RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10 m SPECTRAL REGIONS : EXPERIMENTAL METHODS Ch. Salomon, Ch. Br´eant, Ch. Bord´e, R. Barger

To cite this version: Ch. Salomon, Ch. Br´eant, Ch. Bord´e, R. Barger. RAMSEY FRINGES USING TRANSITIONS IN THE VISIBLE AND 10 m SPECTRAL REGIONS : EXPERIMENTAL METHODS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-3-C8-14. .

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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 Paris-Nord,

de Physique des Lasers, associé F-9S4S0 Villetaneuse, France

(*) Lasedngle, Inc., Rollinsville, de Physique des Lasers, Universite

(**)

au C.N.R.S. n°282,

Université

Colorado 80474, U.S.A. and Laboratoire 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 absorption 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) resolution 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 linewidths 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 stabilized 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 the 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 constant i n time. (Since these 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 negative, random phase f l u c t u a t i o n s w i l l cause the f r i n g e i n t e n s i t y t o average t o zero). These conditions 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 colleagues,' a s well 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 properly 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 obtained 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 plane 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

Figure 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 prop e r t y , commonly c a l l e d t h e "pulley effect,"'wherein 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 the c a t ' s eyes,changes caused by v i b r a t i o n , f o r i n s t a n c e . With a standing wave node formed a t the r e f l e c tion-surface 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 equal 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 these "perfect" c a t ' s eyes, 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 periods a r e long compared t o t h e atomic f l i g h t time, the 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 with Ca, Ramsey f r i n g e s were obtained with 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 higher 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 ~ aligned 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 Fig. Ib the SRR c o n s i s t s of a corner 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 angle) 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 small c a t ' s eye o r corner 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 corner cube and the adjacent 45" m i r r o r on an A 1 block, the c a t ' s eye on a second, and t h e o t h e r 45" mirror on a t h i r d , with t h e blocks r i g i d l y mounted on - 3 cm diam Invar rods. 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 angular adjustement, very s t a b l e with time, i s made by compressing t h r e e metal-metalcontact 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 the 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 within a small f r a c t i o n of a f r i n g e over the 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 central retroreflector of the first SRR. The beam is then retroreflected back around the optical circuit to produce the three standing-wave beams. The reflecting surfaces 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 reference 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 always in the horizontal plane. The Michelson components are a reflecting &face 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 sensivity 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

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observation 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 platform r o t a t i o n about t h e two orthogonal axes oerpendicular 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 st 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 these adiustments, t h e platform 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 then returned t o t h e o r i g i n a l angular p o s i t i o n by r o t a t i n g t h e platform u n t i l t h e two uniformi n t e n s i t y f r i n g e systems a r e again obtained. 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 , then t h e angular s e n s i t i v i t v of t h e platform rad. r o t a t i o n , f o r a 1 cm d i m beam, i s about 3 x Much higher angular s e n s t f i v i t y can be obtained using e l e c t r o n i c d e t e c t i o n . which uses components corresponding t o S , S and An MMI has now been developed 4 the r e t r o r e f l e c t o r c e l i n Fig. 2 t o g e t h e r with a quadrant diode d e t e c t o r . l ~ h i s svstem has an angular s e n s i t i v i t y of a few times 10-l2 rad f o r 100 s i n t e g r a t i o n time, and has been used t o servo t h e angle 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 follows. With t h e Michelson platform i n p o s i t i o n pl 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 give 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 obtained 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 a t o1 m i r r o r a t t h i s angle i s used f o r alignment of output beams 2 and 3. To a l i g n beam 2, t h e Michelson platform 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 (without changing t h e adjustement of S , S 4 , o r S ) where beam 2 5 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 platform i s r o t a t e d t o g l v e t h e two uniform Since t h e s u r f a c e of themercury f r i n g e systems a t t r a n s l a t e d observation p o i n t o l 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 ensures t h a t t h e angle of beam 1 i s t h e same a s f o r platform p o s i t i o n p l ( i . e . , n o r m ~ lt o the 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 give 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 mirror 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 platform t o p , beam 3 i s made p a r a l l e l t o beam 1 with the same procedure. I n t h i s way, the t a r e e plane 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 placed i n t h e p o s i t i o n i n d i cated i n Fig. 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' mirror 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 plane 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 plane 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 "pulley e f f e c t . " j u s t a s f o r t h e c a t ' s eye system. preserves the 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 paths 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 the 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 Invar; however, even with t h e aluminium over periods of s e v e r a l hours blocks used here, r e l a t i v e phase changes of < T L 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 the s i m p l i f i e d expression f o r t h e lineshape derived i n the low f i e l d l i m i t with 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 and cPS are the respective amplitudes and phases laser beam with waist wo , E: 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)

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0 : = 11 !E / 2 6 a r e t h e Rabi p u l s a t i o n s J 1

( 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 expressions taklng the 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 the t r a n s i s t h e decay c o n s t a n t of 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 the 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 population 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 region bounded by (RI , R ) , the following 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 the s l g n a ? : exp

[-yb k1/v]

The e f f e c t i v e f l u x of atoms

Qeff

- exp [-ITb g2 / v] i s given by :

This expression allows d i r e c t comparison between c e l l and beam experiments. The r e s u l t s obtained with t h e experimental apparatus described above w i l l now be b r i e f l y discussed. 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 resolved 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 Fig. 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

Figure 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 increased 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 influence 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 Fig. 4 ,

-2

-1

0

I

2

3

4

2L (v - vo) /u Figure 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 distribution./FlG-B~of Ramsey f r i n g e t h a t would be obtained i n t h e absence of t h e second-order Doppler I n t e n s i t i e s : -, p o s i t i v e ; ---,negas h i f t ) . Contour i n t e r v a l , 5 % , zero. tive;

.

-.-A

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 disappears a s the f i r s t blue-side f r i n g e b u i l d s up, then t h i s f i r s t f r i n g e disappears 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 red s h i f t , p r o p o r t i o n a l t o v , and 2) the period 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 seen i n t h e following. The frequency of t h e i n t e n s i t y maximum of the 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 (and/or high velo0 c i t y ) , t h e second term, t h e second-order Doppler s h i f t t o the r e d , becomes imp 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 red s i d e of l i n e c e n t e r (negative 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 red, and i n t e g r a t i o n over v makes these f r i n g e s broaden and i n t e g r a t e toward zero i n t e n s i t y . However, t h e f r i n g e s on t h e blue s i d e ( p o s i t i v e N) have the 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 blue with 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 versus 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 near v t a l l occur at t about 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 t and sharp f r i n g e with a wldth much narrower than the second-order Doppler width. I n Fig. 3 , t h e SIN i s seen t o be g r e a t l y degraded f o r 2L=21.0 cm. With the 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 the 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 value of 2 L , a s seen i n i s believed t o be due t o a combination of s l i g h t nonFig. 4. Thus t h e degraded S ~ N 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

.

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approximately equal to the linewidth for this resolution), and, possibly, the recently 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