OBSERVATION OF OPTICAL RAMSEY FRINGES IN THE 10 µm SPECTRAL REGION USING A SUPERSONIC BEAM OF SF6

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OBSERVATION OF OPTICAL RAMSEY FRINGES IN THE 10 µm SPECTRAL REGION USING A

SUPERSONIC BEAM OF SF6

Ch. Bordé, S. Avrillier, A. van Lerberghe, Ch. Salomon, D. Bassi, G. Scoles

To cite this version:

Ch. Bordé, S. Avrillier, A. van Lerberghe, Ch. Salomon, D. Bassi, et al.. OBSERVATION OF OPTI- CAL RAMSEY FRINGES IN THE 10 µm SPECTRAL REGION USING A SUPERSONIC BEAM OF SF6. Journal de Physique Colloques, 1981, 42 (C8), pp.C8-15-C8-19. �10.1051/jphyscol:1981802�.

�jpa-00221697�

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Colloque C8, supplément au n°12, Tome 42, décembre 1981 page C8-15

OBSERVATION OF OPTICAL RAMSEY FRINGES IN THE 10 W SPECTRAL REGION USING A SUPERSONIC BEAM OF SF, '(*)

6

Ch. J. Bordé, S. Avrillier, A. Van Lerberghe, Ch. Salomon, D. Bassi (**) and G. Scoles (**) (+)

Laboratoire de Physique des Lasers (Associé au C.N.R.S., L.A. 282), Université Paris-Nord, Avenue J.B. Clément, 93430 Villetaneuse, France

(**)Istituto per la Riaevaa Soient-ifioa e Teenoloqioa and Unitd CNR-GNSM, Dvpartimento di Fisiaa, Uwiversitd di- Tvento, 3805 Povo (TN)3 Italia.

Abstract : We report a first observation of optical Ramsey fringes in the 10 ym spectral region using a supersonic seeded beam of 7% SF, in He, illu- minated by a CO laser in spatially-separated field zones. We have used either three standing waves or four travelling waves and obtained highly contrasted fringes with a 23 kHz half-width corresponding to a 5 mm distance between zones.

Laser excitation of the vibrational energy of molecules in a beam can be con- veniently detected with a cryogenic bolometer [1] and a demonstration of this tech- nique in the case of the V_ mode of SF, excited by CO or N„0 lasers has been re- cently given [2] . With this equipment the spatial analog of coherent transient effects such as the Rabi oscillations of the transition probability and the adiaba- tic rapid passage were shown to occur respectively with plane and curved wavefronts.

In an attempt to investigate the potential use of this method for very high resolu- tion spectroscopy and optical frequency standards we have made a preliminary experiment to detect the Ramsey fringes associated with saturation spectroscopy in an in- teraction geometry comprising three or four field zones [3-14].

For this experiment we used the P(4) F.. and E components of the v. band of SF, which can be reached with a waveguide CO laser oscillating on the P(16) CO line at 10.55 Van. To control the frequency of this laser we locked it, with a tunable frequency offset, to a conventional reference laser locked to the 0(45) vj. SF, line.

1 b

The beam from the waweguide laser was spatially filtered and magnified to have a waist of w = 6 mm. In the case of illumination by this single beam the resulting width

(FWHM) of the observed line was a combination of transit broadening and residual first-order Doppler effect along the optical axis and amounted to 300 kHz.We used the Rabi oscillation to set the laser beam waist precisely on the molecular beam [2].

Four oscillations of the signal could be observed with a 40% contrast with succes- sive minima obtained for a total power of M,4,9 and 16 mW.

To obtain fringes ,part of the laser beam was intercepted before the interac- tion region by a screen which transmitted the light only through 1 mm wide slits.

Two different geometries were used in these experiments. In the first one, three equidistant standing waves were generated by three equidistant slits of 5 mm sepa- ration together with a corner cube placed on the other side of the molecular beam to

(*)Work supported in part by D.R.E.T.

(+)Permanent address : Physics and Chemistry Department, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981802

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C8-16 JOURNAL DE PHYSIQUE

r e t r o r e f l e c t t h e l i g h t back through t h e s l i t s . I n t h e second geometry, o n l y two of t h e p r e v i o u s s l i t s were i l l u m i n a t e d . An o f f s e t between t h e c e n t e r of t h e s l i t s and t h e c e n t e r of t h e c o r n e r cube generated two counter-propagating s e t s of t r a v e l l i n g waves w i t h a 5 mm d i s t a n c e between a d j a c e n t co-propagating waves of each s e t . The spacing between t h e two s e t s can b e a r b i t r a r y and was a c t u a l l y l O m m i n t h i s experiment. Highly c o n t r a s t e d f r i n g e s have been o b t a i n e d i n both c a s e s and a s an example t h e f i g u r e d i s p l a y s t h e s i g n a l corresponding t o t h e f o u r t r a v e l l i n g waves c a s e . Use of p u r e l y t r a v e l l i n g waves t o o b t a i n o p t i c a l Ramsey f r i n g e s h a s been suggested by t h e a n a l y s i s of r e f e r e n c e s [4-5,101 and we have h e r e a f i r s t demonstration of t h i s p o s s i b i l i t y t o g e t h e r w i t h t h e Ca beam experiment of Helmcke e t a1.[14]

.

^The

broad p e d e s t a l has a w i d t h QJ1.4 MHz corresponding t o t h e t r a n s i t broadening width a c r o s s a s i n g l e zone. The f r i n g e s themselves have a 2 3 kHz width (HTm) c o n s i s t e n t with a QJ930 m/sec peak v e l o c i t y of t h e SF6 molecules 1 1 5 1 .

F i g u r e 1. :

Ramsey p a t t e r n o b t a i n e d f o r P(4)F1 SF6 l i n e w i t h f o u r t r a v e l l i n g waves ( i n t e r a c t i o n geometry i l l u s t r a t e d by t h e i n s e t ) . The h o r i z o n t a l s c a l e i s l i n e a r i n frequency and one f r i n g e period corresponds t o 92.5 kHz. The t o t a l l a s e r power b e f o r e t h e s l i t s was 18 mW. The s i g n a l was recorded i n a s i n g l e one minute sweep w i t h a 0.1 second time c o n s t a n t and a 30 Hz modulation frequency of t h e l a s e r amplitude.

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t h e r p e r t u r b a t i v e c a l c u l a t i o n s u s i n g d e n s i t y m a t r i x diagrams o r numerical t r e a t - ments of t h e d e n s i t y m a t r i x e q u a t i o n s i n t h e s t r o n z f i e l d c a s e [ 4 , s 1

.

Another po- w e r f u l t o o l i s t h e 2x2 m a t r i x f o r m a l i s n p r e s e n t e d a t t h i s conference [ 16

l .

S i n c e i t a p p l i e s v e r y w e l l t o t h e p r e s e n t experiment i t i s worth g i v i n g h e r e a b r i e f o u t l i n e of t h i s t h e o r y .

The e v o l u t i o n o p e r a t o r f o r t h e two-component s p i n o r @ ) d e s c r i b i n g a two-level

system is w r i t t e n : 1

g t , t o )

=zp[1

^t ⁽ ^w

^-

^-)²

r

^{d t l}

t

where H

=(: :

⁾⁺ ^{V ( t )} ^an: ⁼

(z ^:,)

a r e e a s i l y expanded on t h e

a +

b a s i s of t h e P a u l i m a t r i c e s I,o.

The time-ordering o p e r a t o r z n b e ignored e i t h e r i n t h e c a s e of t r a v e l l i n g waves w i t h c o n s t a n t f i e l d s i n each zone o r i n t h e c a s e of s t a n d i n g waves w i t h a r b i - t r a r y t r a n s v e r s e dependence of t h e f i e l d s .

I n t h e f i r s t c a s e t h e i n t e r a c t i o n hamiltonian V ( t ) i s time-independent i n a r o t a t i n g frame ( i f we make t h e r o t a t i n g wave approximation) :

0 exp (+ikz+icp)

exp(~ikz-icp) 0

Zhe e v o l u t i o n o p e r a t o r reduces t o a simple 2x2 m a t r i x :

Q ( t - t ) +i - s i n

]

2

n

²

cos(kz+q), i

K

s i n ( k z + d ,

a

ⁱ^kvz⁺i(yb-ya)/2 f i e l d v e c t o r and w i t h

Yba = (yb + ya)/2 ,

a =.-.

^o ^' ^D ²⁼ ^D⁺²

With f o u r t r a v e l l i n g waves and molecules i n i t i a l l y i n s t a t e a , we o b t a i n t h e f i n a l two-component s p i n o r by simple m u l t i p l i c a t i o n of m a t r i c e s :

where T is t h e t i m e of f l i g h t between t h e f i r s t two and l a s t two f i e l d zones. For t h e s a k e of s i m p l i c i t y we have taken Y = Yb and we have ignored t h e time of f l i g h t between t h e two c e n t r a l zones b u t we have w r i t t e n e x p l i c i t l y t h e change of r o t a t i n g frame between t h e s e two counter-propagating f i e l d s .

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C8-18 JOURNAL DE PHYSIQUE

The p a r t of t h e f i n a l upper l e v e l p o p u l a t i o n r e p r e s e n t i n g t h e f r i n g e p a t t e r n i s simply :

The Doppler phase c a n c e l s o u t because i t r e v e r s e s i n t h e second d a r k zone.

( I t i s easy t o f o l l o w t h e corresponding t r a j e c t o r y of t h e pseudo-spin and t h i s w i l l terms b e i l l u s t r a t e d i n a n o t h e r p a p e r ) . The f a c t o r s m u l t i p l y i n g t h e o s c i l l a t i n ,

expf2iQ T have t o b e n u m e r i c a l l y i n t e g r a t e d over t h e v d i s t r i b u t i o n t o o b t a i n t h e e x a c t &ape of t h e f r i n g e s envelope. Let u s f i n a l l y po%t o u t t h a t when t h e f i e l d phases c a n c e l o u t (which i s t h e c a s e ih our experiment) t h e c e n t r a l f r i n g e c o r r e s - ponds t o a n e g a t i v e c o n t r i b u t i o n .

I n t h e c a s e of standing-waves we cannot completely remove t h e time dependence of t h e i n t e r a c t i o n h a m i l t o n i a n which i s w r i t t e n ( i n t h e r o t a t i n g frame a t UJ and i n t h e molecular frame) :

-+ + V = -UE cos(kz + kv t + cp) U(r + v t ) Ox

where U(r) + i s t h e t r a n s v e r s e dependence of t h e f i e l d i n each zone.

The o n l y p o s s i b i l i t y t o reduce t h e t o t a l h a m i l t o n i a n t o an o p e r a t o r commuting w i t h i t s e l f a t d i f f e r e n t times is t o n e g l e c t t h e u term d u r i n g t h e i n t e r a c t i o n w i t h t h e f i e l d . The e v o l u t i o n o p e r a t o r i s t h e n simsly :

w i t h U ( t ) c o s ( k v z t + kz

+

cp)dt

b

- m

The t i m e e v o l u t i o n of t h e two-component s p i n o r i s a g a i n d e s c r i b e d by t h e pro- duct of m a t r i c e s corresponding t o t h e f i v e zones and t h e f i n a l r e s u l t f o r t h e o s c i l l a t i n g p a r t of bb* h a s t h e f o l l o w i n g form a l r e a d y d e r i v e d by D u b e t s k y [ 6 ] w i t h a d i f f e r e n t approach :

bb* =

f

exp(-2ybaT) c o s 2 a T s i n 2Q3 c o s 2a2 s i n 2a1

This formula d i s p l a y s t h e o s c i l l a t i o n c h a r a c t e r b u t , u n f o r t u n a t e l y , does n o t have t h e s i m p l i c i t y of t h e t r a v e l l i n g wave c a s e s i n c e f u r t h e r i n t e g r a t i o n on b o t h z and v a r e r e q u i r e d t o o b t a i n t h e s i g n a l .

A d e t a i l e d comparison of t h e observed l i n e p r o f i l e s w i t h c a l c u l a t e d ones i s p r e s e n t l y under way. The p r e d i c t e d a p p a r e n t s p l i t t i n g of t h e f r i n g e p a t t e r n i n a s t r o n g f i e l d has been observed i n t h e t h r e e - s l i t experiment and is a l s o being in- v e s t i g a t e d .

We expect now t o b e a b l e t o i n c r e a s e s i g n i f i c a n t l y t h e r e s o l v i n g power w i t h Gaussian zones s e p a r a t e d by much l a r g e r d i s t a n c e s using t h e corner cube techniques

d e s c r i b e d i n [ 1 7 ]

.

L e t us f i n a l l y p o i n t o u t t h a t a major advantage of s u p e r s o n i c beams f o r an o p t i c a l frequency s t a n d a r d i s t h e good monochromaticity i n v e l o c i t y space y i e l d i n g a well-defined second-order Doppler s h i f t .

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