WAVE OPTICS WITH COLD NEUTRONS

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WAVE OPTICS WITH COLD NEUTRONS

A. Klein, A. Zeilinger

To cite this version:

A. Klein, A. Zeilinger. WAVE OPTICS WITH COLD NEUTRONS. Journal de Physique Colloques,

1984, 45 (C3), pp.C3-239-C3-242. �10.1051/jphyscol:1984340�. �jpa-00224054�

JOURNAL DE PHYSIQUE

Colloque C3, supplement a u n03, Tome 45, mars 1984 page C3-239

WAVE OPTICS WITH COLD NEUTRONS

A.G. Klein and A. Zeilingerr

School o f P h y s i c s , U n i v e r s i t y o f Melbourne, P a r k v i l l e , 3052, A u s t r a l i a a n d P h y s i c s Department, MIT, Cambridge,

02139, U.S.A.

* p h y s i c s Department, MIT, Cambridge,

02139, U.S.A. a n d A t o m i n s t i t u t d e r d s t e r r e i c h i s c h e U n i v e r s i t a t e n , A-1020 Wien, A u s t r i a

RQsumd - P l u s i e u r s e x p e r Q e n c e s d ' o p t i q u e o n d u l a t o i r e o n t B t B e f f e c t u s e s avec d e s n e u t r o n s d e 20

h L'ILL; p a r exemple d e s f i g u - r e s de F r e s n e l d ' u n bord, d'une f e n t e e t d ' u n e d o u b l e f e n t e a i n s i que l a f o c a l i s a t i o n a v e c d e s rBseaux zones e t l ' i n t e r f 6 r o m e t r i e p a r d i v i s i o n de f r o n t d'onde.

Ces e x p e r i e n c e s s o n t p a s s e e s e n revue e t d i s c u t e e s du p o i n t d e vue d e l e u r s m o t i v a t i o n s e t d e l e u r s f u t u r e s p o s s i b i l i t B s .

A b s t r a c t - V a r i o u s c l a s s i c a l wave o p t i c s e x p e r i m e n t s c a r r i e d o u t w i t h 20 1

n e u t r o n s on t h e H-18 f a c i l i t y a t I.L.L. a r e reviewed, namely F r e s n e l d i f - f r a c t i o n from a s t r a i g h t edge, s i n g l e s l i t and double s l i t ; f o c u s s i n g w i t h zone p l a t e s and i n t e r f e r o m e t r y by wavefront d i v i s i o n .

The m o t i v a t i o n o f t h e above e x p e r i m e n t s i s d i s c u s s e d and f u t u r e e x t e n s i o n s and a p p l i c a t i o n s a r e proposed.

A l o n g o p t i c a l bench b u i l t by G a h l e r , Kalus and 14ampe /1/ was s e t up on t h e c o l d n e u t r o n beam-line H-18 a t t h e High Flux R e a c t o r o f t h e I n s t i t u t Laue-Langevin i n 1979-80 and was o r i g i n a l l y u s e d f o r s e t t i n g a new u p p e r l i m i t o f qn< - 1 . 5 2 1 . 4 x 1 0 - ~ ' e o n t h e c h a r g e o f t h e n e u t r o n . The a p p a r a t u s was s u b s e q u e n t l y used by ~ a h l e r and v a r i o u s c o l l a b o r a t o r s f o r a s e r i e s of wave - o p t i c a l e x p e r i m e n t s which w i l l b e b r i e f l y reviewed h e r e .

The o p t i c a l bench s u p p o r t e d a q u a r t z p r i s m monochromator and a s s o c i a t e d s l i t s w i t h t h e a i d o f which a beam o f 1 5 < X < 30 1( and AX

1 c o u l d b e s e l e c t e d .

e v a c u a t e d f l i g h t p a t h o f 1 0 m , i n two s e c t i o n s o f L

5 m , was followed by a n ex- t r e m e l y w e l l s h i e l d e d d e t e c t o r , i n f r o n t o f which a f i n e s l i t c o u l d b e scanned i n 1

The o v e r a l l l a y o u t i s shown i n F i g . 1. T h i s a p p a r a t u s was found t o be v e r y w e l l s u i t e d f o r F r e s n e l d i f f r a c t i o n s t u d i e s a t A

20 A; t h e c h a r a c t e r i s t i c F r e s n e l l e n g t h was

XL

100 pm.

The d i f f r a c t i o n - t e r n o f a n opaque s t r a i g h t - e d g e was measured by G a h l e r , K l e i n and Z e i l i n g e r

and was found t o be i n e x c e l l e n t agreement w i t h t h e o r y ( F i g . l a ) . From t h i s r e s u l t it was p o s s i b l e t o deduce an upper l i m i t f o r t h e s t r e n g t h of a h y p o t h e t i c a l n o n l i n e a r t e r m i n t h e s c h r 6 d i n g e r e q u a t i o n , o f t h e t y p e proposed by B i a l y n l i c k i - B i r u l a and M y c i e l s k i

Following t h e s u g g e s t i o n o f Shimony 141, a n e u t r o n i n t e r f e r o m e t e r experiment by S h u l l e t a 1 / 5 / p l a c e d a n upper l i m i t of b < 3.4 x 1 0 - l 3 eV on t h e s t r e n g t h of such a term. However, t h e F r e s n e l d i f f r a c t i o n experiment reduced t h i s by a f u r t h e r two o r d e r s o f magnitude. Using t h e same set-up, t h e d i f f r a c t i o n p a t t e r n o f a n a b s o r b i n g w i r e was a l s o measured. A h i g h p r e c i s i o n experiment by Z e i l i n g e r , Gghler, S h u l l and Treimer measured t h e d i f f r a c t i o n p a t t e r n s o f a s i n g l e s l i t and o f a d o u b l e s l i t 1 6 1 . The l a t t e r experiment showed agreement w i t h s t a n d a r d , l i n e a r t h e o r y t o w i t h i n 6 p a r t s i n l o 3 and r e p r e s e n t s t h e most s e r i o u s c h a l l e n g e t o any " h e r e t i c a l " v e r s i o n s o f quantum mechanics, such a s any non- l i n e a r v a r i a n t s o r any o f t h e e v o l u t i o n a r y schemes o f wave p a c k e t r e d u c t i o n / 1 , 8 / .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984340

JOURNAL DE PHYSIQUE

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D i f f r a c t i o n p a t t e r n s o f a) s t r a i g h t edge b) s i n g l e s l i t c ) d o u b l e s l i t .

The v a r i o u s d i f f r a c t i o n p a t t e r n s a r e shown i n F i g . 1 a , b and c .

I n a f u r t h e r a p p l i c a t i o n of F r e s n e l d i f f r a c t i o n , t h e e x p e r i m e n t s o f Kearney e t a 1

and K l e i n e t a 1 / l o / have d e m o n s t r a t e d t h e f o c u s s i n g and imaging of s l o w neu- t r o n s by F r e s n e l zone p l a t e s , Fig. 2 ; b o t h s p h e r i c a l and c y l i n d r i c a l f o c u s s i n g s t r u c t u r e s were found t o work i n a c c o r d w i t h t h e d e s i g n . The zone p l a t e s were manu- f a c t u r e d o n s i l i c o n s u b s t r a t e s by means o f p h o t o - l i t h o g r a p h i c t e c h n i q u e s o f t h e k i n d used i n m i c r o - e l e c t r o n i c s . A l t e r n a t e zones were p l a t e d w i t h a 2.4 u m l a y e r of copper which g i v e s a 180" p h a s e s h i f t f o r n e u t r o n s of 20 a wavelength.

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Following t h e s u c c e s s f u l d e m o n s t r a t i o n of f o c u s s i n g by zone p l a t e s , t h e s p e c i a l con- f i g u r a t i o n shown i n F i g . 3 , which c o r r e s p o n d s t o a s p l i t l e n s , was used by K l e i n e z a 1 /11/ a s a n i n t e r f e r o m e t e r a n a l o g o u s t o t h e B i l l e t experiment i n c l a s s i c a l o p t i c s . T h i s t y p e o f i n t e r f e r o m e t e r , which o p e r a t e s by d i v i s i o n o f t h e wavefront r a t h e r t h a n a m p l i t u d e d i v i s i o n (which is t h e c a s e i n t h e p e r f e c t c r y s t a l i n t e r f e r o - m e t e r s ) s u f f e r s from t h e d i s a d v a n t a g e t h a t w i t h t h e wavelengths a v a i l a b l e t h e sepa- r a t i o n of t h e i n t e r f e r i n g beams was r a t h e r s m a l l , of t h e o r d e r o f a few 100 ym o r l e s s . On t h e o t h e r hand, i t h a s t h e a d v a n t a g e s t h a t i t is s u i t a b l e f o r l o n g wave- l e n g t h s and i s c o n s i d e r a b l y l e s s s e n s i t i v e t o m e c h a n i c a l and t h e r m a l d i s t u r b a n c e s .

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w i t h t h e o r y ( s t r a i g h t l i n e ) . I n s e t : P r i n c i p l e of t h e e x p e r i m e n t .

C3-242 JOURNAL DE PHYSIQUE

A

d o u b l e s l i t i n t e r f e r o m e t e r was u s e d by K l e i n e t a 1 / 1 2 / t o o b s e r v e t h e phase s h i f t induced by t h e motion o f a r e f r a c t i n g medium, i n a n e x p e r i m e n t a n a l o g o u s t o t h e c l a s s i c work of F i z e a u . I n t h i s e x p e r i m e n t , shown s c h e m a t i c a l l y i n Fig. 4 , a q u a r t z p r i s m o f s q u a r e c r o s s - s e c t i o n was r o t a t e d i n t h e two beams b e h i n d t h e s l i t s and t h e r e s u l t a n t f r i n g e s h i f t i n t h e i n t e r f e r e n c e p a t t e r n was determined. The r e s u l t s were found t o be i n good agreement w i t h t h s o r y and c o n s t i t u t e a v e r i f i c a t i o n of t h e t r a n s f o r m a t i o n l a w s obeyed b y t h e

k ) f o u r - v e c t o r f o r de B r o g l i e waves.

A l l t h e above e x p e r i m e n t s may b e s e e n a s v e r i f i c a t i o n s o f quantum mechanical p r i n c i - p l e s and a s tests of non-standard quantum mechanical t h e o r i e s . F u r t h e r e x p e r i m e n t s a l o n g t h e s e l i n e s can be e n v i s a g e d , s h o u l d a long-wavelength beam l i n e become a v a i l - a b l e a g a i n . Among s u c h experiments a r e t h e f o l l o w i n g

e f f e c t s , aimed a t i n v e s t i g a t i n g t h e time-dependent b e h a v i o r of wave-packets, i. e. ,

e x p e r i m e n t s d i r e c t l y i n v o l v i n g t h e time-dependent S c h r 6 d i n g e r e q u a t i o n . b) The Cavendish experiment w i t h n e u t r o n s , i . e . , t h e measurement o f t h e U n i v e r s a l G r a v i t a - t i o n a l c o n s t a n t

by rneans o f a n a c t i v e g r a v i t a t i o n a l mass o t h e r t h a n t h e E a r t h

s e l f . Such a n e x p e r i m e n t , which s h o u l d b e f e a s i b l e w i t h n e u t r o n s of 1 ?, 100 1,

would be t h e f i r s t time t h a t a c t i v e g r a v i t a t i o n a l e f f e c t s produced by o b j e c t s o f l a b o r a t o r y , r a t h e r t h a n cosmic s c a l e , would be observed w i t h e l e m e n t a r y p a r t i c l e s . The f u r t h e r development o f zone p l a t e s a s beam-shaping s t r u c t u r e s would be a s s o c i - a t e d w i t h s u c h e x p e r i m e n t s . Mention s h o u l d be made, f o r example, of t h e p o s s i b i l i t y of p r o d u c i n g condensing l e n s e s which, because o f t h e i r d i s p e r s i v e n a t u r e , could f u n c t i o n a l s o a s monochromators when used i n c o n j u n c t i o n w i t h d e f i n i n g s l i t s p l a c e d a t t h e a p p r o p r i a t e f o c u s . Furthermore, w i t h a l t e r n a t e zones made of f e r r o m a g n e t i c m a t e r i a l , zone p l a t e s c o u l d f u l f i l l t h e r o l e of p o l a r i z e r s as w e l l as monochromators and condensing l e n s e s f o r l o n g wavelength n e u t r o n s .

F i n a l l y , t h e use o f s p l i t - l e n s i n t e r f e r o m e t e r s a t l o n g e r wavelengths c o u l d l e a d t o a new s e t o f e x p e r i m e n t s such a s p r e c i s i o n measurement o f s c a t t e r i n g l e n g t h s a s w e l l as t h e i n v e s t i g a t i o n o f f u r t h e r g r a v i t a t i o n a l , inertia!. and magnetic e f f e c t s . We wish t o acknowledge t h e i n v a l u a b l e c o l l a b o r a t i o n o f 1:r. R. ~ a h l e r i n a l l t h e ex- p e r i m e n t s d e s c r i b e d above, t o e x p r e s s our g r a t i t u d e t o p r o f e s s o r J. Kalus f o r p e r - m i s s i o n t o use h i s a p p a r a t u s and t o P r o f e s s o r C.G. S h u l l f o r a d v i c e and encourage- ment.

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2. ~ g h l e r R, K l e i n A.G., and Z e i l i n g e r A: Phys. Rev. A 3 , 1611, 1981.

3. B i a l y n i c k i - B i r u l a , I. and M y c i e l s k i J: Ann. Phys. N.Y. 100, 62, 1976.

4. Shimony A: Phys. Rev.

0, 394, 1979.

5. S h u l l C . G . , Atwood D.K., A r t h u r J. and Home M.A.

Phys. Rev. L e t t . 44, 765, 1980.

6. Z e i l i n g e r A . , ~ S h l e r R., S h u l l C.G. and Treimer W.

Symp. on Neutron S c a t t e r - i n g , Argonne, A.I.P. Conf. Proc. No. 89, p. 93.

7. P e a r l e P . , : Phys. Rev., D 12, 857, 1976.

8. B a r r e t t a G.P.

Phys. Rev., ( I n p r e s s )

9 . Kearney P.D. , K l e i n A.G. , Opat G . I . and ~ a h l e r R.

Nature 287, 313, 1980.

10. K l e i n A.G., Kearney P.D., Opat G . I . , and ~ g h l e r R.: Phys. L e t t &, 7 1 , 1981.

11. K l e i n A.G. , Kearney P.D., Opat G.

, Cimnino A. and ~ a h l e r R.

Phys. Rev.

L e t t . *, 959, 1981.

12. K l e i n A.G. , Opat G. I . , Cimmino A. , Z e i L i n g e r A. , T r e i m e r W. and ~ g h l e r R.

Phys. Rev. L e t t . 46, 1551, 1981.