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IMPROVED PERFORMANCES IN Cs STANDARDS WITH NEW-DESIGN RESONATORS
A. de Marchi
To cite this version:
A. de Marchi. IMPROVED PERFORMANCES IN Cs STANDARDS WITH NEW- DESIGN RESONATORS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-289-C8-296.
�10.1051/jphyscol:1981836�. �jpa-00221732�
IMPROVED PERFORMANCES IN C s STANDARDS WrTH N E W D E S I G N RESONATORS
I s t i t u t o EZettrotecnico NazionaZe "GaZileo Ferrarisl< To'orino, Itaz$~
A b s t r a c t . - The problems t h a t l i m i t t h e accuracy of p r e s e n t s t a t e - o f - t h e - a r t C s beam primary f r e q u e n c y s t a n d a r d s a r e r e l a t e d t o a t o m s ' v e l o c i t y d i s t r i b u t i o n , c a v i t y - p h a s e - d i f f e r e n c e and magnetic f i e l d inhomogeneity.
Improvements of t h i s s i t u a t i o n may be i n t r o d u c e d by o p t i c a l s t a t e s e l e c t i o n and d e t e c t i o n , b u t o n l y a r e d e s i g n e d microwave s t r u c t u r e u s i n g open Fabry-Perot r e s o n a t o r s a l l o w s thorough e x p l o i t a t i o n of t h i s t e c h n i q u e by p e r m i t t i n g t h e use of v e r y wide beams. The h i g h s i g n a l - t o - n o i s e r a t i o o b t a i n e d i n t h i s way c a n be s p e n t i n d i f f e r e n t ways f o r f r e q u e n c y a c c u r a c y enhancement.
Two c o n f i g u r a t i o n s a r e proposed: a t w o - c a v i t i e s h o r i z o n t a l wide beam and a s i n g l e c a v i t y f o u n t a i n beam. P r o j e c t e d s t a b i l i t y and a c c u r a c y performances a r e r e p o r t e d f o r t h e two schemes; improve- ments of s t a b i l i t y down t o t h e 10-13 l e v e l and a c c u r a c i e s from few p a r t s i n 1 0 - l 4 t o b e t t e r t h a n 1 0 " ~ z r e expected.
I n t r o d u c t i o n . - The a c c u r a c y of l a b o r a t o r y C s beam primary f r e q u e n c y s t a n d a r d s u s i n g magnetic s t a t e s e l e c t i o n , b e n t waveguide Ramsey c a v i t y and h o t wire d e t e c t i o n , a p p e a r s t o have been c a r v e d down t o i t s funda- mental l i m i t a t i o n s i n t h e l a s t decade o f t h e o r e t i c a l s t u d i e s and ex- p e r i m e n t a l improvements [1,2,3]. I n f a c t t h e o r e t i c a l knowledge of t h e v a r i o u s f a c t o r s a f f e c t i n g t h e i r resonance f r e q u e n c y , i n p a r t i c u l a r t h e h i g h degree of u n d e r s t a n d i n g r e a c h e d of t h e r o l e p l a y e d by t h e v e l o - c i t y - t r a j e c t o r y - c a v i t y phase s h i f t c o r r e l a t i o n [ 4 ] caused by magnetic f i e l d s t a t e s e l e c t i o n , h a s lowered t h e i r a c c u r a c y t o t h e 10r13 l e v e l , but i t s e e q s u n l i k e l y t h a t t h e l a t t e r may be pushed even lower u s i n g t h e p r e s e n t scheme. The r e s i d u a l u n c e r t a i n t i e s i n a - p r i o r i f r e q u e n c y d e t e r m i n a t i o n come from second o r d e r Doppler e f f e c t , c a v i t y p h a s e - s h i f t , Majorana t r a n s i t i o n s and p u l l i n g by t h e Rabi t a i l s of n e i g h b o r i n g r e s c nances .
The u s e of o p t i c a l s t a t e s e l e c t i o n and d e t e c t i o n h a s been proposed as a mean t o reduce some of t h e s e problems, and h a s been r e c e n t l y demon- s t r a t e d on a C s beam [5]. The M a j o r ~ a t r a n s i t i o n s problem would v i r - t u a l l y d i s a p p e a r w i t h t h i s t e c h n i q u e , due t o t h e l a c k of s e l e c t i n g magnets, and t h e same would be t r u e f o r t h e problems coming from n e i g g b o r i n g t r a n s i t i o n s i f a n o p t i c a l pumping scheme which pumps a l l atoms i n a s i n g l e mp = 0 h y p e r f i n e magnetic s u b l e v e l were u s e d [ 6 ] . The l a t t e r i s i l l u s t r a t e d i n t h e diagram of f i g . 1 i n one of t h e p o s s i b l e r e a l i s 2 t i o n s . Two l a s e r s of f r e q u e n c i e s dpl and V p 2 , as shown i n f i g . 1 , il- l u m i n a t e t o g e t h e r t h e u s e d s e c t i o n of t h e atomic beam; i f t h e p o l a r i z g t i o n of t h e second l a s e r i s such t h a t i t s r f magnetic f i e l d i s perpen-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981836
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F i g . 1 : Diagram of t h e pumping scheme f o r C s atoms. The r a d i a t i o n Qp2 h a s t o be p o l a r i z e d w i t h i t s magnetic f i e l d p e r p e n d i c u l a r t o t h e C - f i e l d .
d i c u l a r t o t h e q u a n t i z a t i o n DC magnetic f i e l d e x i s t i n g i n t h e a r e a , a l l atoms emerge from t h e pumping r e g i o n i n t h e s t a t e F = 4 , m~ = O . Low C- f i e l d v a l u e s c a n be u s e d f o r t h i s r e a s o n and a s m a l l e r f r e q u e n c y o f f s e t would be p r e s e n t . L a s e r e x c i t a t i o n a t Yd of t h e atoms t h a t have under- gone a microwave t r a n s i t i o n i n t h e Ramsey c a v i t y , and o p t i c a l d e t e c t i o n of t h e i r e m i t t e d f l u o r e s c e n c e , i s t h e n capable of y i e l d i n g 100% e f f i - c i e n c y . The c a v i t y phase s h i f t u n c e r t a i n t y would a l s o be reduced by t h e use of o p t i c a l pumping because no c o r r e l a t i o n would t h e n be p r e s e n t between v e l o c i t y and t r a j e c t o r y and a s a r e s u l t more a c c u r a t e determi- n a t i o n of i t c o u l d be made by beam r e v e r s a l o r o t h e r t e c h n i q u e .
The o t h e r advantage of o p t i c a l pumping i s i n c r e a s e d s i g n a l - t o - n o i s e r a t i o w i t h r e s p e c t t o t h e t r a d i t i o n a l beam. I n f a c t a f a c t o r of 4 i n S/N is g a i n e d by pumping a l l atoms i n a s i n g l e magnetic s u b l e v e l i n - s t e a d of s e l e c t i n g one s u b l e v e l and e l i m i n a t i n g t h e o t h e r s w i t h magnet i c s e l e c t i o n . Furthermore a v e r y s t r o n g s i g n a l can be o b t a i n e d w i t h o p t i c a l d e t e c t i o n a c c o r d i n g t o t h e scheme of f i g . 1 because of t h e i n - t r i n s i c a m p l i f i c a t i o n g i v e n by t h i s t e c h n i q u e v i a m u l t i p l e r e c y c l i n g of t h e o p t i c a l t r a n s i t i o n . The b e s t way t o u s e t h e s e s i g n a l - t o - n o i s e and s i g n a l - l e v e l f e a t u r e s a p p e p r s t o be t o spend i t f o r o b t a i n i n g a more p r e c i s e d e t e r m i n a t i o n of second o r d e r Doppler s h i f t and c a v i t y p h a s e - s h i f t . A number of systems have been proposed f o r t h e r e d u c t i o n of t h e s e two e f f e c t s , from narrowing t h e v e l o c i t y d i s t r i b u t i o n v i a microwave s t r o b i n g [ 7 ] t o t h e use of a narrow beam [8], b u t t h e o n l y fundamental s o l u t i o n remains t h e u s e of slow atoms [ g ] . A l l t h e s e t e c h n i q u e s s u f f e r from low S/N and o p t i c a l pumping may be t h e answer t o t h i s problem.
I n t h i s paper a r e d e s i g n e d microwave s t r u c t u r e , making use of open Fabry-Perot r e s o n a t o r s , i s s u g g e s t e d f o r use i n c o n n e c t i o n w i t h o p t i - c a l l y pumped beam f r e q u e n c y s t a n d a r d s . A l l t h e improvements i n t r o d u c e d toward h i g h e r a c c u r a c y by o p t i c a l pumping a r e enhanced by t h e unique f e a t u r e s of open r e s o n a t o r s . Among t h e l a t t e r most i m p o r t a n t a r e t h e e x c e l l e n t mode d e f i n i t i o n , w i t h a quasi-plane wave i n t h e r e s o n a t o r ' s c e n t e r , and t h e v e r y wide a p e r t u r e . Very h i g h S/N v a l u e s a r e o b t a i n e d
(thin) ribbon beam, and a single-resonator fountain.
Gravitational trapping of Cs in a fountain experiment was tried by Zacharias at MIT in the early '50s, but presumably a combination of excessive scattering of low-velocity atoms from the source and inade- quate sensitivity (solid angle) in the hot wire detector caused him to obtain very disappointing S/N results and abandon the experiment.
A report of those efforts was made at the January '54 meeting of the APS in New York [lo], but no written account is available of the exper- imental set-up, except for a rough description given by Ramsey in his book [ll].
In the following it is shown that laser optical pumping used in con- junction with an open resonator can make this old idea very attractive again, even if 99% of the slow atoms that one would like to use were scattered by the fast ones near the oven.
Microwave resonator
The fundamental gaussian mode in a Fabry-Perot resonator made of two spherical mirrors symmetricallg facing each other across the beam seems to be the ideal mode for exciting the microwave transition.
Phase variation across the cavity and l/e intensity lines for this mode are shown in fig. 2. The phase difference 9 from the cavity center can be expressed near the mode waist by:
- 1
9 = ts (zmtg p Y)X Z$Y for y<(3-' = 3 A
where y is the distance from the waist plane and Zm=~m/120?T is the normalized surface impedance of the mirrors, with the surface resis- tance Rm equal for Copper to 2 . 5 ~ 1 0 - ~ .
Fig. 2 : Diagram of intensity and phase of the mode proposed. The mag- netic field nodal surfaces are indicated.
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This mode h a s t h e f o l l o w i n g a d v a n t a g e s when u s e d t o e x c i t e a t r a n s i t i o n i n a beam:
a ) i f n e c e s s a r y f o r i n c r e a s i n g t h e s i g n a l a v e r y wide beam can be p a s s ed through t h e c a v i t y , w i t h a c r o s s s e c t i o n l i m i t e d o n l y by t h e - changing phase of t h e r f magnetic f i e l d n e a r i t s n o d a l p l a n e s and by t h e mode s i z e a t t h e c e n t e r of t h e c a v i t y . With a mode w a i s t d i a - m e t e r of s e v e r a l wavelengths ( e . g . 3 A ) a beam c r o s s - s e c t i o n of a few A2 ( e .g. 1 . 5 h2) can be u s e d ; i n t h e c a s e of C s t h i s means a
c r o s s s e c t i o n of 1 by 10 cm ( s o u r c e a r e a and o p t i c a l pumping w i d t h s s h o u l d o b v i o u s l y be of t h i s same s i z e i n o r d e r t o f u l l y e x p l o i t t h e p o s s i b i l i t i e s o f f e r e d by t h e open c a v i t y ) ;
b ) t h e mode c r o s s - s e c t i o n a l l o w s l o n g i n t e r a c t i o n t i m e s w i t h t h e atoms and v e r y narrow Rabi r e s o n a n c e s . T h i s i s v e r y u s e f u l i n t h e c a s e t h e r e s h o u l d be i m p e r f e c t o p t i c a l pumping w i t h r e s i d u a l p o p u l a t i o n s i n mF f 0 s u b l e v e l s ;
c ) t h e P o y n t i n g v e c t o r i s v e r y n e a r l y a x i a l about t h e c e n t e r of t h e r e s o n a t o r , and t h e f i r s t o r d e r Doppler e f f e c t i s hence minimized.
Whatever l i t t l e may be p r e s e n t of i t , due t o t r a j e c t o r y i n c l i n a t i o n , i s n o t a s h i f t b u t a b r o a d e n i n g i f t h e beam i s symmetric. By t h e same t o k e n t h e mode i s a p l a n e wave a t t h e w a i s t , and a n atom t r a v e l l i n g p a r a l l e l t o t h e phase p l a n e s e x p e r i e n c e s no phase s h i f t a c r o s s t h e mode. Average phase s h i f t i s due o n l y t o mechanical u n c e r t a i n - t i e s i n t h e beam d e f i n i n g s l i t s . A v e r y t h i n r i b b o n beam can be u s e d i f phase d e f i n i t i o n i s a problem;
d ) p o l a r i z a t i o n of the mode a t t h e w a i s t does n o t depend on t h e p o s i - t i o n . A s a consequence t h e atoms do n o t s e e a change i n t h e d i r e c - t i o n of t h e magnetic f i e l d a s t h e y f l y a c r o s s t h e c a v i t y . The po- l a r i z a t i o n can be imposed and i t a p p e a r s most convenient t o chose i t a l o n g t h e beam s o t h a t t h e C - f i e l d can be e x c i t e d by a s o l e n o i d .
Two-cavities h o r i z o n t a l beam
A s k e t c h of t h e proposed scheme is shown i n f i g . 3. A v e r t i c a l r i b b o n C s bean i s d e f i n e d by beam s t o p s ( n o t shown) and d i r e c t e d h o r i - z o n t a l l y t o p a s s t h r o u g h two e q u a l Fabry-Perot r e s o n a t o r s , a t a d i s - t a n c e I,, a t t h e i r mode w a i s t , which h a s a e'? d i a m e t e r 1 and i s a mag- n e t i c f i e l d a n t i n o d e . G r a v i t y d e f l e c t i o n of t h e slow atoms s u g g e s t s t h e u s e of a v e r t i c a l r i b b o n a s compared t o a h o r i z o n t a l one. A uniform magnetic C - f i e l d i s s u s t a i n e d i n t h e d i r e c t i o n o f t h e beam by a s o l e - n o i d e x t e n d i n g from t h e oven r e e i o n t o t h e d e t e c t i o n r e g i o n , and t h e o p t i c a l pwnpinq scheme d e s c r i b e d above i s adopted a s shown.
Very h i g h v a l u e s of s i g n a l - t o - n o i s e r a t i o can be o b t a i n e d i n t h i s c o n f i g u r a t i o n . For example S/N h i y h e r t h a n l o 5 should be expected i f L = 1 m and 1 - 1 0 cm i n a beam w i t h c r o s s s e c t i o n of 1 by 10 cm, oven t e m p e r a t u r e of about 8 0 0 C and R v e l o c i t y window of +25$ around 120 r/s.
A f i g u r e of m e r i t F [12] i n e x c e s s of 1000 would r e s u l t and one covld a f f o r d t o lower t h i s i n excha,nge f o r a c c u r a c y improvement v i a r e d u c t i o n of a v e r a g e c a v l t y - p h e s e - d i f f e r e n c e , by use of v e r y t h i n r i b b o n beams, and/or r e d u c t i o n of atomic v e l o c i t y r e l a t e d e f f e c t s by microwave
s t r o b i n g v e l o c i t y window n a r r o l ~ i n g . A r i b b o n beam t h i c k n e s s of 1 rnm would reduce S/N (and F ) by a f a c t o r o f m and r e d u c e t h e c a v i t y phase s h i f t below t h e 10-14 l e v e l .
An e f f e c t i v e v e l o c i t y window of 2 276, which i s o b t a i n a b l e by p u l s e d o p e r a t i o n [7], would a l s o reduce s/N by a f a c t o r of a b o u t m i and would r e s u l t i n a r e s i d u a l u n c e r t a i n t y I n the d e t e r m i n a t i o n of t h e second-order-Doppler s h i f t below 10-14. However t h e need t o spend t h e e x c e s s of S/N f o r r e d u c i n g b o t h c a v i t y - p h a s e - s h i f t and second-order- Doppler u n c e r t a i n t i e s l i m i t s t h e a b i l i t y of r e d u c i n g b o t h , and does n o t a l l o w t h e s e l e c t i o n of v e r y low v e l o c i t y atoms because of t h e i r e x c e e d i n g l y s m a l l number. V e l o c i t i e s of t h e o r d e r of 60 m / s a p p e a r t o be t h e l o w e s t u s a b l e , and t h e r e s u l t i n g Doppler f r e q u e n c y b i a s i s
2 x 10'14.
Another problem f o r t h i s c o n f i g u r a t i o n i s t h e s y n c h r o n i z a t i o n of t h e two Fabry-Perot c a v i t i e s . This t a s k can be performed w i t h r e c u r - r e n t c a l i b r a t i o n of a n e x t e r n a l p h a s e - d i f f e r e n c e trimmer by t h e beam r e v e r s a l t e c h n i q u e , o r w i t h c o n t i n u o u s s e r v o i n g of t h e same t o t h e p h a s e - d i f f e r e n c e s i g n a l o b t a i n e d from two p a r a l l e l (superimposed) c o u n t e r d i r e c t e d beams [ l j ] ( w i t h open c a v i t i e s t h e s e beams wouldn't need t o i n t e r f e r e s i n c e t h e y c o u l d p a s s t h r o u g h d i f f e r e n t a n t i n o d e s ) . A s a n a l t e r n a t i v e approach t h i s t a s k could be avoided by a v e r a g i n g o u t t h e c a v i t y phase d i f f e r e n c e w i t h t h e two-frequency t e c h n i q u e [14]
and u s i n g t h e Ramsey envelope f o r resonance p a t t e r n ; however a wide v e l o c i t y d i s t r i b u t i o n would t h e n be needed f o r narrowing t h e l a t t e r and i n c r e a s e d u n c e r t a i n t y would r e s u l t f o r t h e second-order-Doppler s h i f t d e t e r m i n a t i o n .
A s a c o n c l u s i o n a f i g u r e of m e r i t Fn/ 100 ( ~ ( ( r ) c 1 0 - ~ ~ / ~ ) and a n accuracy of a few p a r t s i n a r e p r o b a b l y t h e b e s t performances one can e x p e c t from a 1 m l o n g C s beam s t a n d a r d r e a l i z e d w i t h t h i s c o n f i g u r a t i o n ; a l o n g e r l e n g t h may h e l p some, b u t n o t n e c e s s a r i l y much. A s t a b i l i t y a f a c t o r of 10 b e t t e r can i n s t e a d be o b t a i n e d u s i n g t h e vhole beam c r o s s s e c t i o n and v e l o c i t y window i f v e r y h i g h accura- cy i s n o t d e s i r e d .
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Single-Cavity f o u n t a i n
I n t r i n s i c r e d u c t i o n of c a v i t y - p h a s e - s h i f t and second-order-Doppler s h i f t u n c e r t a i n t i e s i n (Cs) atomic beam f r e q u e n c y s t a n d a r d s i s h e r e proposed by t h e a d o p t i o n of a n o p t i c a l l y pilmped s i n g l e - r e s o n a t o r fountaindbeam c o n f i g u r a t i o n . A s k e t c h of t h i s i s shown i n f i g . 4.
F i g . 4 : Scheme of a s i n g l e - c a v i t y ( C S ) f o u n t a i n s t a n d a r d . D e t e c t i o n - n o i s e f r e e c o u n t i n g of t h e atoms a f t e r t h e microwave t r a n s i - t i o n i s made p o s s i b l e by t h e o p t i c a l r e c y c l i n g produced w i t h l a s e r 3 .
I n t h e proposed scheme a wide C s beam i s d i r e c t e d v e r t i c a l l y up and t h e atoms a r e i n t e r r o g a t e d t w i c e , when going up and when coming back down, i n a n open Fabry-Perot r e s o n a t o r . O p t i c a l pumping i s employed f o r s t a t e p r e p a r a t i o n and f o r d e t e c t i o n b e f o r e t h e f i r s t and a f t e r t h e second p a s s t h r o u g h t h e c a v i t y . The atoms d e s c r i b e a p a r a b o l i c t r a j e c - t o r y i n a m a g n e t i c a l l y s h i e l d e d d r i f t chamber i n which a v e r t i c a l mag- n e t i c C - f i e l d i s m a i n t a i n e d by a l o n g s o l e n o i d . V e l o c i t i e s up t o
-1s a r e u s e d i f t h e d r i f t chamber i s h m t a l l while f a s t e r atoms a r e absorbed o r pumped at t h e upper end of t h e tube.
Very l o n g d r i f t t i m e s T and v e r y h i g h Ramsey l i n e s e l e c t i v i t i e s QL can be o b t a i n e d i n t h i s way, a c c o r d i n g t o t h e f o r m u l a s :
l i n e s e l e c t i v i t i e s i n e x c e s s of 101° a r e o b t a i n e d w i t h a n 8 m t a l l f o u n t a i n . A s f o r S/N i t c a n be n o t e d t h a t i f t h e v e l o c i t y d i s t r i b u t i o n i s Maxwellian ( ~ ( v ) & v 3 f o r low v e l o c i t i e s ) t h e t o t a l number n of
where A i s t h e beam c r o s s s e c t i o n and L = vT = 4h i s t h e equivalent d r i f t l e n g t h f o r t h e average v e l o c i t y i n t h e f o u n t a i n .
N o w assuming f o r t h e f o u n t a i n a s i m i l a r v e l o c i t y window (;s+ 25%) t o what 1s u s u a l i n C s beam t u b e s we can compare t h e s i g n a l - t o - n o i s e f o r a f o u n t a i n ( s / N ) ~ ~ o t h e si.onal-to-noise f o r a beam ( S / N ) ~ and w r i t e , from ( 4 ) :
Here t h e f a c t o r of 4 i n t r o d u c e d by o p t i c a l pumping h a s been t a k e n i n t o account and a n a d d i t i o n a l f a c t o r of fi was i n t r o d u c e d because t h e aver- age beam i n t e n s i t y i n a t r a d i t i o n a l beam i s lower of what would come from t h e u n d e f l e c t e d i',laxwellian. I n t r o d u c i n g f o r example i n ( 5 ) t h e num_
b e r s f o r t h e d e s c r i b e d 10 m / s a v e r a g e v e l o c i t y f o u n t a i n and f o r a s m a l l commercial beam t u b e we o b t a i n A ~ / A ~ ? ~ x lo2, h / ~ & 4 0 and ( s / N ) ~ & l o 3 . The r e s u l t i n g f i g u r e of m e r i t f o r t h i s f o u n t a i n s t a n d a r d would t h e n be F-N 2000 and t h e s h o r t term s t a b i l i t y Cr (7) = (3F R)'lc+ 5 x IO-'~/E.
S c a t t e r i n g of slow atoms n e a r t h e oven mouth w i l l o b v i o u s l y o f f s e t t h e s e numbers somev~hat, i n f a c t i t was measured [15] t h a t s i g n i f i c a n t beam i n t e n s i t y r e d u c t i o n w i t h r e s p e c t t o t h e Tfiaxwellian d i s t r i b u t i o n (up t o 50% f o r h i g h s o u r c e p r e s s u r e ) o c c u r s a l r e a d y a t v e l o c i t i e s of t h e o r d e r of 100 m / s f o r C s , b u t , even i f o n l y 1% of t h e atoms were l e f t i n t h e beam w i t h v e l o c i t i e s i n t h e 10 m/s r a n g e , t h e f i g u r e of m e r i t would s t i l l be a b o u t F s 200 and t h e s t a b i l i t y (Y (T) r 5 x 1 0 ' 1 3 / ~ .
Supposing t h a t s c a t t e r i n g d i m i n i s h e s r a p i d l y w i t h t h e d i s t a n c e from t h e s o u r c e and t h a t s m a l l - a n g l e - c o l l i s i o n p h a s e - s h i f t s produce a n unimportant f r e q u e n c y s h i f t (which is t r u e i f t h e atoms a r e i n t e r r o g a t e d f a r enough from t h e o v e n ) , t h e major s o u r c e s of u n c e r t a i n t y i n a C s f o u n t a i n s t a n d a r d a r e a v e r a g e c a v i t y p h a s e - d i f f e r e n c e , second-order- Doppler e f f e c t , a2d g r a v i t a t i o n a l r e d - s h i f t . The c a v i t y - p h a s e - s h i f t u n c e r t a i n t y i s g i v e n by A ~ / C Q ~ , where d-v i s g i v e n by ( 1 ) $ y , and i s determined by t h e i n a c c u r a c y i n t h e beam-defining s l i t s p o s i t i o n . I f vei 10 m/s and $ y < 1 mm t h i s u n c e r t a i n t y i s lower t h a n 10-16.
The second-order-Doppler s h i f t i s of t h e o r d e r of -5 x f o r v &
10 m/s and t h e r e s i d u a l u n c e r t a i n t y i n i t s e v a l u a t i o n can be probably lowered t o t h e l e v e l a f t e r t i m e - o f - f l i g h t measurement of t h e a c - t u a l v e l o c i t y d i s t r i b u t i o n .
The g r a v i t a t i o n a l r e d s h i f t i s g i v e n by -v2/3c2 f o r a n atom d r i f t i n g a l o n g a p a r a b o l i c t r a j e c t o r y w i t h i n i t i a l v e r t i c a l v e l o c i t y v.
For a v e r a g e v e l o c i t y v ~ 10 m / s t h i s i s about -3 x and a g a i n t h e r e s i d u a l u n c e r t a i n t y c a n p r o b a b l y r e a c h t h e I O " ~ l e v e l .
JOURNAL DE PHYSIQUE
Conclusions
-- - -
I n t h i s paper it was shown t h a t t h e use of open c a v i t i e s i n con- j u n c t i o n w i t h o p t i c a l pumping can l e a d t o r e d e s i g n e d C s beam s t a n d a r d s w i t h g r e a t l y improved performances.
Two c o n f i g u r a t i o n s a r e s u g g e s t e d , of which t h e most p r o m i s i n g i n t e r m s of p r o j e c t e d accuracy and s t a b i l i t y a p p e a r s t o be t h e one based on a f o u n t a i n beam.
The r e a l i z a t i o n of t h i s o l d i d e a , which was abandoned i n t h e e a r l y f i f t i e s because t h e signal l e v e l o b t a i n e d w i t h h o t wire d e t e c t o r s was judged i n s u f f i c i e n t , i s h e r e demonstrated t o be p o s s i b l e w i t h t h e use of a n open c a v i t y anA o p t i c a l r e c y c l i n g d e t e c t i o n .
A more complete e v a l u t a t i o n of t h i s proposed c o n f i g u r a t i o n w i l l be g i v e n e l s e w h e r e .
R e f e r e n c e s
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