PROGRESS AND PROSPECTS IN RUBIDIUM FREQUENCY STANDARDS

(1)

HAL Id: jpa-00221711

https://hal.archives-ouvertes.fr/jpa-00221711

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

PROGRESS AND PROSPECTS IN RUBIDIUM FREQUENCY STANDARDS

J. Vanier, R. Kunski, A. Brisson, P. Paulin

To cite this version:

J. Vanier, R. Kunski, A. Brisson, P. Paulin. PROGRESS AND PROSPECTS IN RUBIDIUM FREQUENCY STANDARDS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-139-C8-150.

�10.1051/jphyscol:1981816�. �jpa-00221711�

(2)

JOURNAL DE PHYSIQUE

CoZZoque C8, supple'ment au nol 2, Tome 4 2 , de'cembre 1981 page C8-139

PROGRESS AND PROSPECTS I N R U B I D I U M FREQUENCY STANDARDS

J . Vanier, R. Kunski, A . Brisson and P. P a u l i n

Laboratoire de Recherche sur Zes OsciZZateurs e t S~jstZmes, De'partement de Ge'nie e'Zectrique, Universitd LavaZ, QuLbec G1K 7P4, Canada

ABSTRACT

Recent r e s u l t s which may l e a d t o improvements of t h e p a s s i v e rubidium frequency s t a n d a r d s a r e d i s c u s s e d . The problem of t h e l i g h t s h i f t i s examined i n r e l a t i o n t o t h e h y p e r f i n e f i l t e r i n g technique used. The power s h i f t and t h e b u f f e r g a s s h i f t a r e d i s c u s s e d . R e s u l t s on t h e use of a w a l l c o a t i n g a r e r e p o r t e d . F i n a l l y , t h e f r e - quency s t a b i l i t y r e a l i z a b l e i s examined.

I n t r o d u c t i o n

The p a s s i v e rubidium frequency s t a n d a r d is, among atomic frequency s t a n d a r d s , t h e system t h a t h a s probably r e c e i v e d most a t t e n t i o n . It h a s been t h e s u b j e c t of i n t e n s i v e r e s e a r c h and development. I n f a c t , i t s c h a r a c t e r i s t i c s a r e such t h a t it i s one of t h e most u s e f u l l frequency s t a n d a r d s where s i z e , r e l i a b i l i t y and moderate frequency s t a b i l i t y i s d e s i r e d . Its p r i n c i p a l f i e l d s of a p p l i c a t i o n a r e n a v i g a t i o n , communication and g e n e r a l l a b o r a t o r y use.

S t i l l today t h e r e i s continuous e f f o r t e i t h e r t o reduce i t s s i z e C l 1 o r t o i m - prove i t s c h a r a c t e r i s t i c s C2,31. Various avenues have been seeked i n o r d e r t o a c h i e - v e t h e s e g o a l s . Some of t h o s e have r e s u l t e d i n p r a c t i c a l systems w h i l e o t h e r s have only been s t u d i e d i n t h e l a b o r a t o r y .

I n t h e p r e s e n t paper, we would l i k e t o examine v a r i o u s approaches. We w i l l f i r s t d i s c u s s and compare t h e techniques of s e p a r a t e d and i n t e g r a t e d h y p e r f i n e f i l t e r i n g . I n t h a t f i r s t s e c t i o n , we w i l l cover t h e important q u e s t i o n of t h e l i g h t s h i f t . Se- condly, we w i l l examine t h e t e c h n i q u e s of p u l s e and l a s e r o p t i c a l pumping. T h i r d l y , t h e q u e s t i o n of t h e b u f f e r g a s s h i f t and of t h e i n t e r r o g a t i n g power s h i f t w i l l b e addressed; a l o n g t h e s e l i n e s , r e s u l t s on t h e w a l l c o a t i n g t e c h n i q u e w i l l b e r e p o r t e d . F i n a l l y , t h e frequency s t a b i l i t y r e a l i z a b l e i n p r a c t i c e w i l l b e d i s c u s s e d .

P r i n c i p l e s of o p e r a t i o n

A block diagram of t h e rubidium c l o c k i s shown i n f i g u r e 1. The system i s com- posed e s s e n t i a l l y of an o p t i c a l package g i v i n g a frequency r e f e r e n c e , and a frequency l o c k loop f o r l o c k i n g t h e frequency of a c r y s t a l o s c i l l a t o r t o t h e o p t i c a l packa- g e r e f e r e n c e . The s u p p o r t i n g e l e c t r o n i c s , such a s temperature r e g u l a t o r s , a r e n o t shown i n f i g u r e 1. The o p t i c a l package c o n s i s t s of a ~ b lamp, a ~b~~ h y p e r f i n e * ~ f i l t e r , a ~b~~ a b s o r p t i o n c e l l , a microwave c a v i t y and a p h o t o d e t e c t o r . A solenord i s used t o c r e a t e a weak magnetic f i e l d and a few l a y e r s of c o n c e n t r i c magnetic s h i e l d s a r e used t o a t t e n u a t e t h e e f f e c t of e x t e r n a l magnetic f i e l d f l u c t u a t i o n s .

The system works i n t h e f o l l o w i n g way. Light from t h e rubidium 87 lamp, f i l t e - r e d by t h e rubidium 85 f i l t e r , f a l l s on t h e a b s o r p t i o n c e l l c o n t a i n i n g rubidium 87 and a b u f f e r gas. The lamp c o n s i s t s of a s m a l l g l a s s envelope approximatly 1 cm i n diameter, c o n t a i n i n g about 1 mg of ~b~~ and krypton a t a p r e s s u r e of 2 t o r r . I t i s e x c i t e d by a n o s c i l l a t o r d e l i v e r i n g a power of t h e o r d e r of one w a t t a t a frequency of 100 MHz. It i s heated t o a temperature around 125 ^OC. The spectrum of t h e l i g h t

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981816

(3)

C8-140 JOURNAL DE PHYSIQUE

e m i t t e d by t h e lamp c o n s i s t s mostly of t h e DL and D2 l i n e s c h a r a c t e r i s t i c of a l k a l i atoms. The wavelenghts a r e :

The energy l e v e l s involved i n t h e t r a n s i t i o n s c r e a t i n g t h o s e l i n e s a r e i l l u s t r a t e d i n f i g u r e 2. Each of t h e l i n e s c o n s i s t s of s e v e r a l l i n e s c r e a t e d by t h e h y p e r f i n e s t r u c t u r e of e i t h e r t h e ground s t a t e o r of t h e e x c i t e d s t a t e . The h y p e r f i n e s p l i t - t i n g i n t h e e x c i t e d s t a t e i s n o t l a r g e and i s normally masked by Doppler broadening, which i s of t h e o r d e r of 500 Emz. The h y p e r f i n e s p l i t t i n g of t h e ground s t a t e , however, i s 6.8 GHz and t h e resonance l i n e s a r e w e l l r e s o l v e d . This i s shown i n f i g u - r e s 3a and 3b. These s p e c t r a were obtained w i t h a h i g h r e s o l u t i o n Fabry P e r o t in- t e r f e r o m e t e r .

-Magnetic shield

Oscillator

Synthesizer -M~crowove cavity

€/I Converter Reference sqnal

Phase Sensbtlve

Error signal Resononce signol

F i g u r e 1

-

Block diagram o f t h e p a s s i v e rubidium frequency s t a n d a r d .

L K J IHG

A

F i g u r e 2 - Ground s t a t e and f i r s t e x c i t e d s t a t e of

t h e Fba7 atom. The diagram shows the hyper- f i n e s p l i t t i n g of t h e Dl and D2 l i n e s . The nllmbers i n c i r c l e s a r e the r e l a t i v e t r a n - s i t i o n p r o b a b i l i t i e s .

F i g u r e 3 b - 02 l i n e spectrum o f ~b~~ and -87. f i g u r e 3a - DI l i n e spectrum o f a 8 5 and me7.

The lamp temperature i s 9S°C. The lamp temperature i s 9S°C.

(4)

The e m i t t e d l i g h t i s allowed t o p a s s through t h e f i l t e r c e l l c o n t a i n i n g ~ b ~ ~ and a b u f f e r g a s such a s argon. The spectrum of t h e ~ b ~ ~ atom i s v e r y s i m i l a r t o t h a t of ~ b ~ ~ e x c e p t f o r t h e h y p e r f i n e s p l i t t i n g of t h e ground s t a t e which i s 3 . 0 GHz. An i n d i c a t i o n of t h e p o s i t i o n of t h e s e l i n e s r e l a t i v e t o t h e RbS7 l i n e s i s b e s t observed w i t h a n a t u r a l rubidium lamp. T h i s i s shown i n f i g u r e s 4a and 4b f o r both Dl and D 2 l i n e s . I t i s observed t h a t one of t h e ~ b ~ ~ l i n e s i s almost c o i n c i d e n t with one of t h e ~ b ~ ~ l i n e s f o r both c a s e s of t h e D l and D2 l i n e s . T h i s p r o p e r t y i s e x p l o i t e d f o r f i l t e r i n g t h e ~ b ~ ~ spectrum. The f i l t e r c e l l c o n t a i n s a b u f f e r g a s which s h i f t s t h e ~ b ~ ~ spectrum s l i g h t l y towards t h e r e d and broadens t h e l i n e s C41.

This i n c r e a s e s t h e e f f i c i e n c y of t h e f i l t e r . A p r e s s u r e of t h e o r d e r of 70 t o 90 t o r r of argon appears t o be optimum [5,61. The f i l t e r a b s o r b s s e l e c t i v e l y l i n e s d c and i k g . However, s i n c e t h e a b s o r p t i o n l i n e s a r e a l s o broadened by t h e b u f f e r gas, l i n e s ef a n d ' jkR of ~ b ~ ~ a r e a l s o p a r t l y absorbed by t h e t a i l s of l i n e s EF and JKL of ~ b This h a s t h e e f f e c t of d i s t o r t i n g l i n e s ef ~ ~ . and jkR w i t h consequences t o be d i s c u s s e d below.

Figure 4b - Same a s 3b, b u t f o r Natural Rubidxum.

Figure Same a s 3a, b u t for 172 % ~ b 8 5 and 28 %

Natural

~ 8 7 ) . Rubidium

When t h e r e s u l t i n g l i g h t i s allowed t o f a l l on t h e a b s o r p t i o n c e l l c o n t a i n i n g RbS7, only atoms i n t h e ground s t a t e , which a r e r e s o n a n t w i t h l i n e s ef and jkR a r e a f f e c t e d . A s s e e n i n f i g u r e 2 , t h o s e atoms a r e e x c i t e d t o t h e P s t a t e s . Then, through e i t h e r spontaneous emission o r r e l a x a t i o n by c o l l i s i o n w i t h b u f f e r gas atoms, t h e y f a l l back t o t h e ground s t a t e . S i n c e t h e p r o c e s s of e x c i t a t i o n i s continuously done from t h e lower ground l e v e l , t h e e f f e c t i s t o i n c r e a s e t h e p o p u l a t i o n of t h e l e v e l F = 2 a t t h e expense of t h e p o p u l a t i o n of l e v e l F = 1. The whole pro- c e s s i s c a l l e d "opticaZ pumping" C71 and a p o p u l a t i o n i n v e r s i o n r e s u l t s . By means of t h e pumping i t s e l f t h e c e l l becomes t r a n s p a r e n t t o t h e i n c i d e n t l i g h t . Ho- wever, i f microwave t r a n s i t i o n s a r e e x c i t e d between l e v e l s F = 2 and F = 1, t h e a b s o r p t i o n c e l l becomes more opaque and t h i s e f f e c t is d e t e c t e d a t t h e photodetec- t o r . Thus, a minimum of l i g h t i n t e n s i t y i s observed a t t h e d e t e c t o r when t h e micrc- wave r a d i a t i o n frequency i s c o i n c i d e n t w i t h t h e r e s o n a n t frequency of t h e ground s t a t e of Rb8' given by:

This resonance i s broadened by v a r i o u s mechanisms t o b e d i s c u s s e d below. I n p r a c t i - c e t h e l i n e i s approximatly 500 Hz wide and has a Lorentz shape. This i s represen- t e d i n f i g u r e 5 which d e f i n e s a l s o v a r i o u s o t h e r symbols used i n t h e t e x t . The m i - nimum i n l i g h t t r a n s m i s s i o n i s used a s t h e i n f o r m a t i o n on t h e c o i n c i d e n c e of t h e i n c i d e n t microwave a t frequency vrf and t h e r e s o n a n t frequency vo.

I n o r d e r t o a c h i e v e a p r a c t i c a l d e v i c e , t h e i n t e r r o g a t i n g frequency a t

vr-

i s modulated a t low frequency and a t a d e p t h s m a l l e r t h a n t h e resonance l i n e width.

The r e s u l t i n g a . c . s i g n a l i s d e t e c t e d w i t h a phase s e n s i t i v e d e t e c t o r (Lock-In) whose o u t p u t i s e s s e n t i a l l y t h e d e r i v a t i v e of t h e a b s p r p t i o n l i n e . This s i g n a l , c a l l e d t h e d i s c r i m i n a t o r p a t t e r n , i s then used t o l o c k t h e frequency of t h e i n t e r r o - g a t i n g microwave o s c i l l a t o r t o t h e ~ b a b s o r p t i o n l i n e . * ~

(5)

C8-142 JOURNAL DE PHYSIQUE

The h y p e r f i n e f i l t e r shown i n f i g u r e 1 and d i s c u s s e d above is o p t i o n a l i n t h e s e n s e t h a t i t can be placed p h y s i c a l l y i n s i d e t h e a b s o r p t i o n c e l l . T h i s l a s t technique i s c a l l e d t h e i n t e g r a t e d f i l t e r approach w h i l e t h e c o n f i g u r a t i o n d e s c r i b e d p r e v i o u s l y i s c a l l e d t h e s e p a r a t e d f i l t e r approach. Both techniques a r e d e s c r i b e d below and t h e i r advantages and d i s a d v a n t a g e s a r e d i s c u s s e d i n d e t a i l .

90

I i..*

4 J 3 A J

3

Figure 5

-

Signal l i n e shape and discriminator Pattern. Various symbols used i n the t e x t are defined i n t h i s fioure.

The above d i s c u s s i o n h a s put emphasis on t h e q u e s t i o n of t h e d e t e c t a b l e s i g n a l . However, v a r i o u s o t h e r phenomena have important e f f e c t s on t h e a c t u a l frequency cha- r a c t e r i s t i c s of t h e s i g n a l . For example, t h e resonance l i n e i s broadened by t h e in- t e r a c t i o n w i t h t h e l i g h t and furthermore, i t s c e n t e r i s d i s p l a c e d by an amount which i s p r o p o r t i o n a l t o t h e l i g h t i n t e n s i t y . The o p e r a t i o n of t h e system r e q u i r e s t h e presence of a s m a l l magnetic f i e l d t o g i v e an a x i s of o r i e n t a t i o n t o t h e atomic en- semble. F i n a l l y , i n o r d e r t o avoid Doppler broadening of t h e microwave t r a n s i t i o n and i n h i b i t r e l a x a t i o n on t h e w a l l of t h e a b s o r p t i o n c e l l , a b u f f e r g a s i s used which c r e a t e s s h i f t s and broadening of t h e resonance l i n e C81.

I s o t o p i c h y p e r f i n e f i l t e r i n g

I n t h e c a s e h y p e r f i n e f i l t e r i n g i s done o u t s i d e t h e a b s o r p t i o n c e l l , i t i s s t a n - dard p r a c t i c e t o u s e pure ~ b i n t h e lamp and i n t h e a b s o r p t i o n c e l l and p u r e Rb8' * ~

i n t h e f i l t e r c e l l . This f i l t e r shapes t h e spectrum of t h e l i g h t i n c i d e n t on t h e a b s o r p t i o n c e l l . T h i s h a s t h e e f f e c t f i r s t of enhancing t h e resonance s i g n a l and secondly of c r e a t i n g a s h i f t of t h e c e n t e r frequency of t h e resonance l i n e . This l a s t e f f e c t i s c a l l e d t h e l i g h t s h i f t C91.

The spectrum of t h e Dl l i n e a t t h e o u t p u t of t h e f i l t e r i s shown i n f i g u r e 6 a s a f u n c t i o n of t h e f i l t e r temperature. The measurements were done w i t h a lamp s l i g h t l y s e l f r e v e r s e d ; t h i s makes v e r y e v i d e n t t h e d i s t o r t i o n i n t r o d u c e d by t h e f i l t e r a b s o r p t i o n . Line "dc" i s h i g h l y d i s t o r t e d a t a l l f i l t e r temperatures. Fur- thermore, i t i s observed t h a t l i n e "fe" i s a l s o absorbed a t high f i l t e r temperature.

The l i g h t s h i f t may b e w r i t t e n :

where I. i s t h e l i g h t i n t e n s i t y a t t h e e n t r a n c e of t h e a b s o r p t i o n c e l l and aI i s given by C101:

(6)

2

x exp

-

^-

2)

⁴^{En2dv dva}

(Av,)

where va i s t h e l i n e c e n t e r frequency of a g i v e n c l a s s of atoms, vo is t h e l i n e c e n t e r frequency of t h e Doppler broadened l i n e , Ava i s t h e n a t u r a l l i n e width, Avo i s t h e Doppler width, oo i s t h e photon a b s o r p t i o n c r o s s s e c t i o n , and J ( v ) i s t h e s p e c t r a l d e n s i t y of t h e i n c i d e n t l i g h t normalized t o u n i t y .

The f i l t e r c a n be used t o make J ( v ) such, t h a t t h e i n t e g r a l v a n i s h . However, s i n c e t h e o p t i c a l pumping i s done by means of both Dl and D 2 l i n e s , i t i s v e r y d i f f i c u l t t o c a l c u l a t e t h e shape of J ( v ) . I t i s t h u s common p r a c t i c e t o r e l y on experimental d a t a . I t i s t h e n p o s s i b l e t o f i n d a f i l t e r temperature to which makes A V ~ S independent of t h e l i g h t i n t e n s i t y 1,. I n such a c a s e , i t i s concluded t h a t t h e l i g h t s h i f t i s z e r o and t h a t a1 = 0. A t y p i c a l r e s u l t i s shown i n f i g u r e 7 where Id i s t h e c u r r e n t a t t h e photo d e t e c t o r developed by t h e i n c i d e n t l i g h t . It is observed t h a t f o r a f i l t e r temperature of t h e o r d e r of 6 5 ' ~ t h e f r e - quency i s independent of t h e l i g h t i n t e n s i t y .

On t h e o t h e r hand, i f t h e frequency i s p l o t t e d a s a f u n c t i o n of f i l t e r tempera- t u r e a t c o n s t a n t i n p u t l i g h t i n t e n s i t y , a graph such a s t h e one shown i n f i g u r e 8 i s o b t a i n e d . This behaviour can b e explained i n t h e following manner.

Figure 6

-

I n f l u e n c e o f t h e f i l t e r on t h e Rb87 lamp.

tr i s t h e f i l t e r temperature.

10 I d [,A]

LIGHT INTENSITY (at the detector)

Figure 8

-

V a r i a t i o n of t h e rubidium resonance frequency vr a s a f u n c t i o n o f t h e f i l t e r c e l l t e m p e r a t u r e , t ~ . The absorption c e l l temperature is 6SeC while t h e lamp tempe- r a t u r e is 125'C. Vs is the s i g n a l m p l i - rude a t t h e peak o f t h e d e r i v a t i v e .

F i g u r e 7 - V a r i a t i o n of t h e rubidium resonance frequency vr a s a f u n c t i o n o f l i g h t i n t e n s i t y It a s measured a t t h e photo- v o l t a i c d e t e c t o r . The parameter 1 s t h e f i l t e r temperature t ~ .

(7)

C8- 1 44 JOURNAL DE PHYSIQUE

The l i g h t s h i f t i s c r e a t e d by a d i s t o r t i o n of t h e pumping l i n e s . I f t h e f i l t e r t e m p e r a t u r e i s i n c r e a s e d above t o t h e v a l u e o f a 1 i n c r e a s e s i n a b s o l u t e v a l u e . However, h i g h e r f i l t e r t e m p e r a t u r e s c a u s e a d e c r e a s e i n t h e i n t e g r a t e d i n t e n s i t y I.

and a d e c r e a s e i n l i g h t s h i f t . E q u a t i o n (1) f o r a c o n s t a n t f i l t e r t e m p e r a t u r e c a n be w r i t t e n :

We assume t h a t b o t h a 1 and I, a r e l i n e a r f u n c t i o n s of t h e f i l t e r t e m p e r a t u r e :

where to i s t h e t e m p e r a t u r e f o r which A v Q s ( ~ ~ ) = 0, KF i s a c o n s t a n t g i v i n g t h e r e l a t i v e change i n t h e a m p l i t u d e I. w i t h t h e f i l t e r t e m p e r a t u r e . The l i g h t s h i f t can t h u s b e e x p r e s s e d a s :

where

Bpo

i s d e f i n e d a s :

The dependence of AVQS upon t~ h a s a s l o p e g i v e n by:

At t~ = to,

aFo

^{i s}t h e f i l t e r c e l l t e m p e r a t u r e c o e f f i c i e n t . I n p r a c t i c e i t i s negative. T h e r e i s a n extremum a t a t e m p e r a t u r e .

A t y p i c a l e x p e r i m e n t a l r e s u l t i s shown i n f i g u r e 8. It i s observed t h a t _{t o =} 6 6 . 4 O C and t h a t tm4 = 90

'c.

I f o n e wanted

tm

⁺to a r e l a t i v e l y l a r g e KF would b e r e q u i r e d . T h i s means t h a t t h e i n t e n s i t y o f t h e whole spectrum must d e c r e a - s e r a p i d l y w i t h i n c r e a s i n g t e m p e r a t u r e . I t would a l s o a p p e a r t h a t to c o u l d b e va- r i e d by a p r o p e r s h a p i n g of t h e spectrum. Up t o now t h e s e a t t e m p t s h a v e been unsuc- c e s s f u l l .

Consequently, i n t h e s e p a r a t e d f i l t e r a p p r o a c h , i f t h e f i l t e r t e m p e r a t u r e i s s e t such t h a t a 1 = 0, one i s l e f t w i t h a r e s i d u a l t e m p e r a t u r e c o e f f i c i e n t of t h e o r d e r of a few p a r t s i n 1 0 l 0 . O n t h e o t h e r hand, i f t h e f i l t e r t e m p e r a t u r e i s s e t a t a v a l u e t h a t makes t h e f i l t e r t e m p e r a t u r e c o e f f i c i e n t e q u a l t o z e r o , t h e n , t h e f r e - quency i s a s t r o n g f u n c t i o n of t h e l i g h t i n t e n s i t y , which i s n o t v e r y d e s i r a b l e . It i s p o s s i b l e t o overcome t h i s problem by r e d u c i n g t h e l i g h t i n t e n s i t y . T h i s h a s t h e e f f e c t of r e d u c i n g t h e f i l t e r t e m p e r a t u r e c o e f f i c i e n t a s shown by e q u a t i o n ( 7 ) . Ho- wever, t h e s i g n a l t o n o i s e r a t i o i s a l s o reduced and t h i s r e s u l t s i n a r e d u c t i o n of t h e s h o r t term f r e q u e n c y s t a b i l i t y . The f i l t e r t e m p e r a t u r e c o e f f i c i e n t remains thus a major problem i n t h i s a p p r o a c h .

I n p r a c t i c e , a b u f f e r g a s i s used i n t h e a b s o r p t i o n c e l l . T h i s b u f f e r g a s cau- ses a f r e q u e n c y s h i f t w i t h a n a s s o c i a t e d t e m p e r a t u r e c o e f f i c i e n t . It would t h u s a p p e a r p o s s i b l e t o a d j u s t t h i s c o e f f i c i e n t t o c a n c e l 1 t h e f i l t e r c e l l t e m p e r a t u r e c o e f f l c i e n t

.

I n p r a c t i c e , t h i s c a n b e done b e s t by i n t e g r a t i n g t h e h y p e r f i n e f i l t e r i n t o t h e a b s o r p t i o n c e l l . A t y p i c a l r e s u l t o b t a i n e d u s i n g t h i s a p p r o a c h i s shown i n f i g u r e 9 where t h e c e l l f r e q u e n c y i s p l o t t e d a s a f u n c t i o n of l i g h t i n t e n s i t y . The parameter

(8)

i s t h e c e l l temperature. The c e l l c o n t a i n s 9 . 5 t o r r of n i t r o g e n and n a t u r a l r u b i - dium whose i s o t o p e r a t i o i s

The lamp c o n t a i n s 2 t o r r of krypton and rubidium w i t h an i s o t o p i c r a t i o of

[6,834,687,000+]

I , * mox.

cell 5102 lomp L1

590&

Figure 9

-

Integrated f i l t e r approach. Variation o f 7 0 80 t.['C] 90

-

the rubidium resonance frequency with the CELL TEMPERATURE

l i g h t i n t e n s i t y . The absorption c e l l tempe- Figure 10 - Integrated f i l t e r approach. Variation o f

r a t m e T, i s the parameter. the rubidium resonance frequency with t h e

c e l l temperature TC. The l i g h t i n t e n s i t i e s indicated correspond t o f i x e d i n t e n s i t i e s s e t by neutral density f i l t e r s .

I t i s seen t h a t a z e r o l i g h t s h i f t e x i s t s i n t h a t c a s e f o r a c e l l temperature of 75 ^OC. A t a l i g h t i n t e n s i t y of 85% of t h e maximum a v a i l a b l e i n t h e p r e s e n t system, t h e frequency i s independent of t h e c e l l temperature. T h i s i s w e l l i l l u s t r a t e d i n f i g u r e 10 where t h e frequency i s p l o t t e d a s a f u n c t i o n of c e l l temperature f o r va- r i o u s l i g h t i n t e n s i t i e s . From t h e s e two graphs i t i s concluded t h a t t h e b u f f e r g a s p r e s s u r e , t h e l i g h t i n t e n s i t y and t h e temperature of o p e r a t i o n a r e i n t e r d e p e n d e n t and cannot b e chosen a r b i t r a r i l y i f z e r o l i g h t s h i f t and z e r o temperature c o e f f i - c i e n t s a r e d e s i r e d .

I n p r a c t i c e , it i s a l s o found t h a t t h e frequency i s independent of t h e r . f . power l e v e l a t t h e lamp, f o r n e a r l y t h e same c o n d i t i o n s a s t h o s e which make t h e f r e - quency independent of t h e l i g h t i n t e n s i t y . However, t h i s i s n o t t r u e of t h e lamp temperature. I n f a c t , i t i s found t h a t a r e s i d u a l lamp temperature c o e f f i c i e n t of s e v e r a l p a r t s i n p e r ^OCremains when t h e c e l l temperature i s s e t a t a v a l u e such a s t o make t h e frequency independent of l i g h t i n t e n s i t y . This i s g e n e r a l l y ex- p l a i n e d by t h e f a c t t h a t changes i n lamp t e m p e r a t u r e s c a u s e changes i n r e l a t i v e in- t e n s i t i e s of t h e v a r i o u s pumping l i n e s .

From t h e above d i s c u s s i o n , i t i s t h u s observed t h a t both t h e s e p a r a t e d and t h e i n t e g r a t e d f i l t e r approach show 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 s b u t a l s o show disadvan- t a g e s . The main disadvantage of t h e s e p a r a t e d h y p e r f i n e f i l t e r approach i s t h e f i l - t e r temperature c o e f f i c i e n t . I n t h e i n t e g r a t e d f i l t e r approach one r e l i e s on t h e c a n c e l l a t i o n of s e v e r a l l a r g e e f f e c t s which a r e d i f f i c u l t t o a d j u s t and t h e q u e s t i o n remains a s t o t h e i r s t a b i l i t y w i t h time.

(9)

JOURNAL DE PHYSIQUE

Other o p t i c a l pumping t e c h n i q u e s

Two o t h e r t e c h n i q u e s of pumping have r e c e n t l y r e c e i v e d some a t t e n t i o n .

1 ) P u l s e

---

^pumping. This technique h a s been implemented r e c e n t l y i n a l a b o r a t o r y system C111. I n t h a t t e c h n i q u e t h e o p t i c a l pumping i s done by means of p u l s e s while t h e i n t e r r o g a t i n g r e f . power i s a p p l i e d between t h e l i g h t p u l s e s . I n p r i n c i p l e , t h e r e should n o t b e any l i g h t s h i f t and t h e problem r e l a t e d t o t h e temperature coef- f i c i e n t of t h e f i l t e r c e l l would b e avoided. However, t h e r e could remain a pseudo l i g h t s h i f t C l l l and a dependence of t h e frequency on t h e i n t e r r o g a t i n g power a s w i l l b e d i s c u s s e d below.

2) Laser pumping. With t h e advent of s o l i d s t a t e l a s e r s g i v i n g a n a p p r o p r i a t e wavelength i t h a s been p o s s i b l e t o o p t i c a l l y pump rubidium. Experiments have been r e p o r t e d i n which a GaAs l a s e r was used i n s t e a d of t h e u s u a l rubidium lamp i n a pas- s i v e s t a n d a r d C121. The experiments, a l t h o u g h p r e l i m i n a r y , were most encouraging i n r e s p e c t t o s i g n a l amplitude. However, t h e o u t p u t wavelenght of t h e s e l a s e r s i s v e r y s e n s i t i v e t o temperature. Consequently, t h e a b s o r p t i o n c e l l frequency i s v e r y s e n s i t i v e t o temperature of t h e l a s e r through t h e l i g h t s h i f t , and extreme tempera- t u r e r e g u l a t i o n of t h e l a s e r i s r e q u i r e d .

One approach which a p p e a r s extremely a t t r a c t i v e i s t h a t i n which t h e o p t i c a l pumping i s done w i t h a l a s e r by means of p u l s e s . One would t h e n g a i n i n l i g h t i n t e n s i t y , i n s i g n a l amplitude and i n s i m p l i c i t y of o p e r a t i o n . Furthermore, t h e r e would b e no l i g h t s h i f t and no power s h i f t .

B u f f e r g a s v s w a l l c o a t i n g

I n o r d e r t o reduce Doppler broadening of t h e microwave resonance i t i s s t a n d a r d p r a c t i c e t o f i l l t h e a b s o r p t i o n c e l l w i t h a n i n e r t gas. The g a s must n o t r e a c t che- m i c a l l y w i t h rubidium. Such g a s e s a s , n i t r o g e n , methane and t h e n o b l e g a s e s a r e v e r y s a t i s f a c t o r y i n t h a t r e s p e c t . U n f o r t u n a t l y , t h e y c r e a t e a frequency s h i f t and a broadening of t h e resonance l i n e . Furthermore, t h e frequency s h i f t i s temperature dependent. However, t h e s e s h i f t and temperature c o e f f i c i e n t can b e c o n t r o l l e d by u s i n g m i x t u r e s of b u f f e r g a s e s a t v a r i o u s p r e s s u r e s . A f a i r amount of s t u d i e s has been done i n t h i s f i e l d [13,14] and r e c e n t s t u d i e s have g i v e n some new i n s i g h t s on t h e s u b j e c t

,

s p e c i a l l y i n r e l a t i o n t o t h e non l i n e a r dependence of t h e frequency on t h e temperature of t h e b u f f e r gas.

For a s e a l e d c e l l , an e x p r e s s i o n which d e s c r i b e s w e l l t h e experimental behaviour of t h e frequency i s :

where P i s t h e p r e s s u r e of t h e b u f f e r g a s i n t h e c e l l upon s e a l i n g , fioT i s t h e p r e s s u r e r c o e f f i c i e n t i n Hz p e r t o r r , SOL. i s t h e t e m p e r a t u r e c o e f f i c i e n t I n Hz p e r t o r r p e r K, 'T, i s t h e t e m p e r a t u r e of r e f e r e n c e i n K and AT i s a temperature d i f f e r e n c e r e f e r r e d t o To. I n p r a c t i c e , w i t h pure b u f f e r g a s e s , t h e q u a d r a t i c term i s n o t observed and t h e b u f f e r g a s can be c h a r a c t e r i z e d by t h e l i n e a r c o e f f i c i e n t s a l o n e . The v a l u e s of 6 'and 6 f o r t h r e e connnonly used b u f f e r g a s e s a r e given i n Table I C141.

Table I

These c o e f f i c i e n t s a r e l a r g e enough t o c a u s e problems i n p r a c t i c a l d e v i c e s . For

(10)

example, a c e l l c o n t a i n i n g n i t r o g e n a t a p r e s s u r e of 1 0 t o r r w i l l have a t e m p e r a t u r e c o e f f i c i e n t of 5 . 4 HZ/OC and e x c e s s i v e t e m p e r a t u r e r e g u l a t i o n would b e r e q u i r e d t o a c h i e v e f r a c t i o n a l f r e q u e n c y s t a b i l i t i e s of t h e o r d e r of 10-13. I n p r a c t i c e , two s o l u t i o n s can b e used t o r e d u c e t h e a b s o r p t i o n c e l l t e m p e r a t u r e c o e f f i c i e n t s .

I n t h e s e p a r a t e d f i l t e r c e l l approach, a m i x t u r e of b u f f e r g a s e s w i t h o p p o s i t e t e m p e r a t u r e c o e f f i c i e n t s c a n b e used. I n t h e c a s e of a m i x t u r e of argon and n i t r o - gen, a p r e s s u r e r a t i o of

would g i v e a z e r o t e m p e r a t u r e c o e f f i c i e n t a t 60 OC. However, due t o t h e q u a d r a t i c n a t u r e of e q u a t i o n ( l o ) , t h e behaviour of t h e b u f f e r g a s s h i f t a t o t h e r temperatures w i l l b e g i v e n by:

A t y p i c a l r e s u l t making e x p l i c i t t h e q u a d r a t i c dependence of t h e r e s o n a n c e frequency on t h e c e l l t e m p e r a t u r e i s shown i n f i g u r e 11. I n t h a t c a s e , a m i x t u r e of A r and N2 i n t h e r a t i o r = 0.731 was used. The p r e s s u r e i n t h e c e l l was 25.36 t o r r . A c a l c u l a t i o n made w i t h e q u a t i o n (10) a p p l i e d t o t h a t m i x t u r e would g i v e a s l o p e a t 60 OC, of 0.63 [HZ/OCI and a maximum a t 67.3 OC. The d a t a of f i g u r e 11 g i v e s a s l o - p e a t 60 OC, of 0.96 C H Z / O C I and a maximum a t 74 OC. The d i s c r e p a n c y i s b e l i e v e d t o b e due t o t h e u n c e r t a i n t i e s i n t h e p a r a m e t e r s of t a b l e I and i n u n c e r t a i n t i e s i n t h e p r e s s u r e upon s e a l i n g of t h e c e l l . The t o t a l u f f e r g a s s h i f t a t 60

S

O C was measured as 4979 Hz w h i l e t h e c a l c u l a t i o n gave 5072 Hz.

Figure 11

-

Observed quadratic behaviour of the buffer gas s h i f t i n the case of a mixture of argon and nitrogen.

On t h e o t h e r hand, when a b u f f e r g a s i s used t h e rubidium atoms a r e more o r l e s s f i x e d i n s p a c e d u r i n g t h e t i m e of i n t e r a c t i o n w i t h t h e r . f . f i e l d . T h i s e f f e c t may c a u s e inhomogeneous b r o a d e n i n g of t h e r e s o n a n c e l i n e i f f o r example a non-homoge- neous p e r t u r b a t i o n i s p r e s e n t . The l i g h t s h i f t i s s u c h a p e r t u r b a t i o n s i n c e i t i s n o t i n g e n e r a l c o n s t a n t throughout t h e c e l l . T h i s e f f e c t may c a u s e t h e s o - c a l l e d power s h i f t . T h i s e f f e c t may a l s o b e p r e s e n t i n t h e c a s e of p u l s e pumping i f t h e d i f f u s i o n r a t e of rubidium atoms i s n o t l a r g e enough t o remove s p a t i a l inhomogeneity i n t h e a b s o r p t i o n c e l l .

(*) J. V a n i e r , R. Kunski, J.Y. Savard and M. T s t u , "On t h e p r e s s u r e and t e m p e r a t u r e c o e f f i c i e n t s of b u f f e r g a s e s used i n o p t i c a l l y pumped p a s s i v e rubidium frequen- c y s t a n d a r d s " , t o b e p u b l i s h e d .

(11)

JOURNAL DE PHYSIQUE

Attempts have been made a t avoiding t h i s e f f e c t by removing t h e b u f f e r g a s and l e t t i n g t h e atoms a v e r a g e o u t t h e inhomogeneity. Such a n approach r e q u i r e s t h e u s e of w a l l c o a t i n g . Experimental r e s u l t s have been r e p o r t e d and no power s h i f t was observed C31.

However, t h e w a l l c o a t i n g produces a non n e g l i g i b l e frequency s h i f t i n t h e resonance. T h i s frequency s h i f t , f u r t h e r m o r e , i s temperature s e n s i t i v e . T h i s i s i l l u s - t r a t e d i n f i g u r e 1 2 .

Rbe' Paraflint

Figure 12 - Temperature dependence of the w a l l s h i E t i n a 2 . 5 cm w a l l coated c e l l . P a r a f l i n t i s used a s the w a l l c o a t l n g and the i s o t o p e i s ~ b 8 7 .

-120 ^" ^" ^" ^'

0 $0 20 30 40 50 PC]

TEMPERATURE (T-40°C)

I t should b e p o i n t e d o u t t h a t t h e temperature c o e f f i c i e n t of t h e f i l t e r c e l l i s s t i l l p r e s e n t i n such a n approach. However, due t o t h e p o s i t i v e temperature c o e f f i - c i e n t of t h e w a l l s h i f t i t would b e p o s s i b l e , i n p r i n c i p l e , t o u s e t h e i n t e g r a t e d f i l t e r approach and t o o b t a i n a system w i t h a zero temperature c o e f f i c i e n t , a z e r o l i g h t s h i f t and a z e r o power s h i f t .

Frequency s t a b i l i t y

S h o r t term frequency s t a b i l i t y

...

The s h o r t term s t a b i l i t y of t h e p a s s i v e rubidium frequency s t a n d a r d i s l i m i t e d by t h e l i n e q u a l i t y f a c t o r and by t h e s i g n a l t o n o i s e r a t i o r e a l i z a b l e i n p r a c t i c a l u n i t s . The s h o r t term s t a b i l i t y i s given by C21:

3 3 Frequency domain: S y r ( f ) = 21"9,2

Time domain : U ( T ) =

-

0.2 T-+

Q9, (S/N)

where Q t i s t h e l i n e q u a l i t y f a c t o r measured w i t h a l l broadening m e c h a n i s m s ~ r e s e n t , SIN i s t h e s i g n a l t o n o i s e r a t i o i n a one H e r t z bandwidth and T i s t h e measure- ment time. Low index of modulation i s assumed.

The l i n e Q i s a f u n c t i o n of t h e width of t h e resonance l i n e . I n normal opera- t i n g c o n d i t i o n s i t i s of t h e o r d e r of

l o 7 .

The s i g n a l t o n o i s e r a t i o i s e s s e n t i a l l y determined by t h e s l o p e of t h e d i s c r i m i n a t o r p a t t e r n a s shown i n f i g u r e 5 and by t h e s h o t n o i s e produced a t t h e d e t e c t o r by t h e i n c i d e n t l i g h t . I n g e n e r a l , t h e s i g n a l t o n o i s e r a t i o i n c r e a s e s w i t h l i g h t i n t e n s i t y up t o a p o i n t where l i g h t broadening of t h e resonance l i n e becomes important. I n t h a t c a s e , t h e l i n e Q i s a l s o a f f e c - ted. I n p r a c t i c e , i t i s p o s s i b l e t o o b t a i n a S / N of t h e o r d e r of 75 dB. T h i s g i v e s a s h o r t term s t a b i l i t y

(12)

This i s e s s e n t i a l l y what i s observed i n p r a c t i c a l d e v i c e s .

I n p r a c t i c e , f o r a v e r a g i n g times longer t h a n about 100 seconds i t i s found t h a t u2(,) becomes independent of T

.

^This^{i s}c h a r a c t e r i s t i c of t h e presence of f l i c - k e r frequency n o i s e and i t s o r i g i n i s n o t w e l l understood y e t . I n t h a t r e g i o n one has

(TI = 4 x 10-13 ⁹ (14)

corresponding t o

I n t h e o t h e r hand, t h e long term frequency s t a b i l i t y of t h a t t y p e of frequency standard depends on t h e s t a b i l i t y of a l l t h e b i a s e s examined above. It i s q u i t e c l e a r t h a t s i n c e t h e frequency i s a f u n c t i o n of many parameters, some of them being r a t h e r i m p o r t a n t , one cannot e x p e c t from p r a c t i c a l u n i t s , t h e s t a b i l i t y achieved i n hydro- gen masers o r cesium beam frequency s t a n d a r d s where t h e frequency i s a weak f u n c t i o n of only a few parameters.

Furthermore, i t i s found i n p r a c t i c e t h a t t h e frequency i s a l s o a f u n c t i o n of t h e h i s t o r y of t h e a b s o r p t i o n c e l l . For example, thorough o u t g a s i n g of t h e absorp- t i o n c e l l d u r i n g f a b r i c a t i o n i s of extreme importance, o t h e r w i s e a d r i f t of many H e r t z is observed a t t h e e a r l y s t a g e of o p e r a t i o n . The p r o c e s s e s involved a r e n o t w e l l known a l t h o u g h i t i s b e l i e v e d t h a t a r e a c t i o n of rubidium w i t h i m p u r i t i e s on t h e w a l l of t h e c e l l , g i v i n g s m a l l q u a n t i t i e s of gas, could b e r e s p o n s i b l e f o r t h e observed d r i f t

.

I n p r a c t i c e , i t h a s been found v e r y d i f f i c u l t t o a c h i e v e f r a c t i o n a l frequency s t a b i l i t i e s b e t t e r t h a n 10-'I per month. It i s o n l y through proper s e l e c t i o n of u n i t s t h a t b e t t e r s t a b i l i t i e s a r e r e a l i z e d .

Conclusion

I n t h i s paper, we have examined t h e techniques of s e p a r a t e d and i n t e g r a t e d hy- p e r f i n e f i l t e r i n g . Both methods appear t o have advantages a s w e l l a s d i s a d v a n t a g e s . The s e p a r a t e d h y p e r f i n e f i l t e r approach, however, a p p e a r s t o g i v e more freedom i n t h e s e t t i n g s of v a r i o u s parameters. On t h e o t h e r hand, t h e t e c h n i q u e of p u l s e pumping coupled w i t h t h e u s e of a diode l a s e r a s t h e l i g h t s o u r c e o f f e r s a v e r y i n t e - r e s t i n g a l t e r n a t i v e .

R e l a t i v e t o s h o r t term s t a b i l i t y i t a p p e a r s d i f f i c u l t t o do much b e t t e r w i t h t h e p r e s e n t approaches. A few d e c i b e l s could b e gained i n S / N r a t i o b u t t h i s could probably b e done only a t t h e expense of a l o s s i n l i n e Q o r an i n c r e a s e i n t h e v a r i o u s temperature c o e f f i c i e n t s d i s c u s s e d above. A l o g i c a l c h o i c e of compro- mises has t o be made i n r e l a t i o n t o t h e p a r t i c u l a r a p p l i c a t i o n a t end. . F o r avera- g i n g times l a r g e r t h a n 100 seconds, i t a p p e a r s t h a t f l u c t u a t i o n s of t h e v a r i o u s pa- r a m e t e r s examined above s t a r t t o i n f l u e n c e t h e frequency s t a n d a r d s t a b i l i t y . It i s only through a v e r y c a r e f u l 1 d e s i g n of t h e o p t i c a l package and of t h e e l e c t r o n i c system t h a t a n improvement i n s t a b i l i t y can be expected.

F i n a l l y , t h e e x a c t cause of long term d r i f t i s y e t t o b e known. Although b e t t e r o u t g a s i n g of t h e a b s o r p t i o n c e l l produces l e s s d r i f t , o t h e r c a u s e s of e l e c t r o n i c o r i g i n s cannot b e e n t i r e l y n e g l e c t e d . New approaches u s i n g w a l l coated c e l l s w i t h o u t b u f f e r g a s e s appear t o be v e r y promissing C21.

Acknowledgments

This work has been made p o s s i b l e through t h e sponsorship of t h e f o l l o w i n g agencies : l e MinistSre de l l E d u c a t i o n de l a Province de Qusbec, l e Conseil de

(13)

JOURNAL DE PHYSIQUE

de Recherches en Sciences N a t u r e l l e s e t e n Gdnie du Canada e t l e MinistSre de l a DQfense Nationale du Canada. We would l i k e t o thank M. TStu and J.Y. Savard f o r t h e i r h e l p i n t h e course of t h i s work.

References

[l] H. Fruhauf and W. Weidemann, "Development of a Sub-miniature Rubidium O s c i l l a - t o r f o r SEEKTALK Application", Proceedings of t h e Twelfth Annual P r e c i s e Time and Time I n t e r v a l (PTTI) A p p l i c a t i o n and Planning Meeting, Dec. 1980.

C21 J. Vanier, L.G. B e r n i e r , A. Brisson, M. TStu and J . Y . Savard, " P o s s i b l e Avenues of Improvement of t h e S h o r t and Long Term S t a b i l i t y of O p t i c a l l y Pumped P a s s i v e Rubidium Frequency Standards", Proc. 34th Ann. Freq. Control Symp., p. 376, 1980.

131 A. R i s l e y , S. J a r v i s J r . and J. Vanier, "The Dependence of F r e uency upon M i - crowave Power of Wall-coated and Buffer-gas-filled Gas C e l l Rba7 Frequency Standards", J. Appl. Phys.,

51,

4571, 1980.

C41 F.Y. Chen and M. Takeo, "Broadening and S h i f t of S p e c t r a l Lines Due t o t h e Pre- sence of Foreign Gases", Rev. of Mod. Phys.,

3,

20, 1957.

C53 N. Kuramochi, I. Matsuda and H. Fuku o, "Analysis of t h e E f f e c t of Foreign ga- s e s i n t h e F i t t e r i n g Action of a Rb8% Cell", J. O2t. Soc. Ann.,

E,

1087, 1978.

C61 J.P. Gourber, "Etude e t r b a l i s a t i o n d e deux b t a l o n s d e frLquence 1 vapeur d e rubidium", ThPse, U n i v e r s i t b d e P a r i s , non publibe.

J.P. Gourber, "Horloges atomiques 1 vapeur d e rubidium", Ann. d e R a d i o b l e c t r i - c i t b ,

20,

191, 1965.

C71 A. K a s t l e r , "Les mdthodes o p t i q u e s pour l ' b t u d e d e s rLsonances h e r t z i e n n e s " , Annales d e Phys.,

2,

113, 1967.

[83 J. Vanier, J.F. Simard and J.S. Boulanger, "Relaxation and Frequency S h i f t s i n t h e Ground S t a t e of ~ b ~ ~ " , Phys. Rev. A,

9,

1031, 1974.

C9] J.P. B a r r a t e t C. Cohen-Tannoudji, "Etude du pompage o p t i q u e dans l e fonnalisme d e l a m a t r i c e d e n s i t s " e t "Elargissement e t dgplacement d e s r 9 i e s d e rzsonance magndtique causds p a r une e x c i t a t i o n optique", J. Phys. e t l e Radium,

22,

329

e t 443, 1961.

[10] J. Vanier, "Basic Theory of L a s e r s and Masers", Gordon and Breach, New York, 1971.

[Ill T.C. English, E. J e c h a r t and T.M. Kwon, "Elimination of t h e L i g h t S h i f t i n Ru- bidium Gas C e l l Frequency Standards Using Pulsed O p t i c a l Pumping", Proceedings of t h e Tenth Annual P r e c i s e Time and Time I n t e r v a l (PTTI) A p p l i c a t i o n and Plan- ning Meeting, 147, 1978.

1123 L.L. Lewis and M. Feldman, "Optical Pumping by L a s e r s i n Atomic Frequency Stan- dards", 35th Annual Frequency C o n t r o l Symposium, May 1981.

C131 P.L. Bender, E.C. Beaty and A.R. Chi, "Optical D e t e c t i o n of Narrow Hyper- f i n e Absorption Lines", Phys. Rev. L e t t e r s ,

1,

311-313, 1958.

El41 G. Missout and J. Vanier, "Pressure and Temperature C o e f f i c i e n t s of t h e More Commonly Used Buffer Gases i n Rubidium Vapor Frequency Standards", IEEE Trans.

on I n s t r . and Meas.,

6,

180-184, 1975.

[ I 5 1 V.S. Zholnerov, "Buffer Mixtures f o r t h e Gas C e l l of an O p t i c a l l y Pumped Fre- quency Standard", Opt. S p e c t r o s c . , USSR,

3,

566-568, 1977.