LASER COOLING OF ATOMS AND ITS APPLICATION IN FREQUENCY STANDARDS

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LASER COOLING OF ATOMS AND ITS APPLICATION IN FREQUENCY STANDARDS

V. Letokhov, V. Minogin

To cite this version:

V. Letokhov, V. Minogin. LASER COOLING OF ATOMS AND ITS APPLICATION IN FREQUENCY STANDARDS. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-347-C8-355.

�10.1051/jphyscol:1981842�. �jpa-00221738�

JOURNAL DE PHYSIQUE

CoZZoque C8, suppZ6ment a u n012, Tome 42, de'cembre 1981 page C8-347

LASER C O O L I N G OF ATOMS AND ITS A P P L I C A T I O N I N FREQUENCY STANDARDS V.S. Letokhov and V.G. Minogin

I n s t i t u t e o f Spectroscopy, U. S . S . R. Academy o f S c i e n c e s , 142092, T r o i t s k , illoscow Region, U. S . S . R.

Abstract.- The r e s u l t s of s t u d i e s i n t o t h e l a s e r c o o l i n g of atoms have been summarized and t h e p o s s i b i l i t i e s of a p p l i c a t i o n of c o l d atoms i n frequency s t a n d a r d s have been considered. It h a s been shown t h a t t h e o p t i c a l frequency s t a n d a r d on t h e b a s i s of l a s e r - c o o l e d atoms Mg, C a o r S r may have t h e long-term s t a b i l i t y of about 10-15.

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

-

T h i s approach h a s culminated i n c a r d i n a l improvement of t h e s t a b i l i - t y and r e p r o d u c i b i l i t y of l a s e r frequency s t a n d a r d s which i n case of t h e He-EJe/CH4 ." ( A = 3 . 3 9 ~ ) s t a n d a r d have achieved t h e v a l u e s of I C 14 and 5.1 o-'~' r e s p e c t i v e l y /6/. F u r t h e r i n c r e a s e i n accuracy of o p t i - c a l frequency s t a n d a r d s i s b a s i c a l l y l i m i t e d by s u c h fundamental e f - f e c t s a s the second-order Doppler s h i f t and t i m e - o f - f l i g h t broade- ning. Por t h e He-Ne/CHO s t a n d a r d , f o r example, t h e frequency s h i f t caused by t h e second-order Doppler e f f e c t a t t h e ambient temperature T = 300 K e q u a l s $3 = (K T / M C ~ ) V = 150 Hz, t h e t i m e - o f - f l i g h t bro- adening, even f o r t h e l a s g r beam d i m a e t e r a s l a r g e a s d=10 cm, h a s a c o n s i d e r a b l e v a l u e A 9 = ( 2 Kg ~ / @ ' / ~ d - ' = 560 Hz.

A r a d i c a l way t o reduce c o n s i d e r a b l y t h e second-order Doppler s h i f t and t i m e - o f - f l i g h t broadening may be t h e deep c o o l i n g of ab- s o r b i n g p a r t i c l e s . According t o t h e above-written formulas, i n c a s e of t h e He-Ne/CH s t a n d a r d , i n o r d e r t o redu t h e second-order Dopp- l e r s h i f t t o t h 8 r e l a t i v e value ~Y/I, = t h e temperature i s t o be d e c r e a s e d down t o

0

and, t o reduce t h e t i m e - o f - f l i g h t broadening t o A ~ / V = l0'I3, i t i s t o be d e c r e a s e d t o t h e v a l u e

if t h e d i a m e t e r of l g s e r beam i s d=lO cm.

Such low t e m p e r a t u r e s of a b s o r b i n g p a r t i c l e s , of c o u r s e , cannot be o b t a i n e d w i t h s t a n d a r d cryogenic techniques. N e v e r t h e l e s s ,

t h e s i t u a t i o n i s n o t t o be considered a s h o p e l e s s because of the e f - f e c t i v e method of l a s e r c o o l i n g of a b s o r b i n g p a r t i c l e s h a s been d i s - covered / 7 - 9 / . T h i s method a l l o w s t o c o o l atoms o r i o n s t o a tempe- r a t u r e 10-3

-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981842

C8-348 JOURNAL DE PHYSIQUE

I n connection w i t h t h e p o s s i b i l i t y t o d e c r e a s e s h a r p l y t h e se- cond-order Doppler s h i f t and time-of-flight broadening i t i s of con- s i d e r a b l e i n t e r e s t t o a n a l i z e t h e use of l a s e r cooled p a r t i c l e s i n o p t i c a l frequency standards. There a r e two p o s s i b i l i t i e s here. One of them io t h e use of an o p t i c a l t r a n s i t i o n i n t h e c o l d i o n s l o c a l i - zed i n a radio-frequency electromagnetic t r a p o r i n a Penning t r a p /11-14/. The second p o s s i b i l i t y i s t h e use of l a s e r - c o o l e d n e u t r a l

atoms which can be l o c a l i z e d i n an o p t i c a l t r a p /15/.

R e a l i z i n g each of t h e s e p o s s i b i l i t i e s p r e s e n t s c e r t a i n prob- lems. It i s q u i t e easy t o l o c a l i z e i o n s m electromagnetic t r a p s , but deep c o o l i n g of i o n s i s p o s s i b l e only f o r s m a l l number of ions.

Because of this i t may be d i f f i c u l t t o o b t a i n s u f f i c i e n t l y s t r o n g feedback s i g n a l in t h e frequency s t a n d a r d based on c o l d l o c a l i z e d ions. Besides, t h e frequency of t h e clock i o n i c t r a n s i t i o n undergoes t h e S t a r k shift due t o both t h e e l e c t r i c f i e l d of t h e t r a p and t h e e l e c t r i c f i e l d s of a d j a c e n t ions. These problems do n o t extend t o c o l d atoms, but t h e p o s s i b i l i t y of t h e i r l o c a l i z a t i o n h a s been s o f a r s u b s t a n t i a t e d only t h e o r e t i c a l l y /15/, and i t i s n o t c l e a r y e t t o what e x t e n t i t i s d i f f i c u l t t o l o c a l i z e atoms experimentally.

lyevertheless, s i n c e i o n i c clock resonance i s undergone t h e in- f l u e n c e of e x t e r n a l p e r t u r b a t i o n s t o a g r e a t e r degree than atomic resonance t h e l a s e r cooled and trapped atoms seem t o be t h e b e s t o b j e c t s f o r frequency standards. From t h i s s t a n d p o i n t , i n t h i s pa- p e r we summarize t h e r e s u l t s of s t u d i e s of atomic c o o l i n g by l a s e r s and analyze g e n e r i c problems which may be encountered i n c r e a t i n g t h e o p t i c a l frequency s t a n d a r d based on cold trapped atoms. The an- a l y s i s shows t h a t u s i n g t h e forbidden o p t i c a l t r a n s i t i o n s of such laser-cooled atoms as IQ 24, Ca40 o r ~r~~ it i s p o s s i b l e t o c r e a t e o p t i c a l frequency standards w i t h l o n g term s t a b i l i t y about ,0-15.

Laser production of c o l d atoms.

-

The g e n e r a l scheme of l a s e r c o o l i n g of atomic beam i s a s f o l l - ows. The beam i s d i r e c t e d c o u n t e r t o t h e l i g h t wave, which frequ- ency r e d - s h i f t e d r e l a t i v e t h e frequency of resonant atomic t r a n s i - t i o n . A t such c o n d i t i o n s t h e atoms d e r i v i n g t h e momentum of absor- bed counter-running photons reduce t h e i r v e l o c i t y and, b e s i d e s , a r e grouped i n a narrow v e l o c i t y ensemble. The e f f e c t of v e l o c i t y gro- uping is due t o t h e f a c t t h a t t h e l i g h t p r e s s u r e f o r c e i s a Loren- t z i a n v e l o c i t y f u n c t i o n and i t d e c e l e r a t e s t h e atoms more e f f e c t i - v e l y a s t h e i r v e l o c i t y n e a r s t h e resonant v e l o c i t y vre,= -(a-'.),)/k, where w i s t h e l a s e r wave frequency, andc), i s t h e a t o m c t r a n s i t i o n frequency. The t y p i c a l deformation of atomic beam v e l o c i t y d i s t r i - b u t i o n v e r s u s t h e t i ~ l e of atomic i r r a d i a t i o n by t h e counter-running wave i s shown i n Fig. I. The detuning fi -- o-o, i s chosen so t h a t t h e resonant v e l o c i t y vr c o i n c i d e s w i t h t h e v e l o c i t y of t h e i n i t i - a l thermal d i s t r i b u t i o n %gximurn: fi = o - w , = -kv,. ^{A s} may be seen from Fig.1, a t such a detuning t h e wave c o o l s a considerable p a r t of atoms.

D e c e l e r a t i o n of atoms and monochromatization of atomic veloci- t i e s cause a cloud of cold atoms t o be formed a t a d e f i n i t e d i s t a n c e

" t u r n from t h e p o i n t of entrance of t h e atomic beam i n t o t h e l a s e r beam (Fig. 2 ) . Near t h e t u r n i n g p o i n t ztum t h e b a s i c f r a c t i o n of

Pig.1. E v o l u t i o n of v e l o c i t y d i s t r i b u t i o n f o r a sodium atomic beam i r r a d i a t e d by t h e counter-running l a s e r 8ave

w i t h i n t e n s i t y 10 W/cm and d e t u n i n g a = -270?, where t h e r e s o n a n t t r a n s i t i o n l i n e h a l f - w i d t h a*. = 2% '5 MHz.

The time u n i t i s 3 . 2 ~ ~ . The l a s e r wave i s i n reso- nance w i t h atomic t r a n s i t i o n 3s-3P (4 = 5890 8 ) .

Fig. 2: Deformation of v e l o c i t y d i s - t r i b u t i o n f o r a calcium atomic beam a s a f u n c t i o n of d e p t h of p r o p a g a t i - on i n t o t h e counter-running l a s e r wave. The l a s e r wave w i t h i n t e n s i t y 0.6 'vV/cm 2 i s i n resonance w i t h t h e t r a n s i t i o n 4s-4P (A= 4226 2). De- t u n i n g L?. = -60r, where T = 2 s 17.4 MHz. The c u r v e s correspond t o t h e c o o r d i n a t e s z=0; 10.4 cm; 209 cm;

418 cm; 836 cm.

atoms a c q u i r e s z e r o v e l o c i t y , and t h e v e l o c i t y d i s t r i b u t i o n width becomes much narrower t h a n t h e i n i t i a l v e l o c i t y w i d t h of t h e beam.

According t o t h e c a l c u l a t ' o n s /16, IT/, a t moderate i n t e n s i t i e s of l i g h t wave 11 1 + 10 iV/cm3 t h e l e n g t h of atomic beam d e c e l e r a t i o n e q u a l s 100 cm, by o r d e r of ma n i t u d e and t h e cloud of c o l d atoms h a s t h e c h a r a c t e r i s t i c s i z e ^N 10-5 cm. The temperature of t h e c o l d atoms n e a r t h e p o i n t zt,, i s determined by t h e value of d e t u n i n g

T = A ~ / K ,

.

P o r Kv, 2 ~ . 1 GHz t h e temperature ~ ~ 0 . 1 K.

The f i r s t s u c c e s s f u l experiments on l a s e r c o o l i n g of atoms were r e a l i z e d a t t h e I n s t i t u t e of Spectroscopy u s i n g sodium atomic beam and cw l a s e r r a d i a t i o n /18/. Recently t h e v e l o c i t y monochromatiza- t i o n of a sodium atomic beam d e c e l e r a t e d by countercnuuzing l a s e r r a d i a t i o n was s t u d i e d /19/. The toms were e x c i t e d by cw dye l a s e r on t h e t r a n s i t i o n 3s-3P ( 3 ~ 5 8 9 0

1).

t h e two-mode l a s e r was used. One l a s e r mode e x c i t e d t h e atoms on t h e t r a n s i t i o n 3SIl2(F=1)

-

-

-

1I L -If L

was recorded w i t h t h e u s e of t h e f l u o r e s c e n c e s i g n a l i n i t i a t e d by a probing t u n a b l e dye l a s e r (Fig.3).

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Big.3: Experimental s e t u p f o r l a s e r Fig. 4: Experimental p r o f i - c o o l i n g of a sodium atomic beam. l e of v e l o c i t y d i s t r i b u t i o n 1

-

-

-

-

ned f r e q u e n c y , 5

-

e q u a l s 2.25 * l o 4 cuds (465 MHz).

Fig.$ shows a t y p i c a l e x p e r i m e n t a l p r o f i l e of v e l o c i t y d i s t r i b u - t i o n f o r a d e c e l e r a t e d beam of Na atoms. T h i s p r o f i l e was produced a t t h e l a s e r beam f r e q u e n c i e s tuned t o t h e maxima

05

.

I n t h e experiments, when a thermal beam w i t h i n i t i a l average ve- l o c i t y of 8 * ? 0 4 cm/s was used t h e s h i f t of t h e v e l o c i t y d i s t r i b u - t i o n m a x i m u m reached 1.5 l o 4 cuds. The width of f i n a l monochroma- t i c v e l o c i t y d i s t r i b u t i o n made up 1/19 of t h e i n i t i a l v e l o c i t y width which corresponded t o t h e r e d u c t i o n of t h e t e m p e r a t u r e of r e l a t i v e atomic motion from 573 K t o 573/(19) 2 = 1.5 K.

Atomic s t o r a a e i n l a s e r f i e l d .

-

i n

The b a s i s of such a n o p t i c a l t r a p a r e d i v e r g e n t counter-running l a s e r beams whose f r e u e n c i e s a r e r e d - s h i f t e d r e l a t i v e t h e atomic t r a n s i t i o n f r e q u e n c y b i g . 5 ) . Because of this t h e l i g h t p r e s s u r e f o r c e a c t i n g on an atom i n o p t i c a l t r a p i s always d i r e c t e d o p p o s i t e t o t h e atomic v e l o c i t y and, b e s i d e s , t h e a b s o l u t e value of t h e f o r c e i n c r e a s e s a s t h e atom r e c e d e s from t h e c e n t r e of t h e t r a p (Fig.5b).

Thus, in the scheme illustrated in Fig.5 the light pressure force performs two functions. First, it provides continuous cooling of the atoms and, second, forms for the atoms a potential well the depth of which is maximal near the centre of the trap.

Fig.5: Schematic diagram of a one- Fig.6: Scheme of a three- dimensional optical trap of cold dimensional trap (a) and atoms (a) and the light pressure the distribution of stored force as a function of atom velo- atoms according to their ve- city for three sections of the locity (b) and coordinate

trap (b) (c).

The quantitative calculations show /15/ that, with the frequen- cy detuning of laser fields optimal .Q = ~ 3 - 0 ~ = - 7 and the beam intensities corresponding to the saturation parameter Grl, a three- dimensional optical trap (Fig.6) can cool the atoms to the tempera- ture

where p is the line half-width of the optical dipole transition excited by laser fields. The spatial distribution of the cold atoms in the trap is the Boltzmannls type

with the width

2~

(g)'-

( 7 ) where b is the laser beam invariant that can be taken to be about

10 cm.

Optical traps do not provide, of course, an infinite conf'ine- ment time. Because of collisions, and first of all, the collisions with the thermal residual particles, the atoms will escape the trap. The characteristic time of coflisional escap dep nds on the residual particle density n l , and with n * = log cm-3, for ex- ample, it equals

C8-352 JOURNAL DE PHYSIQUE

i f i n (8) t h e c o l l i s i o n a l c r e c t i o n between a c o l d atom and a r e s i d u a l p a r t i c l e 6% 1 O-ya&9 and t h e average v e l o c i t y of r e s i - d u a l p a r t i c l e s u t ^n, 104 c d s . The r a t e of atomic escape c o n d i t i o - ned by c o l l i s i o n s i s e s t i m a t e d t o be

no

v

=

-

~ C O ~ L ( 9

For example, w i t h t h e d e n s i t y of c o l d atoms 12, cm-3 and t h e volume of t h e l o c a l i z a t i o n r e g i o n V 1 ~ i - ' ~ - loe5 cm3 t h e r a t e of atomic escape i s (dJT/dt) tolls 10 a t / s . 3

The l o s s of atoms may be a l s o caused by t h e i r escape through t h e boundary of t h e c o n f i n i n g l a s e r f i e l d s i n c e a t t h e l a s e r f i e l d boundary t h e r e i s d e f i n i t e atomic d e n s i t y

and non-zero atomic f l u x

= O d G ,

(11) where i s t h e average v e l o c i t y of c o l d atoms. The r a t e of atomic e s c a p i n g through t h e boundary w i t h t h e a r e a Sg = ~ T G^{can be} ~

found from t h e e x p r e s s i o n

According t o t h e e s t i m a t i o n s , because of a d r a s t i c d e c r e a s e of a t o - mic d e n s i t y towards t h e p e r i p h e r y of t h e t r a p t h e r a t e ( 1 2 ) i s much

lower t h a n t h e c o l l i s i o n a l r a t e (9). F o r example, w i t h t h e l a s e r beam d i a m e t e r s r b n 0 . 3 cm and i s 0 . 0 3 cm, d e n s i t y n , ~ 1 0 ' ~ cm -3 ,

average v e l o c i t y of c o l d atoms .v 10-100 c ~ ~ / s , t h e r a t e of atomic escape through t h e boundary i s (clE/dt)6~10' atoms/s.

Thus, t h e main cause of atomic escape from t h e t r a p i s t h e c o l - l i s i o n s w i t h t h e r e s i d u a l p a r t i c l e s . I n o r d e r t h a t t h e l o s s of atoms be compensated f o r , t h e t r a p should be f e d a d d i t i o n a l l y w i t h c o l d atoms from t h e atomic beam. I n t h i s connection t h e scheme f o r atomic s t o r a g e must comprise b o t h ^8x1 atomic t r a p and a system f o r c o l d atom i n j e c t i o n (Fig.7). The i n t e n s i t y of t h e beam of c o l d atoms i n j e c t e d i n t o t h e t r a p I,, may be s u f f i c i e n t l y low

S t o r e d c o l d atom o p t i c a l frequency s t a n d a r d .

-

112t.

T R A P P E D COOLING

L A S E R W A V E

Pig. 7: General scheme of atomic accumulation, t r a p - ping and s t o r a g e .

of t h e t r a p p i n g l a s e r f i e l d can be e s t i m a t e d from t h e c o n d i t i o n

V / f ^E r ,

-

(13) which means t h a t atomic d i s t r i b u t i o n does n o t d i f f u s e w i t h t h e con- f i n i n g f i e l d o f f . With i. = 3 3m ^{and P = 10 i} 100 c d s , t h e commutation frequency i s t o be f -10 t 1 0 3 ~ ~ .

Table 1 I s o t o p e

~g~~ Ca 40

S t r o n g o p t i c a l t r a n s i t i o n 1 1 1 1 1

3 so-?' p1 4 s0-4'p1 5 so-5 P,

Wavelength, 1 ^{285 2}

Natural line h a l f -width, MHz 39.4 S a t u r a t i o n i n t e n s i t y , -

ifi/ cm 2 0.44 0.06 0.03

Temperature of l a s e r

cooled atoms, K 2 . 1 0 ' ~ 8 * 1 0 - ~ 6 * 1 0 - ~

Weak c l o c k t r a n s i i o n Wavelength,

1

R a d i a t i v e width, H z Doppler h a l f - w i d t h a f t e r

l a s e r cooling, MHz 2.6 8.7 4.9

Second-order Doppler

s h i f t , IIz 5 . 1 0 ' ~ 8 . 1 0 ' ~ 3 * 1 0 - ~

The main f a c t o r s which determine t h e long-term s t a b i l i t y of t h e proposed o p t i c a l s t a n d a r d a r e second-order Doppler s h i f t , time- o f - f l i g h t broadening, c o l l i s i o n a l s h i f t and broadening due t o modu- l a t i o n of t h e c o n f i n i n g l a s e r f i e l d i n t e n s i t y ,

The frequency s h i f t caused by t h e second-order Dop l e r s h i f t a t t h e temperature of s t o r e d atoms i s of t h e o r d e r of 10-9 Hz (Table 1 ) .

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STRONG LASER WAVE FOR OPTICAL COOLING AND TRAPPING

PROBE L A S E R WAVE

Fig.8: Scheme of t h e o p t i c a l t r a n - s i t i o n s s u i t a b l e f o r atomic s t o r a g e and f r e q u e n c y st a- b i l i z a t i o n i n case of ~ a 4 0 i s o - tope.

The t i m e - o f - f l i g h t broadening f o r t h e c o l d atoms s t o c , h a s t i c a - l l y moved i n s i d e t h e t r a p i s a l s o of t h e o r d e r of 10-3 Hz. It may be e s t i m a t e d a s t h e i n v e r s e time of atomic c o o r d i n a t e d i f f u s i - on t o t h e value e q u a l t o t h e probe l a s e r beam d i a m e t e r which should be t a k z n e q u a l t o t h e dimension of t h e s p a t i a l d i s t r i b u t i o n of c o l d atoms r.

The s h i f t due t o t h e c o l l i s i o n s w i t h t h r e s i d u a l p a r t i c l e s , as i t f o l l o w s from ( 8 1 , i s of t h e o r d e r of Hz. The c o l l i s i o n s between c o l d atoms a l s o r e s u l t i n a s h i f t of about 10- HZ ( w i t h no s ~ ~ 1 0 cm-3).

F i n a l l y , t h e broadening caused by i n t e n s i t y modulation i s of

2 3

t h e o r d e r of 10 t o 10 Hz.

Thus, t h e f r e q u e n c y s t a b i l i t y of t h e s t a n d a r d on t h e b a s i s of c o l d s t o r e d atoms w i l l be determined by t h e a c c u r a c y of t y i n g t o t h e s a t u r a t e d a b s o r p t i o n resonance w i t h i t s width l o 2

-

(Table 1 1. I f t h e accuracy of t u n i n g e q u a l s t h e long-term frequency s t a b i l i t y w i l l be about The s h o r t - t e r m frequency s t a b i l i t y w i l l depend e s s e n t i a l l y on t h e signal-to-noise r a t i o re- a l i z e d i n experiments.

I n summary i t i s t o be n o t e d t h a t t h e f r e q u e n c y s t a n d a r d on t h e base of narrow resonance of two-photon a b s o r p t i o n i s an a l t e r - n a t i v e of t h e approach c o n s i d e r e d herewith.

References.

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