behave as an i s o t r o p i c probe o f a t o m i c l e v e l s and i s n o r m a l l y s e n s i t i v e o n l y t o t h e p o p u l a t i o n s o f t h e l e v e l s connected by t h e l a s e r /2/, i n c o n t r a s t w i t h f l u o r e s c e n t l i g h t w h i c h i s s e n s i t i v e t o a l i g n m e n t and o r i e n t a t i o n o f t h e l e v e l s as w e l l as p o p u l a t i o n . (Atomic a1 i gnment m i g h t be expected t o be d e t e c t a b l e u s i n g o p t o g a l v a n i c spectroscopy under c e r t a i n d i s c h a r g e c o n d i t i o n s / 3 , 4 / , and i n d e e d t h e r e has been a v e r y r e c e n t r e p o r t / 5 / o f d e t e c t i o n o f a l i g n m e n t i n o p t o g a l v a n i c s i g n a l s f r o m a neon d i s c h a r g e o p e r a t e d i n a magnetic f i e l d o f about 1 kG ) . I n o p t o g a l v a n i c experiments where t h e l i g h t source i s a cw l a s e r , one may e x p l o i t t h e f a c t t h a t t h e t r a n s i t i o n may be s a t u r a t e d o r p a r t i a l l y s a t u r a t e d . Under t h e s e c o n d i t i o n s , t h e r e may o c c u r i n t h e v i c i n i t y o f a l e v e l - c r o s s i n g a r e d i s t r i b u t i o n o f p o p u l a t i o n between t h e upper and l o w e r l e v e l s , which i s r e f l e c t e d as a resonance /6,7/ i n t h e o p t o g a l v a n i c c u r r e n t . L e v e l - c r o s s i n g s a t u r a t i o n resonances o f t h i s t y p e had p r e v i o u s l y been observed i n fluorescence/8,9/ and a b s o r p t i o n /10/ experiments, and i t was p r e d i c t e d /11/ t h a t t h e y s h o u l d a l s o be observed w i t h o p t o g a l v a n i c d e t e c t i o n . A t h e o r e t i c a l t r e a t m e n t of t h e l e v e l - c r o s s i n g o p t o g a l v a n i c resonances, based on a s i m p l e r a t e - e q u a t i o n approach, has been r e p o r t e d r e c e n t l y by Dodd /12/.

The r e d i s t r i b u t i o n o f p o p u l a t i o n t h a t occurs i n t h e v i c i n i t y o f a l e v e l - c r o s s i n g under c o n d i t i o n s o f s a t u r a t i o n can be e a s i l y u n d e r s t o o d by c o n s i d e r i n g t h e s i m p l e case o f a z e r o - f i e l d c r o s s i n g f o r a Ja=O t o Jb=1 t r a n s i t i o n ( F i g . 1 ) . The l a s e r l i g h t i s assumed t o be l i n e a r l y p o l a r i z e d i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e magnetic f i e l d d i r e c t i o n so t h a t t h e ^'0 and ^{0 -} t r a n s i t i o n s a r e s t i m u l a t e d . F o r s i m p l i c i t y i t i s assumed t h a t these t r a n s i t i o n s a r e c o m p l e t e l y s a t u r a t e d by t h e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983709

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S p l ~ t t ~ n g > 2 Gb 2 lransltlons 2 veloc~ty groups

2Gb > spl~lt~ng > G Zero s p l ~ t t ~ n g 2 lrans~t~ons l trans111on 1 veloc~ly group

F i g . 1

-

R e d i s t r i b u t i o n o f a t o m i c p o p u l a t i o n t h a t can o c c u r i n t h e v i c i n i t y o f a z e r o - f i e l d l e v e l - c r o s s i n g under c o n d i t i o n s o f s a t u r a t i o n . The t h r e e r e g i o n s

correspond t o ( a ) h i g h magnetic f i e l d , where t w o d i f f e r e n t v e l o c i t y groups (2n atoms) i n t e r a c t w i t h t h e l a s e r , ( b ) l o w f i e l d , where o n l y one group ( n atoms) i n t e r a c t s , and ( c ) z e r o f i e l d , where t h e r e i s a c o h e r e n t s u p e r p o s i t i o n o f of and G-

t r a n s i t i o n s .

l a s e r f i e l d and t h a t c o l l i s i o n a l r e l a x a t i o n between t h e mb = 0, +l s u b l e v e l s i s n e g l i g i b l e .

A t h i g h m a y n e t i c f i e l d s ( F i g . l a ) t h e s p l i t t i n g o f t h e mb = +l s u b l e v e l s i s such t h a t t h e o and ^U- t r a n s i t i o n s a r e r e s o l v e d w i t h r e s p e c t t o t h e i r homogeneous w i d t h 2 r a b (where Tab i s t h e r e l a x a t i o n r a t e o f t h e o p t i c a l coherence, i n t h e n o t a t i o n o f Decomps, Dumont and D u c l o y / 8 / ) , and two d i s t i n c t " h o l e s " a r e burned i n t o t h e v e l o c i t y d i s t r i b u t i o n o f t h e atoms by t h e l a s e r . Under c o n d i t i o n s o f s a t u r a t i o n , t h e l a s e r f i q l d e q u a l i z e s t h e p o p u l a t i o n s i n t h e upper and l o w e r l e v e l s f o r each o f t h e ^U- and o t r a n s i t i o n s . Thus i f t h e r e a r e n atoms i n k e r a c t i n g w i t h t h e l a s e r w i t h i n each v e l o c i t y group, t h e t o t a l number o f atoms i n t h e J b = 1 upper l e v e l a t e q u i l i b r i u m w i l l be n/2

+

n/2 = n . A t l o w m a g n e t i c f i e l d s ( F i g . l b ) where t h e of, ^U- s p l i t t i n g i s s m a l l e r t h a n 2rab3 atoms i n t h e same v e l o c i t y group a r e s t i m u l a t e d t o make of and o- t r a n s i t i o n s , and o n l y a s i n g l e h o l e i s burned i n t o t h e v e l o c i t y d i s t r i b u t i o n ; so t h a t i f t h e s p l i t t i n g i s g r e a t e r t h a n t h e

homogeneous w i d t h o f t h e upper l e v e l r b , t h e l a s e r f i e l d e q u a l i z e s t h e p o p u l a t i o n s i n each o f t h e t h r e e s u b l e v e l s m, = 0, rnb = +l and mb = -1. The t o t a l number o f atoms i n t h e upper l e v e l i s t h e n n / 3 + n/3 = 2n/3. A t z e r o f i e l d , t h e mb = +l s u b l e v e l s a r e degenerate ( F i g . l c ) and t h e r e i s a c o h e r e n t s u p e r p o s i t i o n o f t h e o+ and o- t r a n s i t i o n s which i s e q u i v a l e n t t o a s i n g l e ⁿ t r a n s i t i o n ; s o t h a t n / 2 a r e e x c i t e d t o t h e upper l e v e l . The same r e s u l t i s f o u n d by assuming l i n e a r - o p o l a r i z a t i o n and i n c l u d i n g t h e r e s u l t i n g u p p e r - l e v e l Zeeman coherence i n t h e c a l c u l a t i o n . Thus as t h e magnetic f i e l d i s swept t h r o u g h a l e v e l - c r o s s i n g a t z e r o f i e l d , t h e p o p u l a t i o n i n t h e upper l e v e l (and hence t h e o p t o g a l v a n i c c u r r e n t ) e x h i b i t s a resonance c h a r a c t e r i z e d by t h e homogeneous w i d t h o f t h e t r a n s i t i o n 2rab ( o r 2hrab/gbpB i n u n i t s o f magnetic f i e l d ) , upon which i s superimposed a narrower resonance c h a r a c t e r i z e d b y t h e homogeneous w i d t h o f t h e upper l e v e l rh.

For t h e p r e s s u r e c o n d i t i o n s i n a rare-gas d i s c h a r g e , t h e w i d t h 2 r a b i s expected t o be much g r e a t e r t h a n r b because t n e o p t i c a l coherence i s more s e n s i t i v e t o c o l l i s i o n s t h a n i s t h e Zeeman coherence /g/. The broad resonance i s sometimes c a l l e d t h e p o p u l a t i o n e f f e c t o r h o l e - b u r n i n g e f f e c t and t h e narrow resonance t h e Zeeman coherence o r non- l i r i c a r Hanle e f f e c t . The s t r e n g t h o f t h e p o p u l a t i o n e f f e c t resonance ( r a t i o of S i z e of d i p t o h i g h - f i e l d s i g n a l ) p r e d i c t e d by t h i s s i m p l e model i s S = ( n

-

2 n / 3 ) / n = 0.33 and t h e s t r e n g t h o f t h e Zeeman coherence resonance S = ( 2 n / 3

-

n / 2 ) / ( 2 n / 3 ) = 0.25.

I n p r a c t i c e t h e s t r e n g t h s o f t h e resonances a r e reduced by c o l l i s i o n a l r e l a x a t i o n between t h e mb = 0,

+

¹ s u b l e v e l s /12/ and a l s o by t h e f a c t t h a t t h e r e i s i n c o m p l e t e s a t u r a t i o n i n t h e wings o f t h e frequency i n t e r a c t i o n p r o f i l e and i n t h e wings of t h e s p a t i a l p r o f i l e o f t h e l a s e r beam. For t r a n s i t i o n s w i t h c e r t a i n combinations of J-values, one m i g h t e x p e c t t o see a d d i t i o n a l e f f e c t s , such as resonances due t o

B + B In 2 r f , t CHOPPER

FIELD COILS

L O C K - I N

I

- _-

^J

REF

F i g . 2 - Experimental arrangement f o r o p t o g a l v a n i c d e t e c t i o n o f l e v e l - c r o s s i n g s . W i t h s w i t c h i n p o s i t i o n ( a ) l o c k - i n i s r e f e r e n c e d t o m o d u l a t i o n f r e q u e n c y o f l a s e r

( f 2 ) , and t o t a l o p t o g a l v a n i c c u r r e n t i s d e t e c t e d , ( b ) l o c k - i n i s r e f e r e n c e d t o f l + f 2 (where f l i s a m o d u l a t i o n f r e q u e n c y a p p l i e d t o c o i l s ) , and t h e f i e l d - dependent p a r t o n l y o f t h e o p t o g a l v a n i c c u r r e n t i s d e t e c t e d .

c r o s s i n g s i n t h e l o w e r l e v e l , e f f e c t s o f o p t i c a l pumping i n t o s u b l e v e l s which do n o t i n t e r a c t w i t h t h e l a s e r , and v e r y h i g h - o r d e r e f f e c t s .

A schematic diagram o f t h e e x p e r i m e n t a l arrangement used f o r o p t o g a l v a n i c d e t e c t i o n o f l e v e l - c r o s s i n g s i s shown i n F i g u r e 2. An atomic vapour o f t h e element o f i n t e r e s t (e.g. Z r ) i s produced by c a t h o d i c s p u t t e r i n g i n a low-pressure neon o r argon d i s c h a r g e and e x c i t e d i n t h e presence o f a magnetic f i e l d b y a single-mode cw dye l a s e r . The l a s e r l i g h t i s s u f f i c i e n t l y s t r o n g t o s a t u r a t e , o r p a r t i a l l y s a t u r a t e , t h e atomic t r a n s i t i o n and i s l i n e a r l y p o l a r i z e d i n a d i r e c t i o n p e r p e n d i c u l a r t o t h e magnetic f i e l d .

The l o c k - i n can be r e f e r e n c e d e i t h e r t o ( a ) t h e m o d u l a t i o n f r e q u e n c y o f t h e l a s e r ( f ~ ) , which a l l o w s t h e t o t a l o p t o g a l v a n i c c u r r e n t t o b e d e t e c t e d as a f u n c t i o n o f a p p l i e d f i e l d B; o r t o ( b ) t h e sum f r e q u e n c y f l + f2, where f l i s t h e f r e q u e n c y o f a s m a l l modulated component ( B l s i n 2nflt) a p p l i e d t o t h e f i e l d c o i l s . The double- m o d u l a t i o n mode o f d e t e c t i o n a l l o w s a d e r i v a t i v e s i g n a l o f t h e f i e l d - d e p e n d e n t p a r t o n l y o f t h e o p t o g a l v a n i c c u r r e n t t o be d e t e c t e d as a f u n c t i o n o f B.

I1

-

ZERO-FIELD LEVEL CROSSINGS.

F i g u r e 3 shows a z e r o - f i e l d l e v e l - c r o s s i n g resonance r e c o r d e d i n t h e o p t o g a l v a n i c c u r r e n t f o r t h e 613.5nm ( a 3 ~ 2 - ~ 3 ~ 2 ' ) t r a n s i t i o n i n Z r a t t h r e e l a s e r power d e n s i t i e s . The resonance vanishes when t h e d i r e c t i o n o f p o l a r i z a t i o n o f t h e l a s e r l i g h t i s r o t a t e d t h r o u g h r/2 so t h a t i t c o i n c i d e s w i t h t h e magnetic f i e l d d i r e c t i o n , and i t remains unchanged, b o t h i n shape and s t r e n g t h , i r r e s p e c t i v e o f t h e d i r e c t i o n o f t h e d i s c h a r g e c u r r e n t r e l a t i v e t o t h e d i r e c t i o n of p o l a r i z a t i o n . The s t r e n g t h o f t h e resonance S ( r a t i o o f s i z e o f d i p t o h i g h - f i e l d s i g n a l ) i s s t r o n g l y

dependent on t h e power d e n s i t y o f t h e l a s e r ( F i g . 4), e x h i b i t i n g t y p i c a l s a t u r a t i o n b e h a v i o u r . F o r t h e p a r t i c u l a r c o n d i t i o n s i n F i g . 3 (0.8 t o r r neon, single-mode l a s e r w i t h beam d i a m e t e r = l mm), S has a s a t u r a t i o n v a l u e of S ( m ) = 0.14 and t h e l a s e r power e q u i r e d t o r e a c h S(m)/2 i s P ( S ) = 0.3 mW. The a c t u a l values o f S(-) and P('! a r e q u i t e s e n s i t i v e t as p r e s s u r e : o v e r t h e range 0.5 - 3 t o r r Ne,

9 3

S(-) v a r i e s from 0.17 t o 0.06 and P S f r o m 0.15 t o 0.45 mW. The w i d t h o f t h e resonance a t v e r y low l a s e r power approaches a v a l u e o f 4 G, o r 3.8 MHz i n frequency u n i t s ( u s i n g t h e Land6 g - f a c t o r f o r e i t h e r t h e upper o r l o w e r l e v e l ) . T h i s v a l u e i s g r e a t e r t h a n t h e pressure-broadened homogeneous w i d t h o f t h e upper l e v e l , r b / 2 r ~ 1 . 2 MHz, as determined f r o m t h e l i n e a r Hanle e f f e c t i n f:uorescence, b u t v e r y much s m a l l e r t h a n t h e Doppler w i d t h o f t h e t r a n s i t i o n ( a b o u t 600 MHz) and t h e homogeneous w i d t h o f t h e t r a n s i t i o n e x p e c t e d a t t h e p r e s s u r e s used i n t h e discharge.

I t i s a l s o g r e a t e r t h a n t h e s h o r t - t e r m ( < 10 ms) bandwidth o f t h e l a s e r , < 2 MHz, and remained unchanged when a f r e q u e n c y - s t a b i l i z e a l a s e r h a v i n g a l o n g - t e r m bandwidth o f

JOURNAL DE PHYSIQUE

F i g . 3

-

Z e r o - f i e l d l e v e l - c r o s s i n g resonance i n t h e o p t o g a l v a n i c c u r r e n t f o r t h e 613.5 nm (a3F2-z3F20) t r a n s - i t i o n i n Z r

,

t a k e n a t t h r e e l a s e r powers: ( a ) 0.5 mW, ( b ) 1 mW, ( c ) 2.5 mW. Single-mode l a s e r , beam d i a m e t e r

= l mm. Neon d i s c h a r g e , 0.8 t o r r .

-10 0 +l0

MAGNETIC FIELD (G)

F i g . 4

-

S t r e n g t h o f resonance S ( r a t i o o f s i z e o f d i p t o h i g h - f i e l d s i g n a l ) as a f u n c t i o n o f l a s e r power f o r t h e 613.5 nm t r a n s i t i o n i n Z r I . S i n g l e mode l a s e r , beam d i a m e t e r = 1 mm.

LASER POWER (mW)

0.5 MHz was employed. The shape o f t h e resonance i s f a i r l y c l o s e t o L o r e n t z i a n a t l o w l a s e r power ( F i g . 3 ( a ) ) , b u t becomes v e r y n o n - L o r e n t z i a n as t h e power i s r a i s e d : t h e resonance broadens a p p r e c i a b l y i n t h e wings and t h e c e n t r a l r e g i o n sharpens ( F i g . 3 ( c ) ) . An i n t e r p r e t a t i o n o t t h i s b e h a v i o u r i s t h a t a t l o w l a s e r power t h e resonance c o n s i s t s p r e d o m i n a n t l y o f Zeeman coherence components f r o m t h e upper and l o w e r l e v e l s , w h i l e a t h i g h e r powers an a d d i t i o n a l narrow Zeeman coherence component i s c o u p l e d t o t h e p o p u l a t i o n o f t h e l e v e l s by t h e l a s e r f i e l d . The a d d i t i o n a l component c o u l d b e a

lam1 = 4 coherence w h i c h e v o l v e s a t f o u r t i m e s t h e Larmor f r e q u e n c y and so i s d e s t r o y e d by a weaker magnetic f i e l d . A d e t a i l e d t h e o r e t i c a l a n a l y s i s f o r t h e case o f a Ja = 2 t o J b = 2 t r a n s i r i o n i s c u r r e n t l y b e i n g pertormed. The reason f o r t h e d i f f e r e n c e between t h e w i d t h o t t h e o p t o g a l v a n i c resonance a t low l a s e r power (3.8 MHz) and t h e pressure-broadened homogeneous w i d t h o t t h e upper l e v e l ( = 1.2 PlHz) i s n o t c l e a r and w i l l be t n e s u b j e c t o f f u r t h e r study.

Z e r o - f i e l d o p t o g a l v a n i c resonances have a l s o been s t u d i e d f o r a l a r g e number o f o t h e r Z r t r a n s i t i o n s l y i n g w i t h i n t h e t u n i n g range o f rhodamine 66. These t r a n s i t i o n s o r i g i n a t e f r o m e i t h e r t h e ground o r m e t a s t a b l e s t a t e s and p r o v i d e a wide range o f t r a n s i t i o n p r o b a b i l i t i e s and combinations o f J - v a l u e s and g - f a c t o r s . Q u i t e l a r g e values o f S (>0.05) a r e found i n a l l cases, p r o v i d e d t h e power d e n s i t y o f t h e l a s e r i s s u f f i c i e n t l y h i g h t o s a t u r a t e t h e t r a n s i t i o n . The s a t u r a t i o n curves f o r t h e 614.3 nm (a3F3 - z3F30) nm (a3F4 - z 3 F 4 ~ ) tr a n s i t i o n s a r e v e r y s i m i l a r t o F i g . 4, y i e l d i n g S ( W )

-a:i,dd6;f53 -

v a l u e s e s s e n t i a l l y t h e same as f o r t h e 613.5 nm (a3F2

-

z3F20) t r a n s i t i o n . The s a t u r a t i o n c u r v e f o r t h e 602.5 nm

(a3F4

-

z5F40) i n t e r c o m b i n a t i o n l i n e a l s o y i e l d s a s i m i l a r v a l u e o f S ( m ) , b u t i s h i g h e r by a f a c t o r o f 25 t o 30. The h i g h P ( S ) - v a l u e can be e x p l a i n e d i n terms of t h e v e r y s m a l l b r a n c h i n g r a t i o (0.03) f o r t h e 602.5 nm t r a n s i t i o n : about 30 t i m e s more l a s e r power i s r e q u ' r e d t o a c h i e v e t h e same l e v e l o f s a t u r a t i o n . S i m i l a r l y , l a r g e values o f P ( s ~ a r e found f o r o t h e r Z r t r a n s i t i o n s h a v i n g s m a l l b r a n c h i n g r a t i o s , w h i l e f o r t r a n s i t i o n s f o r which J a f Jb, t h e S(-)-values a r e s m a l l e r by f a c t o r s o f 1.5 t o 2.5. S t r o n g z e r o - f i e l d o p t o g a l v a n i c resonances have a l s o been observed f o r t r a n s i t i o n s i n y t t r i u m and samarium, and r e c e n t l y by B a r b i e r i e t a1 1131 f o r t r a n s i t i o n s i n neon and calcium.

I 1 1

-

LEVEL-CROSSINGS AT FINITE FIELDS.

I n some systems i t i s p o s s i b l e t o have c r o s s i n g s between l ~ m l = 2 s u b l e v e l s w h i c h o r i g i n a t e f r o m d i f f e r e n t n e i g h b o u r i n g l e v e l s , and i n p a r t i c u l a r f r o m d i f f e r e n t h y p e r f i n e l e v e l s . L e v e l s o f y t t r i u m p r o v i d e a good example o f t h i s ( F i g . 5 ) . Y t t r i u m c o n s i s t s o f 100% 8 9 ~ ( I = 4 ) , which has a s m a l l magnetic moment

(-0.1368 n.m.), and t h e r e a r e a number o f s u i t a b l e t r a n s i t i o n s t h a t l i e w i t h i n t h e t u n i n g range o f rhodamine 66. Th p a r t i c u l a r t r a n s i t i o n s o f i n t e r e s t a r e t h o s e between t h e groung l e v e l s 4d5s2 a503/2,5/2 and l e v e l s w i t h i n t h e terms

4d5s5p z2D0 and z Do. The h y p e r f i n e s t r u c t u r e s f o r t h e s e t r a n s i t i o n s a r e n o r m a l l y u n r e s o l v e d i n t h e presence of Doppler broadening 1141, and t h e o n l y a c c u r a t e h y p e r f i n e s t r u c t u r e d a t a a v a i l a b l e p r i o r t o t h i s i n v s t i g a t i o n have been t h e

5

atomic-beam magnetic resonance measurements on t h e a D3/2,5/2 ground l e v e l s 1151.

The f i r s t system i n v e s t i g a t e d was t h e Y 619.2 nm ( a 2 ~ 3 1 2

-

z2D$2 ) t r a n s i t i o n , f o r which, s i n c e J =3/2 and I = %

,

two lnml = 2 c r o s s i n s s a r e t o be expected i n b o t h t h e upper and l o w e r l e v e l s ( F i g . 5 ) . f i g u r e 6 shows t h e l e v e l - c r o s s i n g resonances observed i n t h e range 0-1506 ( u s i n g t h e double-modulation mode o f

d e t e c t i o n

-

F i g . 2 ) . A s t r o n g z e r o - f i e l d resonance i s found, f o l l o w e d b y f o u r weake\r resonances, l a b e l l e d Bla, BZa, BIZ and BZZ. The r a t i o o f t h e m a g n e t i c f i e l d

values a t which t h e f i r s t two weaker resonances o c c u r , B a / ~ 2 a , and t h e c o r r e s p o n d i n g

Z / ~ f o r t h e second p a i r o f resonances, a r e bott! v e r y c l o s e t o t h e v a l u e

;i;:0=Bb.74$4 p r e d i c t e d by t h e B r e i t - R a b i f o r m u l a f o r systems h a v i n g J =3/2, I = %.

F i g . 5 - Zeeman e n e r g y - l e v e l diagram f o r t h e up e r and 1 wer l e v e l s o f t h e 619.2 nm

(aqDaI2

-

z ~ 5 1 2 ) t r a n s i t i o n i n 8 9 ~

B

I ( I = 4 ) . L o w e r - l e v e l parameters : A = -57.23 MHz,

g ~ = 0.79927. U p p e r - l e v e l parameters : A = 89.9 MHz, g ~ = 0.797. The lnml = 2 l e v e l - c r o s s i n g s a r e i n d i c a t e d by open c i r c l e s . The v e r t i c a l l i n e s r e p r e s e n t t h e paths by w h i c h t h e = 2 c r o s s i n g s can be reached.

0 50 100 150

MAGNETIC FIELD ( G )

JOURNAL DE PHYSIQUE

F i g . 6

-

L e v e l - c r o s s i n g resonances i n t h e o p t o g a l v a n i c s i n a l f o r he 619.2 nm (aqD3/2 - z5D3/2 ) t r a n s i t i o n i n y t t r i u m I . S i n g l e scan o n l y . Laser : 12 mW s i n g l e mode, beam d i a m e t e r 1 2 mm.

Argon d i s c h a r g e , 0.5 t o r r . Magnetic f i e l d m o d u l a t i o n .

I l I I

0 50 100 150

MAGNETIC W D ( G 1

The f i r s t two resonances appear a t t h e same magnetic f i e l d v a l u e s f o r o t h e r Y I t r a n s i t i o n s (602.3, 622.3 and 608.3 nm) h a v i n g t h e same l o w e r l e v e l , and t h e s e a r e t h e r e f o r e i d e n t i f i e d as a r i s i n g f r o m c r o s s i n g s i n t h e a2D l e v e l The second p a i r i s i n t e r p r e t e d as a r i s i n g f r o m c r o s s i n g s i n t h e uppe?'?evel,

;2~3/2.

L e v e l - c r o s s ' n g s a t f i n i t e magnetic f i e 1 sohave a l s o been s u d i e d f o r t h e 622.3 nm _{(a2D 12}

_-

_z2DtI2),

h

_{688;3 nm}

₂

_{z D1}

If 2i,

502.3 nm (a5D / 2

-

and 613.3 nm ( a DSi2

-

z D5!2) t r a n s l i i o ~ s of

4 ^.

^{The J =} 5/2 i e v e l s have f o u r Inml = 2 c r o s s i n g s , whi e t h e J - 4 l e v e l does n o t have a c r o s s i n g . The resonances

observed f o r t h e 608.3 nm t r a n s i t i o n a r e t h e r e f o r e due s o l e l y t o l e v e l - c r o s s i n g s i n t h e a2D3/2 ground l e v e l , and so t h i s t r a n s i t i o n was u s e f u l f o r i d e n t i f i c a t i o n o f a2D312 resonances i n o t h e r t r a n s i t i o n s .

The l o c a t i o n o f t h e l e v e l - c r o s s i n g s a1 lows

I A / ~ ~ I

t o be determined f o r each l e v e l , where A i s t h e m a g n e t i c h y p e r f i n e i n t e r a c t i o n c o n s t a n t . The g J - f a c t o r s a r e u s u a l l y known f r o m e a r l i e r work, a l t h o u g h n o t always w i t h t h e d e s i r e d p r e c i s i o n . They can, however, be determined i n d e p e n d e n t l y , i f r e q u i r e d , u s i n g t h e o p t o g a l v a n i c method d e s c r i b e d i n t h e f o l l o w i n g s e c t i o n . Furthermore t h e s i g n s o f t h e A - f a c t o r s can be determined i n some cases by s t u d y i n g t h e r e s p e c t i v e w i d t h s o f t h e z e r o - f i e l d o p t o g a l v a n i c resonance w i t h t h e l a s e r t u n e d f i r s t t o one s i d e o f t h e Doppler a b s o r p t i o n p r o f i l e , and t h e n t o t h e o t h e r . F o r t h e Y I 619.2nm t r a n s i t i o n , f o r example, t h e z e r o - f i e l d resonance ( F i g . 7 ) i s b r o a d e r by a f a c t o r o f about 1.6 when t h e l a s e r i s t u n e d t o t h e h i g h frequency s i d e o f t h e Doppler p r o f i l e ( t r a c e

l a b e l l e d b ) t h a n when i t i s t u n e d t o t h e low f r e q u e n c y s i d e ( t r a c e a ) . The m a j o r F i g . 7

-

L e v e l - c r o s s i n g o p t o g a l v a n i c s i g n a l s t o r t h e 619.2nm ( a 2 ~ 3 / 2

-

^{z 2 ~ 3} 2) t r a n s i t i o n i n

Y

I , w ~ t h t h e l a s e r t u n e d t o t h e low-frequency s i d e ( l a b e l l e d a ) and t h e h i g h -

o f r e q u e n c y s i d e ( l a b e l l e d b ) o f

t h e Doppler absor t i o n p r o f i l e .

b The i n s e t shows tRe h y p e r f i n e

s t r u c t u r e components a t z e r o f i e l d f o r t h e 619.2 nm t r a n s - i t i o n .

I I I I I l J

0 40 80 120

MAGNETIC FIELD ( G )

Table 1. Hyperfine i n t e r a c t i o n constants (A) i n l e v e l s o f Y I . A(MHz)

Level g J

This work a Other work

4 d 5 ~ ( ~ ~ ) 5 ~ z ~ D & ~ 1.38(3jC -133.7(1)

a I n d i c a t e d ~ n c e r t a i n t i e s ~ d o n o t i n c l u d e c o n t r i b u t i o n from gJ ( c o l . 3 ) . b Ref. 16. C Ref. 17. Ref. 15. Ref. 14.

hyperfine components i n t h e 619.2 nm t r a n s i t i o n a r e t h e F = 1 t o F ' = 1 and F = 2 t o F ' = 2 (see i n s e t t o Fig. 7). The g F - f a c t o r s f o r t h e h y p e r f i n e l e v e l s F = 1 and F' = 1 a r e b o t h c l o s e t o 1.0, w h i l e those f o r t h e l e v e l s F = 2 and F ' = 2 a r e b e t h close t o 0.6. I f , on t h e one hand, t h e A

-

f a c t o r s f o r t h e l e v e l s a2D3/ and

r

(A" and Az) have d i f f e r e n t signs, then t h e s p l i t t i n g o f t h e l + l and

l

^{-t 2}

h y p e r f i n e components i s 1 2l + 1 2 ~ ' 11300 MHz, which i s comparable w i t h t h e Doppler ~ ~ w i d t h ( = 600 MWz) ,and one would expect the w i d t h o f t h e z e r o - f i e l d - r e s o n a n c e t o be governed e s s e n t i a l l y e i t h e r by g ~ = 2 = 0.6 o r by g ~ = l = 1.0, depending on

whether t h e l a s e r i s tuned c l o s e t o t h e 2 + 2 component o r t h e l + 1 component.

On t h e o t h e r hand, i f Aa and A' have t h e same s i g n , then the s p l i t t i n g o f t h e 1 ⁺ 1 and 2 ⁺ 2 components i s o n l y 12Aal

-1

2AZl =70 MHz and one would expect t h e w i d t h o f t h e z e r o - f i e l d resonance t o be r e l a t i v e l y i n s e n s i t i v e t o l a s e r t u n i n g . The observed r a t i o of widths (1.6) i s c l o s e t o t h e r a t i o g ~ = ~ / g ~ , ~ = 5/3 and i s compatible o n l y w i t h t h e assignment A ~ < 0, AZ> 0.

The A - f a c t o r s determined i n t h i s study a r e summarised i n Table 1, t o g e t h e r w i t h the r e s u l t s o f o t h e r workers. The g,,-factors used i n t h e a n a l y s i s are a l s o shown.

The u n c e r t a i n t i e s i n t h e A-factors a r e t y p i c a l l y 1 p a r t i n 500, i f t h e c o n t r i b u t i o n from g ~ i s n b t included.

I V - MULTIFIODE SATURATION RESONANCES

When the l a s e r source i s r u n multimode, a d d i t i o n a l resonances a r e observed i n t h e optogalvanic c u r r e n t a t magnetic f i e l d s where t h e Zeeman s p l i t t i n g i n e i t h e r t h e upper (ZgbpBB/h) o r lower ( 2 9 , ~ B/h) l e v e l s i s equal t o a m u l t i p l e o f the mode s e p a r a t i o n o f t h e l a s e r (Fig. 87. Under these c o n d i t i o n s , f o r one and t h e sarne v e l o c i t y group o f atoms, t h e a' t r a n s i t i o n i s e x c i t e d by one mode and t h e o- t r a n s i t i o n e x c i t e d by another mode. When the o+ and ^CJ- t r a n s i t i o n s a r e s a t u r a t e d

Fig. 8 - Z e r o - f i e l d resonance and multimode s a t u r a t i o n resonances i n the op ogalvanic s i g n a l f o r t h e 612.7nm ( a

5

F4

- z 3 ~ ; )

t r a n s i t i o n i n Z r I . Laser r u n multimode. Magnetic f i e l d modulation.

I I I I

0 5 0 100 150

MAGNETIC FIELD (G1

C7-114 JOURNAL D€ PHYSIQUE

o r p a r t i a l l y s a t u r a t e d by t h e l a s e r , t h e i r simultaneous e x c i t a t i o n can l e a d t o a r e d u c t i o n i n t h e number o f atoms i n the upper l e v e l , and hence t o a resonance i n t h e optogalvanic c u r r e n t . The l o c a t i o n o f these multimode s a t u r a t i o n resonances a l l o w s Land6 g - f a c t o r s t o be determined f o r t h e upper and lower l e v e l s , provided t h e mode separation o f t h e l a s e r i s known. S i m i l a r multimode s a t u r a t i o n resonances have p r e v i o u s l y been observed i n fluorescence f o r t r a n s i t i o n s i n neon /18,19/.

I n t h e p u b l i c a t i o n i n which we f i r s t r e p o r t e d these multi-mode resonances 1201 we a t t r i b u t e d t h e i r occurrence t o t h e p o p u l a t i o n e f f e c t , n o t t o the Zeeman coherence e f f e c t , on the grounds t h a t t h e coherence time o f our l a s e r was s h o r t compared w i t h the l i f e t i m e s o f t h e atoms studied. As a r e s u l t o f f u r t h e r experiments i t now appears l i k e l y t h a t , under t h e c o n d i t i o n s i n which t h e multimode resonances appear, t h e s h o r t - term coherence t i m e o f t h e l a s e r (which i s t h e s i g n i f i c a n t q u a n t i t y ) i s , i n f a c t , considerably longer than t h e l i f e t i m e o f t h e e x c i t e d atoms, and o u r present view i s t h a t t h e Zeeman coherence e f f e c t , n o t t h e p o p u l a t i o n e f f e c t , i s t h e dominating mechanism. This was t h e i n t e r p r e t a t i o n o f f e r e d by t h e authors o f t h e work i n neon 1 8 1 9 I n those experiments a l s o the coherence time o f the l a s e r was long compared w i t h t h e l i f e t i m e s o f t h e atomic l e v e l s .

The t r a c e shown i n F i g . 8 was recorded i n t h e optogalvanic c u r r e n t f o r t h e 612.7 nm (a3F4- :3F$) t r a n s i t i o n i n Zirconium, u s i n g a multimode r i n g l a s e r as t h e source.

The i r s resorlance i s the f a m i l i a r z e r o - f i e l d s i g n a l , and the o t h e r two ( a t 66 and 132 G), which vanish when t h e l a s e r i s r u n n i n g single-mode, are t h e nearest-mode and nest-nearest-mode s a t u r a t i o n resonances, r e s p e c t i v e l y . The g - f a c t o r s f o r t h e upper and lower l e v e l s of t h e 612.7 nm t r a n s i t i o n a r e almost i d e n t i c a l (gb = 1.25 /20/ and ga = 1.24987 /21/) and consequently each o f t h e observed multimode resonances f o r t h i s t r a n s i t i o n represents an unresolved superposi t i o n o f resonances associated w i t h t h e upper and lower l e v e l s . The upper- and l o w e r - l e v e l resonances were found t o be resolved f o r c e r t a i n Zr I t r a n s i t i o n s such as t h e 613.5 nm (ga = 0.66981, gb = 0.696) and 614.0 nm (ga = 1.26472, gb = 1.51).

The multimode s a t u r a t i o n technique has r e c e n t l y been applied, using a l i n e a r dye l a s e r having a c c u r a t e l y determined mode separation, t o o b t a i n Land6 g - f a c t o r s f o r a number o f l e v e l s i n Zr I 1201 and Y I 171.

V

-

SUMMARY AND CONCLUDING REMARKS

The l e v e l - c r o s s i n g optogalvanic technique described i n t h i s paper allows small hyper- f i n e i n t e r a c t i o n constants t o be determined, both i n magnitude and sign, f o r t h e upper and lower l e v e l s o f c e r t a i n atomic t r a n s i t i o n s . The optogalvanic mode o f d e t e c t i o n i s h i g h l y s e n s i t i v e , a l l o w i n g t h e study o f very weak t r a n s i t i o n s , and i t should a l s o a l l o w t h e study o f h i g h l y - e x c i t e d atomic s t a t e s t h a t are d i f f i c u l t o r impossible t o study by o p t i c a l d e t e c t i o n methods. The use o f m a g n e t i c - f i e l d scanning i n these experiments allows h y p e r f i n e s p l i t t i n g s t o be determined w i t h a h i g h l e v e l o f p r e c i s i o n ( t y p i c a l l y one p a r t i n 500 i n t h e present i n v e s t i g a t i o n ) . The technique i s w e l l s u i t e d t o t h e study o f l e v e l s i n r e f r a c t o r y metal atoms, which can be r e a d i l y produced by s p u t t e r i n g i n a rare-gas discharge. F i n a l l y , t h e technique does n o t r e q u i r e a l a s e r w i t h frequency s t a b i l i z a t i o n o r frequency-scanning f a c i l i t i e s .

ACKNOWLEDGEMENTS

We a r e p a r t i c u l a r l y g r a t e f u l t o Dr. R.J. McLean f o r h e l p f u l discussions and f o r c r i t i c a l reading o f t h e manuscript; a l s o t o Drs. R.J. Sandeman and H.A. Bacher ( A u s t r a l i a n National U n i v e r s i t y , Canberra) f o r t h e use o f t h e i r f r e q u e n c y - s t a b i l i z e d r i n a l a s e r i n a t e s t exueriment.

REFERENCES.

1. SERIES G.W., O p t i c a l pumping and r e l a t e d t o p i c s , Quantum O p t i c s : Proc. S c o t t . Univ. Summer School, Eds. S.M. Kay and A. M a i t l a n d (Academic Press, 1969) p 395.

2. HANNAFORD P. and SERIES G.W., Laser Spectroscopy V : Proc. F i f t h I n t . Conf., Jasper Park, Eds. A. R. W. M c K e l l a r , T. Oka and B. P. S t o i c h e f f ( S p r i n g e r , B e r l i n , 1981) p 94.

3. SERIES G . W . , C0mmen.t A t . Mol. Phys.

10

(1981) 199.

4. JULIEN L. and PINARD M., J. Phys. B

15

(1982) 2881.

5. PENDRILL L. R., PETTERSSON M. and ~ S T E R B E R G U., Phys. S c r i p t .

27

(1983) 306, and paper presented a t t h i s Colloquium.

6. HANNAFORD P. and SERIES G.W., J . Phys. B 14 (1981) 1661.

7 . HANNAFORD P. and SERIES G.W., Phys. Rev. L e t t .

g

(1982) 1326.

8. DECOMPS B., DUMONT M. and DUCLOY M., i n Laser Spectroscopy o f Atoms and Molecules, Ed. H. Walther ( S p r i n g e r , B e r l i n , 1976) p 283.

9. GORLICKI M.

,

and DUMONT M.

,

Opt. Comm.

11

(1974) 166.

10. FELD M. S., SANCHEZ A., JAVAN A. and FELDMAN B. J., Colloques I n t e r n a t i o n a u x du CNRS No 217 ( P a r i s , CNRS, 1974) p 87.

11. BEVERINI N. and INGUSCIO M. Nuov. Cim. L e t t .

2

(1980) 10.

12. DODD J. N., J . Phys. B - 16 (1983) 2721.

13. BARBIERI B., BEVERINI N., BIONDUCCI G., GALL1 M., INGUSCIO M. and STRUMIA F., Laser Spectroscopy V1 : Proc. S i x t h I n t . Conf., I n t e r l a k e n , Eds. H.P. Weber and W . L u t h y ( S p r i n g e r , B e r l i n , 1983), and paper presented a t t h i s Colloquium by F. Strumia.

14. KUHN H. and WOODGATE G.K., Proc. Phys. Soc., London, Sect. A

63

(1950) 830 15. FRICKE G., KOPFERMANN H. and PENSELIN S.

,

Z. Phys.

154

(1959) 218.

16. PENSELIN S., Z . Phys.

154

(1959) 231.

17. McNALLY J . R. and HARRISON G. R., J. Opt. Soc. Am.

35

(1945) 584.

18. FORK R.L., HARGROVE L.E. and POLLACK M.A., Phys. Rev. L e t t .

12

(1964) 705.

19. DECOMPS B . and DUMONT M., C.R. Acad. S c i . , Ser. B

265

(1967) 249.

20. HANNAFORD P. and SERIES G.W., Opt. Comm.

41

(1982) 427.

21. B~TTGENBACH S., DICKE R. and GEBAUER H., Phys. L e t t .

58 A

(1976) 56.