RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10 µm SPECTRAL REGIONS : EXPERIMENTAL METHODS

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RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10 µm SPECTRAL REGIONS :

EXPERIMENTAL METHODS

Ch. Salomon, Ch. Bréant, Ch. Bordé, R. Barger

To cite this version:

Ch. Salomon, Ch. Bréant, Ch. Bordé, R. Barger. RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10µm SPECTRAL REGIONS : EXPERIMENTAL METHODS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-3-C8-14. �10.1051/jphyscol:1981801�. �jpa-00221696�

JOURNAL DE PHYSIQUE

Colloque C8, supplément au n°12, Tome 42, décembre 1981 page C8-3

RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10 ym SPECTRAL REGIONS : EXPERIMENTAL METHODS*

Ch. Salomon, Ch. Bréant, Ch. J. Bordé and R.L. Barger (*) (**)

Laboratoire de Physique des Lasers, associé au C.N.R.S. n°282, Université Paris-Nord, F-9S4S0 Villetaneuse, France

(*) Lasedngle, Inc., Rollinsville, Colorado 80474, U.S.A. and Laboratoire de Physique des Lasers, Universite Paris-Nord, F-93430 Villetaneuse, France

Abstract. - A description is given of the experimental system which was used for obtaining Ramsey fringes with an atomic beam for the Ca 657 nm line, and for the system which is being set up to obtain fringes with a large absorp- tion cell for various molecules in the 10 vim region. Details of the cat's eye and segmented retroreflector optical systems are discussed. Results obtained with Ca include fringe widths as small as 1 kHz HWHM , resolution of

the recoil splitting, and resolution of second-order Doppler broadening and shift. The experiment at 10 \sxs\ is in progress and has already yielded a

1.25 kHz linewidth (HWHM) for the single zone signal with the SF, molecule.

Introduction. - The optical Ramsey fringe technique has been developed over the last few years to the point where extremely high resolution can now be obtained. Fringes have been observed for several atoms and molecules, including Ne (by Bergquist, Lee and Hall > ) , CH, (by Bergquist, by Kramer, and by Baba and Shimoda ) , Ca (by Barger, Bergquist, English and Glaze ' ' , and by Helmcke et al., ) , and SF, (by Borde et al., ) . The use of this technique in investigations of the Ca 657 nm line at the National Bureau of Standards has produced linewidths as narrow as 1 kHz HWHM.

This resolution has resulted in 1) complete resolution of the 23 kHz recoil splitting, 2) observation of the power contraction of this splitting, and 3) reso- lution of the second-order Doppler broadening and shift (1.7 kHz) and the attendant resolution-dependent distortion and shift of the Ramsey fringe profile. Experiments using the Ramsey technique in the 10 iJm region with OsO. are now under way at the Laboratoire de Physique des Lasers. The experimental parameters should yield line- widths of less than 100 Hz and result in resolution of the superfine and hyperfine

structures present in the 10 Via region spectra of many molecules. In this paper we shall discuss some of the experimental techniques which have been used in the visible and 10 \m experiments.

Ca : Experiment

The calcium atomic beam and fast-stabilized dye laser system used in this experiment (Fig. la) are described in detail elsewhere. ' Briefly, the Ca S - Pi , m- = 0 => m: = 0 transition was excited in three standing-wave excitation zones with a laser beam of mode radius w = 0.18 cm. The dye laser frequency was stabi- lized to have short-term rms noise of about 1 kHz and long-term drift of less than 2 kHz/In The total separation 2L of the three excitation zones was varied up to 21 cm, and the signal obtained by detecting fluorescence from a region about 10 cm downstream.

+ Work supported in part by DRET, NBS, C.N.R.S. and NATO

(**) The research on Ca was done while this author was a member of the National Bureau of Standards, Boulder, Colorado.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981801

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I n o r d e r t o produce Ramsey f r i n g e s , t h e l a s e r beams i n t h e t h r e e zones must have wavefronts p a r a l l e l t o a small f r a c t i o n of a f r i n g e and must have t h e i r r e l a - t i v e phases c o n s t a n t i n time. (Since t h e s e phases determine whether t h e f r i n g e i n t e n s i t y i s p o s i t i v e o r n e g a t i v e , random phase f l u c t u a t i o n s w i l l cause t h e f r i n g e i n t e n s i t y t o average t o z e r o ) . These c o n d i t i o n s were met i n t h e experiment where t h e f i r s t o b s e r v a t i o n of o p t i c a l Ramsey f r i n g e s was achieved by J.L. H a l l and h i s c o l l e a g u e s , ' a s w e l l a s i n t h e e a r l y experiments6 on Ca, by t h e use of two opposing c a t ' s eye r e t r o r e f l e c t o r s a s i n d i c a t e d i n t h e c i r c l e d i n s e r t of F i g . l a . With t h e c a t ' s eyes p r o p e r l y focused and f r e e of a b e r r a t i o n s t h r e e beams a r e o b t a i n e d which a r e e s s e n t i a l l y p o r t i o n s of a " s i n g l e p l a n e wave", thus s a t i s f y i n g t h e requirements of p a r a l l e l i s m and c o n s t a n t r e l a t i v e phases.

Cdcium Dye Laser Spectrometer

F i g u r e 1

Experimental system f o r Ca. a ) S t a b i l i z e d l a s e r and c a t ' s eye o p t i c a l system.

b) Segmented r e t r o r e f l e c t o r o p t i c a l system.

The opposing c a t ' s eye system a l s o has t h e b e a u t i f u l and very important pro- p e r t y , commonly c a l l e d t h e " p u l l e y e f f e c t , " ' w h e r e i n t h e r e l a t i v e phases of t h e s t a n - ding wave beams a r e n o t a f f e c t e d by changes i n s e p a r a t i o n of t h e c a t ' s e y e s , c h a n g e s caused by v i b r a t i o n , f o r i n s t a n c e . With a s t a n d i n g wave node formed a t t h e r e f l e c - t i o n - s u r f a c e of t h e c e n t r a l beam i n t h e back c a t ' s eye of F i g . l a , t h e l o c a t i o n s of the e q u a l phase p o i n t s i n t h e t h r e e beams a r e determined by t h e d i s t a n c e from t h i s node and f o r t h e s e " p e r f e c t " c a t ' s e y e s , l i e on a s t r a i g h t l i n e . I f t h e upper c a t ' s eye moves away from t h e lower one by a d i s t a n c e + 6 , the c e n t r a l beam phase p o i n t moves by + 6 , t h e r i g h t beam phase p o i n t by - 6 , and t h e l e f t beam phase p o i n t by + 2 6 . Thus t h e equal phase p o i n t s s t i l l l i e on a s t r a i g h t l i n e , and, a s long a s t h e v i b r a t i o n p e r i o d s a r e long compared t o t h e atomic f l i g h t time, t h e f r i n g e i n t e n s i t y i s n o t changed.

I n t h e e a r l y experiments w i t h Ca, Ramsey f r i n g e s were o b t a i n e d w i t h opposing c a t ' s eyes f o r beam s e p a r a t i o n s 2L up t o 7 cm. With t h e o p t i c s a v a i l a b l e t o u s , i t was n o t p o s s i b l e t o o b t a i n wavefronts of good enough q u a l i t y t o produce Ramsey f r i n g e s f o r l a r g e r s e p a r a t i o n s ; t h u s , f o r h i g h e r r e s o l t i o n an i n t e r f e r ~ m e t r i c a l l ~ a l i g n e d segmented r e t r o r e f l e c t o r (SRR) was developed. l' As can be seen i n F i g . Ib t h e SRR c o n s i s t s of a c o r n e r cube t o g i v e r e t r o r e f l e c t i o n , two 45" m i r r o r s (one a d j u s t a b l e i n a n g l e ) t o t r a n s l a t e t h e r e t r o r e f l e c t e d beam, and a s m a l l c a t ' s eye o r c o r n e r cube t o r e t r o r e f l e c t t h e c e n t r a l beam. A mechanically s t a b l e s t r u c t u r e i s obtained by mounting t h e c o r n e r cube and t h e a d j a c e n t 45" m i r r o r on an A 1 block, t h e c a t ' s eye on a second, and t h e o t h e r 45" m i r r o r on a t h i r d , w i t h t h e blocks r i g i d l y mounted on - 3 cm diam I n v a r r o d s . To o b t a i n long-term mechanical s t a b i - l i t y , most of t h e o p t i c a l components a r e epoxied t o t h e blocks. The f i n a l a n g u l a r adjustement, very s t a b l e with time, i s made by compressing t h r e e m e t a l - m e t a l c o n t a c t p o i n t s on t h e mount f o r the 45' a d j u s t a b l e m i r r o r . The SRR o f f s e t s and r e t r o r e f l e c t s t h e i n c i d e n t l a s e r beam s o t h a t t h e two beams a r e p a r a l l e l t o w i t h i n a s m a l l f r a c - t i o n of a f r i n g e over t h e mode diameter.

Two opposing SRR's form the three parallel standing wave beams for Ramsey fringes, as indicated in Figr lb. The input plane wave laser beam enters the first

S m at zone I in Fig. lb and is retroreflected by it to zone 3. The beam is then retroreflected by the opposing SRR from zone 3 to zone 2,where it enters the cen- tral retroreflector of the first SRR. The beam is then retroreflected back around the optical circuit to produce the three standing-wave beams. The reflecting sur- faces of the SRR's must be interferometrically aligned to obtain the required parallelism between input and reflected beams.

The first step in the interferometric alignment procedure is to obtain parallel laser beams (three in this case) with the desired spacing. These are then used to align the components of the SRR's. The experimental set-up is indicated in Fig. 2.

Figure 2

Interferometric alignment system

All components are mounted on a rigid tabletop. The components for obtaining the parallel beams are the input beam and small reference mirror r m , both fixed with respect to the table, and a modified Michelson interferometer (MMI), which can be translated parallel to the input beam. The input beam passes through optical isolator i and beam-expanding telescope t , which produces a plane wave of the desired mode diameter (- 1 cm in this case). The MMI consists of flat beamsplitters S, , S2,and S (one for each desired beam, positioned to give the desired beam spacing), £la$ beam splitting end mirror S O , flat beam splitter S , mercury refe- rence mirror Hgm, and cat's eye or corner cube retroreflecting en2 mirror ce

1 ' Beam splitter S reflects a beam vertically down to mercury mirror Hgm, which forms a reflecting &face always in the horizontal plane. The Michelson components are mounted on a separate rigid platform that can be translated (without changing the mirror adjustment and rotated about the three orthogonal axes.

The interferometer is of the Michelson type but modified by replacing the plane end mirror in one of the arms with the retroreflector. This destroys the symmetry of reflections from the two arms and thereby greatly increases the sen- sivity to relative changes of the angles between the input beam, the reflected beam, and the interferometer axis. This is seen from the following consideration. If the interferometer platform is rotated by angle 8 , the angle of reflection from one arm changes by 8 and that from the other by - 8 , resulting In localized fringes corresponding to the wedge 2 8 . In contrast, for the normal Michelson with two flat end mirrors, the rotation would produce equal angles of reflection for the two arms, resulting in the relatively angle-insensitive circular fringe pattern. A fixed angular position of the Michelson platform is obtained bv adjustinn beam splitters S, , S 4 . and S5 to give two uniform-intensity fringe svstems at

C8-6 JOURNAL DE PHYSIQUE

o b s e r v a t i o n p o i n t o . These svstems a r e formed bv i n t e r f e r e n c e of t h e beams r e f l e c t e d from e e l 'and beam s p l i t t e r S4 and from e e l and h o r i z o n t a l r e f e r e n c e m i r r o r Hgm. The f i r s t system s p e c i f i e s t h e p l a t f o r m r o t a t i o n about t h e two ortho- gonal axes o e r p e n d i c u l a r t o t h e i n p u t l a s e r beam, while t h e second s ~ e c i f i e s t h e r o t a t i o n about t h e t h i r d orthogonal a x i s , t h a t of t h e i n p u t l a s e r beam. A f t e r t h e s e a d i u s t m e n t s , t h e p l a t f o r m can be r o t a t e d , g i v i n g l i n e f r i n g e s , and t h e n r e t u r n e d t o t h e o r i g i n a l a n g u l a r p o s i t i o n by r o t a t i n g t h e p l a t f o r m u n t i l t h e two uniform- i n t e n s i t y f r i n g e systems a r e a g a i n o b t a i n e d . Tf t h e f r i n g e non-uniformity i s d e t e c t e d v i s u a l l y t o about 1/5 f r i n g e , t h e n t h e a n g u l a r s e n s i t i v i t v of t h e p l a t f o r m r o t a t i o n , f o r a 1 cm d i m beam, i s about 3 x r a d .

Much h i g h e r a n g u l a r s e n s t f i v i t y can be o b t a i n e d u s i n g e l e c t r o n i c d e t e c t i o n . An MMI has now been developed which uses components corresponding t o S , S and t h e r e t r o r e f l e c t o r c e l i n F i g . 2 t o g e t h e r w i t h a quadrant diode d e t e c t o r . l ~ h i s 4 svstem has an a n g u l a r s e n s i t i v i t y of a few times 10-l2 r a d f o r 100 s i n t e g r a t i o n time, and h a s been used t o s e r v o t h e a n g l e of a l a s e r beam t o be c o n s t a n t t o about t h i s l e v e l of p r e c i s i o n .

The t h r e e o u t p u t beams of t h e i n t e r f e r o m e t e r a r e made p a r a l l e l by a l i g n i n g a l l t h r e e normal t o f i x e d r e f e r e n c e m i r r o r r m a s f o l l o w s . With t h e Michelson platform i n p o s i t i o n p l i n F i g . 2, beam s p l i t t e r s S , S 4 , and S a r e a d j u s t e d t o 5 g i v e t h e two uniform f r i n g e systems a t o . Then r e i e r e n c e m i r r o r r m i s placed i n p o s i t i o n t o r e f l e c t o u t p u t beam 1 and rokated u n t i l a uniform f r i n g e i s o b t a i n e d a t o1 . Output beam 1 i s now normal t o t h e r e f e r e n c e m i r r o r , and t h e r e f e r e n c e m i r r o r a t t h i s a n g l e i s used f o r alignment of o u t p u t beams 2 and 3.

To a l i g n beam 2, t h e Michelson p l a t f o r m and mercury m i r r o r Hgm a r e t r a n s l a t e d t o p o s i t i o n p2 ( w i t h o u t changing t h e adjustement of S , S 4 , o r S ) where beam 2 i s i n c i d e n t on t h e r e f e r e n c e m i r r o r . The p l a t f o r m i s r o t a t e d t o g l v e t h e two uniform 5 f r i n g e systems a t t r a n s l a t e d o b s e r v a t i o n p o i n t o l . Since t h e s u r f a c e of themercury r e f e r e n c e m i r r o r Hgm always l i e s i n t h e h o r i z o n t a l p l a n e , t h i s r o t a t i o n e n s u r e s t h a t t h e a n g l e of beam 1 i s t h e same a s f o r p l a t f o r m p o s i t i o n p l ( i . e . , n o r m ~ l t o t h e r e f e r e n c e m i r r o r ) . By now r o t a t i n g beam s p l i t t e r S t o g i v e a uniform f r i n g e a t o2 , beam 2 i s made normal t o t h e r e f e r e n c e m i r r o r 2and p a r a l l e l t o beam I . By t r a n s l a t i n g t h e p l a t f o r m t o p , beam 3 i s made p a r a l l e l t o beam 1 with t h e same procedure. I n t h i s way, t h e t a r e e p l a n e wave l a s e r beams a r e obtained with a l l t h e wave f r o n t s p a r a l l e l . With t h e r e f e r e n c e m i r r o r removed,these beams can now be used f o r alignment of t h e SRR.

For i n t e r f e r o m e t r i c alignment of t h e SRR. i t i s p l a c e d i n t h e p o s i t i o n i n d i - c a t e d i n F i g . 2 t o g i v e s u p e r p o s i t i o n of t h e r e f l e c t e d and i n p u t beams. By r o t a t i o n of t h e a d j u s t a b l e 45' m i r r o r i n t h e SRR, t h e f r i n g e systems a t o l and o3 can be made t o have uniform i n t e n s i t i e s . This c o n d i t i o n i n s u r e s t h a t an i n p u t p l a n e wave a t 1 i s r e t r o r e f l e c t e d a t 3 a s a p l a n e wave p a r a l l e l t o t h e i n p u t beam. The c e n t r a l r e t r o r e f l e c t o r a t p o s i t i o n 2 i n s u r e s t h a t t h e r e f l e c t e d beam 2 i s p a r a l l e l t o i n p u t beam 2.

The " p u l l e y e f f e c t . " j u s t a s f o r t h e c a t ' s eye system. p r e s e r v e s t h e r e l a - t i v e phase r e l a t i o n s h i p s between t h e t h r e e beams i f t h e r e i s r e l a t i v e motion between t h e SRR's. With thermal d r i f t s of t h e SRR's. however, t h e o p t i c a l p a t h s of beam 2 and of t h e o f f s e t beam change d i f f e r e n t l y w i t h i n t h e SRR, and t h i s produces c h a q g e s i n t h e r e l a t i v e phases. Thus i t would be d e s i r a b l e t o reduce thermal d r i f t s by making t h e SRR mounting blocks from I n v a r ; however, even with t h e aluminium blocks used h e r e , r e l a t i v e phase changes of < T L over p e r i o d s of s e v e r a l hours have been achieved f o r a beam o f f s e t of 21 cm by p l a c i n g each r e f l e c t o r i n a n e a r l y a i r t i g h t i n s u l a t i n g box.

Ca : R e s u l t s

Let u s f i r s t r e c a l l t h e s i m p l i f i e d e x p r e s s i o n f o r t h e l i n e s h a p e d e r i v e d i n t h e low f i e l d l i m i t w i t h a 4 t h o r d e r p e r t u r b a t i o n approach .14

The velocity distribution of atoms per unit volume is written :

A v

where A is a function describing the angular distribution of the unit vector n=;;

For a cel1,A is a constant and for a beam in the x direction it is a very slow function of x .

The complex representation of the laser field propagating in the z direction is written

I

+ * + + ^i?*

+ ^{S- E} G- (y) G; (x - ^{L) e} ) exp (iot T ikz)

3 3 3 (2)

where $: is the polarizatiq unit veftor, G; is the Gaussian distribution of each laser beam with waist wo , E: and cPS are the respective amplitudes and phases

J J

of the six fields. The fringe signal expressed as the power absorbed in units of quanta ho is :

(excitation efficiency) (effective flux)

(effective velocity distribution)(relaxation)

(phases) (oscillating term)

+ 3 similar terms obtained by exchanging +-- and 6-+-6 (3)

JOURNAL DE PHYSIQUE

0: = 11 !E / 2 6 a r e t h e Rabi p u l s a t i o n s ( s e e r e f e r e n c e 19 f o r more d e t a i l e d express-

J 1

i o n s t a k l n g t h e p o l a r i z a t i o n i n t o account) ; y = (I - v * / c ~ ) - ' / ~ accounts f o r t h e t r a n s - v e r s e Doppler e f f e c t and 2 6 i s t h e r e c o i l s p l i t t i n g ; y i s t h e decay c o n s t a n t of

t h e o p t i c a l coherence and W i s t h e p r o b a b i l i t y functionbafor complex argument.

For beam experiments, i f t h e r e i s a decay of t h e upper l e v e l p o p u l a t i o n with a r e l a x a t i o n c o n s t a n t yb , between t h e l a s t zone and t h e d e t e c t i o n r e g i o n bounded by (RI , R ) , t h e f o l l o w i n g e x t r a - f a c t o r should be added i n t h e v i n t e g r a l t o o b t a i n t h e s l g n a ? :

exp

[-

[-

The e f f e c t i v e f l u x of atoms Qeff i s given by :

This e x p r e s s i o n allows d i r e c t comparison between c e l l and beam experiments.

The r e s u l t s o b t a i n e d w i t h t h e experimental a p p a r a t u s d e s c r i b e d above w i l l now be b r i e f l y d i s c u s s e d . The s e p a r a t e Ramsey f r i n g e p a t t e r n s of t h e r e c o i l d o u b l e t , s p l i t by 23 kHz, have now been completely r e s o l v e d 6 3 7 using beam s e p a r a t i o n s up t o 2 L = 2 1 cm, a s i s shown i n t h e comparison of experimental and t h e o r e t i c a l p r o f i l e s i n F i g . 3. The curves i n t h e f i g u r e a l s o show t h e i n f l u e n c e of second-order Doppler

Frequency Offset, kHz

F i g u r e 3

Comparison between experimental (. ... ⁾ and t h e o r e t i c a l (----) o p t i c a l Ramsey f r i n g e p r o f i l e s

broadening and s h i f t on t h e Ramsey f r i n g e p r o f i l e s 8 a s r e s o l u t i o n i s i n c r e a s e d from 2 L = 3 . 5 cm, where t h e r a t i o of f r i n g e width (FWHM) t o second-order Doppler s h i f t (1.7 kHz f o r v = u ) i s about 3, t o 2 L = 2 1 cm, where t h e r a t i o i s about 112. This i n - f l u e n c e i s c l e a r l y i l l u s t r a t e d i n t h e computer-generated contour p l o t of F i g . 4 ,

- 2 - 1 0 I 2 3 4

2L (v - ^{vo) /u}

F i g u r e 4

Contour p l o t of Ramsey f r i n g e i n t e n s i t y v e r s u s normalized frequency ( v - v o ) / (u/2L) a s a f u n c t i o n of r e s o l u t i o n . The r e s o l u t i o n parameter Z i s t h e r a t i o (FWHM of second-order Doppler d i s t r i b u t i o n . / F l G - B ~ of Ramsey f r i n g e t h a t would be o b t a i n e d i n t h e absence of t h e second-order Doppler s h i f t ) . Contour i n t e r v a l , 5 % . I n t e n s i t i e s : - , p o s i t i v e ; ---, nega- t i v e ; -.-A , zero.

which shows t h a t with i n c r e a s i n g r e s o l v i n g power t h e c e n t r a l f r i n g e d i s a p p e a r s a s t h e f i r s t b l u e - s i d e f r i n g e b u i l d s up, t h e n t h i s f i r s t f r i n g e d i s a p p e a r s a s t h e second b u i l d s up, e t c . These e f f e c t s a r e caused by t h e d i f f e r e n t - o r d e r dependence2 on atomic v e l o c i t y v of 1) t h e second-order Doppler r e d s h i f t , p r o p o r t i o n a l t o v ,

and 2) t h e p e r i o d of t h e Ramsey f r i n g e f o r a s i n g l e v e l o c i t y p r o p o r t i o n a l t o v , a s i s s e e n i n t h e following.

The frequency of t h e i n t e n s i t y maximum of t h e Nth s i d e f r i n g e f o r a s i n g l e v e l o c i t y v i s v -vo = (Nv/2L) - v v2 /2c . With high r e s o l u t i o n ( a n d / o r h i g h velo- c i t y ) , t h e second term, t h e second-order Doppler s h i f t t o t h e r e d , becomes 0 i m - p o r t a n t . As v i n c r e a s e s , t h e f r i n g e s on t h e r e d s i d e of l i n e c e n t e r ( n e g a t i v e N) and t h e c e n t r a l f r i n g e (N=O) s h i f t monotonically t o t h e r e d , and i n t e g r a t i o n over v makes t h e s e f r i n g e s broaden and i n t e g r a t e toward z e r o i n t e n s i t y . However, t h e f r i n g e s on t h e b l u e s i d e ( p o s i t i v e N) have t h e i n t e r e s t i n g c h a r a c t e r i s t i c of a l i n e a r s h i f t t o t h e b l u e w i t h v and a q u a d r a t i c s h i f t t o t h e r e d , and t h e s l o p e of t h e t o t a l s h i f t v e r s u s v curve changes s i g n f o r a turnaround v e l o c i t y v = ~ c ~ / 2 L v ~ . With t h i s turnaround, t h e Nth f r i n g e s f o r v e l o c i t i e s n e a r v t a l l occur a t about t

t h e same frequency. I f v i s near u , i n t e g r a t i o n over v can r e s u l t i n a s t r o n g and s h a r p f r i n g e with a wldth much narrower than t h e second-order Doppler width. t

I n Fig. 3 , t h e SIN i s s e e n t o be g r e a t l y degraded f o r 2 L = 2 1 . 0 cm. With t h e o p t i c a l Ra sey f r i n g e technique, SIN should not be g r e a t l y reduced a s r e s o l u t i o n i s increased,lP2 and r e s o l u t i o n of t h e second-order Doppler broadening should reduce t h e f r i n g e h e i g h t (Imax- I in) by only about 10X f o r t h i s v a l u e of 2 L , a s s e e n i n F i g . 4. Thus t h e degraded S ~ N i s b e l i e v e d t o be due t o a combination of s l i g h t non- p a r a l l e l i s m of t h e l a s e r beams, r e s i d u a l laser-frequency j i t t e r ( t h e rms j i t t e r i s

C8-I0 JOURNAL DE PHYSIQUE

approximately equal to the linewidth for this resolution), and, possibly, the re- cently measured angle jitter of our laser beam. The SIN degradation due to these effects could be reduced greatly as follows. The parallelism of the laser beams could be improved to the limit imposed by optics imperfections by use of a quadrant diode with the MMI alignment system to detect fringe uniformity. The frequency jitter could be reduced to a level of <I00 Hz (less than the 400 Hz natural line- width of th Ca line) by use of the recently developed sideband frequency servo techniques . ( j 3 Also, the angle jitter, which degrades the fringe intensity by intro- ducing changes in the relative phases between the interaction zones during the atomic flight time, could be reduced to an uninteresting level with the angle servo interferometer. '

'

An additional effect which we have observed is the power contraction of the recoil splitting predicted by ~ o r d 6 . l ~ As power was increased, the splitting first contracted by about 2 kHz, and then with higher power expanded and then le- velled off. The low power cotltraction fits fairly wellTa,with the low power limit of

dependence. The theory Bords's 6th order theory which predicts the observed 2

for higher power is now being developed.

These results show that in order to achieve the ultimate line-center preci- sion for this Ca line, it would be necessary to greatly reduce the Ramsey fringe power-dependent and resolution-dependent asymmetry and shift caused by the second- order Doppler shift. This can in principle be done, 'y8 by either using velocity selection techniques or by laser cooling of the Ca beam. Systematic errors due to the power contraction of the recoil splitting can be reduced sufficiently through use of techniques discussed elsewhere.

It should be possible to increase the present low SIN of the fringe signal to about lo4 through us8 of photon-amplification techniques and optimization of atomic beam design, leading to a pointing precision of about Av/v= 10- 15~-f??

where t is integration time. This high p~intinf~precision should make it possible to correct systematic errors to better than 10- , giving a very high accuracy frequency standard in the visible spectrum.

10 ~ u n experiment

In spite of many theoretical works optical Ramsey frin es using 3 field zones in an absorption cell have been very little explored

In order to keep a reasonable solid angle for molecules intersecting all three beams large diameter optical beams and correspondingly large retroreflectors have to be used. Such large retroreflectors have been made by optically contacting three 1/10 (in the visi le) zerodur mirrors to form our 22 cm-aperture corner cubes with a (5-10) x lo-' radians angular accuracy. After deposition of gold coatings,the junctions between faces were not visible.

The optical set-up is similar to the calcium experiment. The 10 cm-diameter folded standing wave with a beam spacing of 2 L = 5 4 cm is represented in Fig. 5.

The two retroreflector structures (2, 3, 4, 5) and (5, 6, 7) are inside the large absorption cell and separated by 18 meters. The optics are mounted on massive aluminium blocks which are rigidly clamped to four Invar rods of 4 cm diameter to define the beam spacing L and to reduce thermal phase drifts between the three excitation zones. Phase modulation of the fringes can be achieved with PZT ceramics located under the 3 mounting points of corner cube n o 2. Helmholtz coils and a so- lenoid reduce the earth magnetic field inside the cell to less than 10% of its value. The three beams are made parallel within a small fraction of a fringe at 10 w with a multiple beam interferometer similar to the one described above for the Calcium experiment. However this interferometer has a corner cube instead of the cat's eye Cel of Fig. 2 and has optics large enough for a 70 mm aperture.

For the final parallelism adjustment, mirrors 3 and 7 in Fig. 5 are rotated by means of three stainless steel metal-metal deformation contacts.

Fig.5 : Ramsey f r i n g e o p t i c a l s e t - u p optics d i a m e t e r : 1 1 c m b e a m s p a c i n g : 2 L = 5 4 c m

cell l e n g t h 18 m

As shown i n Fig. 6 , t h e o u t p u t beam of a very s t a b l e frequency c o n t r o l l e d CO l a s e r i s expanded by a f a c t o r of " 7 t o a 2w

-

- -. L A S E R CO, c w

w.= 2.9- lnput Parabola

f = 4 0 2 mm

Delector

- - ^{~ 1 4 plate}

Spallal Cd S

ftlter

d=800urn - -

Cell wall

Converging beam ~nsode the c e l l w t t h w-3.65cm located at 3 0 0 m Confocal parameter : I km

Fig.6 : ln p u t o p t i c s f o r Ramsey f r i n g e s e t - u p

C8- 12 JOURNAL DE PHYSIQUE

l o c a t e d a t t h e t e l e s c o p e f o c u s t o produce a n a p p r o x i m a t e l y G a u s s i a n beam ( w i t h i n a few p e r c e n t ) . Then by measuring t h e s p o t s i z e of t h e beam a t v a r i o u s d i s t a n c e s (up t o 54 m e t e r s ) , we have been a b l e t o d e t e r m i n e t h e w a i s t and c u r v a t u r e v a l u e s shown i n F i g . 6. F i n a l l y w i t h t h e 10 cm d i a m e t e r beam and t h e 1 km c o n f o c a l p a r a - meter t h e w a v e f r o n t s i n t h e 3 zones a r e f l a t and p a r a l l e l t o a b o u t 1 / 1 0 o f a f r i n g e a t 10 1~m.

As a f i r s t t e s t of t h e o p t i c a l q u a l i t y of t h i s s e t - u p , we have u s e d t h e mo-

d i f i e d V i l l e t a n e u s e s p e c t r o m e t e r , t o i n v e s t i g a t e t h e s i n g l e zone s a t u r a t e d ~ ( 2 8 ) ~ ~ l i n e o r 8 t h e v band of 3 2 S ~ 6 . S i n c e t h e h y p e r f i n e s t r u c t u r e of t h i s l i n e i s w e l l 2

known , p r e c i s e l i n e s h a p e s t u d i e s c a n be made. ³ . -

A g e n e r a l d i a g r a m of t h i s s p e c t r o m e t e r c a n be found i n t h e s e p r o c e e d i n g s . ^{I I} B r i e f l y , t h e CO? l a s e r used f o r p r o b i n g t h e l a r g e a b s o r p t i o n c e l l i s f r e - quency-offset-locked rom a second r e f e r e n c e l a s e r . T h i s l a s e r i s i n t u r n locked t o a s a t u r a t i o n l i n e of a heavy molecule l i k e Os04 o b t a i n e d w i t h a s e p a r a t e a b s o r p t i o n c e l l u s i n g a l i n e c e n t e r l S t ( o r 3rd ) d e r i v a t i v e l o c k . Frequency t u n i n g i s accomplished through v a r i a t i o n of t h e s y n t h e s i z e r f r e q u e n c y u s e d i n t h e f r e q u e n c y - o f f s e t - l o c k .

The s t a b i l i t y of t h e l a s e r s i s i l l u s t r a t e d i n F i g . 7 , which shows a spec- t r a l p u r i t y of

-

F I ~ , 7 : Beat frequency spectrum of two C02

lasers locked to ~ ( 2 8 ) ~ ; ~ line of S F 6 and to a

strong line of Os04 .

The frequency scale is 200 Hz/div. The vertical scale is linear and the resolution of the spectrum analyzer is 30 Hz.

T h i s l a s e r l i n e w i d t h i s of t h e o r d e r of t h e Ramsey f r i n g e w i d t h (180 Hz FWHM) e x p e c t e d f o r o u r 54 cm beam s e p a r a t i o n f o r SF . W i t h t h e l a s e r s u n l o c k e d , t h e f r e e running s p e c t r a l p u r i t y i s of t h e o r d e r of 1 @HZ w i t h d r i f t s of a few kHz o v e r s e v e r a l m i n u t e s . Also t h e same o r d e r of s t a b i l i t y h a s been a c h i e v e d w i t h a wave- g u i d e C02 l a s e r t u n a b l e o v e r 500 MHz. T h i s s h o u l d p r o v i d e a g r e a t d e a l of new hy- p e r f i n e r e s u l t s f o r many m o l e c u l e s l i k e S F 6 , O s 0 4 , S i H 4 , S i F 4 , P F 5 , NH3 ...

T h i s l a s e r s t a b i l i t y w i l l be improved i n t h e n e a r f u t u r e through a c o u s t i c i s o l a t i o n and b e t t e r s e r v o s y s t e m s .

F i g . 8 shows t h e 1 s t d e r i v a t i v e h y p e r f i n e spectrum of t h e ~ ( 2 8 ) ~ ; c l u s t e r of 3 2 ~a t 28.464 691 306 THz. The e x p e r i m e n t a l l i n e w i d t h i s 1.2 kHz (HWHM). A l s o ~ shown i s t h e t h e o r e t i c a l spectrum c a l c u l a t e d by 6 3. Bord6 f o r t h e two o v e r l a p p i n g 1 = 3 (7 components) and I = 1 ( 3 components) m u l t i p l e t s . The c e n t r a l t h r e e compo- n e n t s a r e d o u b l e t s w i t h s p l i t t i n g s of a b o u t 1 . 6 ; 1.1 ; 1.5 kHz. The l i n e w i d t h i s c l o s e t o t h e v a l u e e x p e c t e d f o r o u r l a s e r beam d i a m e t e r a s can b e s e e n from t h e main c o n t r i b u t i o n s t o t h e o b s e r v e d w i d t h (HWM) : g e o m e t r i c a l e f f e c t s : 650 H z ; c o l l i s i o n s :200 H z ; power b r o a d e n i n g : 100 H z ; m o d u l a t i o n b r o a d e n i n g : 100 Hz ; s p e c t r a l p u r i t y of t h e l a s e r : l o 0 H z ; r e s i d u a l Zeeman e f f e c t from t h e e a r t h

CLUSTER R ( 2 8 ) A2, 0 H W H M = ^{1.25 kHz}

I I

14 321.5 14 4 0 4 . 8

F R E Q U E N C I E S I N k H z

F i g u r e 8

P r o f i l e s o f t h e ~ ( 2 8 ) ~ ; !ine of t h e v3 band of 3 2 ' 3 ~

.

- Upper : e x p e r i m e n t a l f r r a t d e r i v a t i v e spectrum (sG6 p r e s s u r e : T o r r ; l a s e r power: 4 p Watt; time c o n s t a n t : I sweep time : 5 min.)

F ~ e q u e n c i e s a r e i n k i l o h e r t z from t h e lBiOn04 l i n e a t 28 464 676 938.5 kHz

- Lower: c a l c u l a t e d p r o f i l e ( l i n e w i d t h (HWHM) = 1.25 kHz).

magnetic f i e l d a f t e r compensation 20 Hz; o t h e r e f f e c t s s u c h a s n a t u r a l l i n e w i d t h , r e c o i l s p l i t t i n g , and 2nd o r d e r Doppler e f f e c t a r e a l s o n e g l i g i b l e .

I n c o n c l u s i o n , we have p r e s e n t l y r e a c h e d t h e t h e o r e t i c a l t r a n s i t - t i m e l i m i t e d l i n e w i d t h f o r s i n g l e zone s a t u r a t e d a b s o r p t i o n showing t h a t t h e w a v e f r o n t s are of good q u a l i t y o v e r t h e 1 1 crn o p t i c s d i a m e t e r . We have d e m o n s t r a t e d t h a t open c o r n e r cubes c a n be u s e d t o produce good q u a l i t y l a r g e i n f r a r e d r e f l e c t e d beams and t h i s i s a n i m p o r t a n t advance f o r h i g h a c c u r a c y i n f r a r e d s a t u r a t i o n s p e c t r o s c o p y .

The n e x t s t e p w i l l be t o improve b o t h t h e long-term s t a b i l i t y of t h e l a s e r s and t h e s i g n a l - t o - n o i s e r a t i o i n o r d e r t o d e t e c t t h e f r i n g e s .

JOURNAL DE PHYSIQUE

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-

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17 CLAIRON A., VAN LERBERGHE A., BREANT Ch., SALOMON Ch., CAMY G . , a n d B0RDECh.J.

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