GENERALIZED AHARONOV-BOHM AND WHEELER-TYPE DELAYED CHOICE EXPERIMENTS WITH NEUTRONS

HAL Id: jpa-00224049

https://hal.archives-ouvertes.fr/jpa-00224049

Submitted on 1 Jan 1984

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.

GENERALIZED AHARONOV-BOHM AND WHEELER-TYPE DELAYED CHOICE

EXPERIMENTS WITH NEUTRONS

A. Zeilinger

To cite this version:

A. Zeilinger. GENERALIZED AHARONOV-BOHM AND WHEELER-TYPE DELAYED CHOICE

EXPERIMENTS WITH NEUTRONS. Journal de Physique Colloques, 1984, 45 (C3), pp.C3-213-C3-

216. �10.1051/jphyscol:1984335�. �jpa-00224049�

JOURNAL DE PHYSIQUE

Colloque C3, supplkment a u n03, Tome 45, mars 1984 page C3-213

GENERALIZED AHARONOV-BOHM AND WHEELER-TYPE DELAYED CHOICE EXPERIMENTS WITH NEUTRONS

A. Zeilinger

A t o m i n s t i t u t der Oesterreichischen Universitaeten, Schuettektrasse 115, A -1 020 Wien, A ustda

and Department of Physics, Massachusetts l h s t i t u t e o f Technology, Cambridge, MA 02139, U.S.A.

R@sum&. De nouvelles experiences de'pendantesdutemps d l ' a i d e d ' i n t e r - f 6 r o m 6 t r i e t i n e u t r o n s sont proposBes. E l l e s permettraient de dgmontrer d'une p a r t l e r61e p a r t i c u l i e r que joue l l B n e r g i e p o t e n t i e l l e dans l a mgcanique quantique e t d ' a u t r e p a r t l a compl@rnentarit6dansles phenomenes d ' i n t e r - ference quantique.

Abstract. Novel time-dependent neutron i n t e r f e r o m e t r y experiments a r e pro- posed. These would e l u c i d a t e t h e p e c u l i a r r o l e of p o t e n t i a l energy i n quantum mechanics on t h e one hand and t h e complementarity in quantum i n t e r - f e r e n c e on t h e o t h e r hand.

I - GENERALIZED AHARONOV-BOHM EFFECT

The magnetic Aharonov-Bohm (AB) e f f e c t / I / has found several b e a u t i f u l experimental v e r i f i c a t i o n s /2,3 and r e f s . t h e r e i n / , thus demonstrating t h e p a r t i c u l a r s i g n i f i - cance of t h e vector p o t e n t i a l i n quantum mechanics /4/. In c o n t r a s t , t h e v e r i f i c a - t i o n of t h e e l e c t r i c AB-effect demonstrating t h e r o l e of t h e s c a l a r p o t e n t i a l s t i l l f a c e s considerable problems, because i n such an experiment one would have t o switch a voltage apolied t o a Faraday cage on and off while t h e e l e c t r o n i s i n s i d e . With t h e small beam s e p a r a t i o n of present e l e c t r o n i n t e r f e r o m e t e r s , arranging two s e p a r a t e Faraday cages on t h e two beam paths i s a n o n t r i v i a l problem. Also, due t o t h e high e l e c t r o n speed GHz switching frequencies a r e required. With t h e s e frequen- c i e s , nonequilibrium c u r r e n t s may be non-negligible.

The concept of t h e e l e c t r i c AB-effect can e a s i l y be generalized i f we r e a l i z e , t h a t t h e o p e r a t i o n a l l y s i g n i f i c a n t f e a t u r e of t h a t e f f e c t i s t h e demonstration of phase e f f e c t s i n an i n t e r f e r o m e t e r due t o a time-dependent p o t e n t i a l energy i n t h e Schroedinger equation

where V ( t ) i s chosen such, t h a t t h e only change of t h e wave f u n c t i o n f i n a l l y i s the phase f a c t o r

with a l l o t h e r observables being unchanged. Thus, t h e only way t o d e t e c t experiment- a l l y the presence of V ( t ) i s i n t e r f e r e n c e with an unperturbed beam. This i s q u i t e d i f f e r e n t from a phase s h i f t produced by a s t a t i c p o t e n t i a l . There, besides t h e phase s h i f t a time r e t a r d a t i o n o r advancement of t h e wave packet occurs. Such is not

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984335

C3-2 14 JOURNAL DE PHYSIQUE

the case i n an AB-type s i t u a t i o n , because the phase s h i f t ( 2 ) i s non-dispersive.

Recently, Aharonov / 5 / has proposed "AB-experiments o f t h e second kind", which he i n t e r p r e t s as exchanges o f modular momentum and modular energy.

The i n t e r a c t i o n o f t h e neutron most e a s i l y a c c e s s i b l e t o time-dependent s w i t c h i n g i s t h e magnetic d i p o l e i n t e r a c t i o n V ( t ) = y o . B ( t ) . Thus i t i s proposed here t o apply a time-dependent magnetic f i e l d onto one beam p a t h o f an i n t e r f e r o m e t e r w i t h t h e o t h e r beam path being screened from t h a t f i e l d . I n t h e s i m p l e s t case, t h e time-dependent f i e l d would be switched on t o a constant value a f t e r t h e neutron wave packet entered t h e magnet f i e l d r e g i o n and i t would be switched o f f again b e f o r e i t leaves t h a t region. Therefore, i n t h e i d e a l s i t u a t i o n , the wave packet would n e i t h e r be advanced nor r e t a r d e d / 6 / . I t i s evident, t h a t t h e magnetic f i e l d need n o t be o f constant magnitude w h i l e i t i s on, which might be a h e l p f u l f e a t u r e i n t h e experimental r e a l i - z a t i o n o f t h e e f f e c t .

An i n t e r e s t i n g p o i n t a r i s e s w i t h respect t o t h e p o l a r i z a t i o n o f t h e neutrons used.

I f t h e beams used a r e p o l a r i z e d , they have t o be p o l a r i z e d such t h a t they are i n an e i g e n s t a t e o f t h e magnetic f i e l d . I f such were n o t t h e case, we would have another observable, namely t h e p o l a r i z a t i o n which would c a r r y t h e i n f o r m a t i o n about t h e magnetic f i e l d . This a r i s e s , because the two d i f f e r e n t e i g e n s t a t e s would experience i d e n t i c a l phase s h i f t s , b u t w i t h opposite s i g n which r e s u l t s i n t h e Larmor precession angle a being j u s t t w i c e the phase s h i f t o f Eq. 2. Another p o s s i b i l i t y i s t h e use o f u n p o l a r i z e d neutrons, s i n c e Larmor precession t h e r e leaves t h e d e n s i t y m a t r i x i n - v a r i a n t and thus i s undetectable.

One p o s s i b l e experimental v e r i f i c a t i o n can be done u s i n g t h e Laue-case double- c r y s t a l i n t e r f e r o m e t e r (Fig. 1) i n a way s i m i l a r t o t h a t o f the s p i n o r r o t a t i o n /7/

o r s p i n s u p e r p o s i t i o n /8/ experiments.

F i g . 1: Generalized Aharonov-Bohm experiment u s i n g time-dependent magnetic f i e l d s i n a 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 . The magnetic f i e l d s a r e t o be switched on and o f f w h i l e t h e neutron i s i n t h e magnetic f i e l d region.

The magnetic f i e l d s necessary can e a s i l y be switched f a s t enough, which i m p l i e s s w i t c h i n g i n the MHz frequency range. From the p u r i s t p o i n t o f view a problem i s , t h a t i n such an experiment the d i f f e r e n c e t o s t a t i c f i e l d s can h a r d l y be shown.

This i s t h e p r o p e r t y t h a t such time-dependent f i e l d s do n o t l e a d t o a decrease o f i n t e r f e r e n c e c o n t r a s t , w h i l e s t a t i c ones do. The problem a r i s e s because a magnetic f i e l d t h a t l a r g e t h a t i t s h i f t s t h e wave packet (coherence l e n g t h a 50 - 200 wave l e n g t h s ) f a r enough i n t h e s t a t i c case would be t o o s t r o n g ( a 10 kG) t o be employ- a b l e reasonably i n these experiments.

Such would n o t be the case f o r an experiment w i t h c o l d neutrons analogous t o t h e

d o u b l e - s l i t i n t e r f e r e n c e experiment performed w i t h a 20 1 neutrons a t t h e I L L /9/.

I n t h a t experiment, t h e coherence l e n g t h was o n l y about 6 wavelengths, which i m p l i e s s i g n i f i c a n t l y smaller phase s h i f t s f o r a d e s t r u c t i o n o f i n t e r f e r e n c e c o n t r a s t . Also, i n such an experiment, the s w i t c h i n g can be done s i g n i f i c a n t l y slower due t o t h e lower neutron speed. The r a t h e r small beam separation o f

100 pm makes t h e a p p l i c a - t i o n o f d i f f e r e n t magnetic f i e l d s on the beams r a t h e r d i f f i c u l t . This may be achiev- a b l e using a c u r r e n t sheet (Fig. 2 ) .

; I =

;bC

t

Entrance Exit

Slit Double Slit Slit

Fig. 2: Generalized Aharonov-Bohm experiment employing a c u r r e n t sheet i n a double- s l i t i n t e r f e r o m e t e r f o r c o l d neutrons. The c u r r e n t i s switched on and o f f such t h a t a time s t r u c t u r e f o r t h e magnetic f i e l d r e s u l t s as shown.

Longer wavelength neutrons ( A % 100 a) would imply l a r g e r beam separations and hence t h e a p p l i c a t i o n o f a c u r r e n t sheet should be f a c i l i t a t e d s i g n i f i c a n t l y .

I 1 - DELAYED CHOICE EXPERIMENTS

It i s commonly w e l l known, t h a t t h e i n t e r f e r e n c e p a t t e r n and t h e i n f o r m a t i o n about t h e path o f a p a r t i c l e i n s i d e an i n t e r f e r o m e t e r a r e complementary q u a n t i t i e s . For t h e double s l i t experiment i t has been shown i n t h e famous Bohr-Einstein dialogue / l o / , t h a t i t i s decided by t h e s p e c i f i c p r e p a r a t i o n o f t h e experiment, i.e. t h e double s l i t o r t h e entrance s l i t , which o f the two complementary types o f informa- t i o n are obtained. I t had r e c e n t l y been argued by Wheeler / ? I / , t h a t t h i s d e c i s i o n can be delayed t o times s i g n i f i c a n t l y a f t e r t h e passage o f t h e neutron through t h e double s l i t . I n p a r t i c u l a r , he proposes an experiment, where i n a d o u b l e - s l i t arrangement e i t h e r a d e t e c t o r f o r t h e i n t e r f e r e n c e f r i n g e s o r beam path d e t e c t o r s a r e swung i n p l a c e a t t h e l a s t i n s t a n t .

This experiment would be r e a l i z a b l e u s i n g the d o u b l e - s l i t i n t e r f e r o m e t e r f o r c o l d neutrons mentioned above ( F i g . 3 ) . I t i s proposed here t o p l a c e behind t h e d e t e c t o r s l i t two d e t e c t o r s (e.g. s c i n t i l l a t o r s ) i n c l o s e c o n t a c t o f each other. I f now the d e t e c t o r s l i t i s wide, t h e two beams can pass through i t w i t h o u t s i g n i f i c a n t d i f f r a c - t i o n and w i t h p r o p e r l y a l i g n e d detectors, the f i r i n g o f a given d e t e c t o r provides t h e i n f o r m a t i o n about t h e beam path f o l l o w e d by t h e neutron. But, i n c o n t r a s t , i f t h e d e t e c t o r s l i t i s narrow compared t o t h e w i d t h o f the i n t e r f e r e n c e f r i n g e s , the i n t e r f e r e n c e p a t t e r n can be obtained. D i f f r a c t i o n a t t h a t s l i t now prevents us from o b t a i n i n g any i n f o r m a t i o n about t h e path t h e neutron took. For t h e parameters of the d o u b l e - s l i t experiments a l r e a d y performed /9/ t h e two s l i t w i d t h correspond t o about 100 pm and 20 pm, r e s p e c t i v e l y . The delayed choice s i t u a t i o n i s then r e a l i z e d by s w i t c h i n g from one s l i t w i d t h t o t h e o t h e r w h i l e t h e neutron i s i n f l i g h t between double s l i t and observation screen. I n t h e experiment mentioned t h e time a v a i l a b l e f o r t h a t s w i t c h i n g i s as long as 25 ms. Again, A % 100 a neutrons would imply l o n g e r

f l i g h t times and l a r g e r i n t e r f e r e n c e p a t t e r n s t r u c t u r e s .

JOURNAL DE PHYSIQUE

-;+~f=+ Entrance ^Double Adjustable Width Detectors

Slit Slit Exit Slit

Fig. 3: Experimental setup f o r t h e demonstration o f i n t e r m e d i a t e w a v e - p a r t i c l e behavior u t i l i z i n g a cold-neutron d o u b l e - s l i t i n t e r f e r o m e t e r w i t h an e x i t s l i t o f v a r i a b l e width. The delayed choice s i t u a t i o n r e s u l t s o f t h e s l i t w i d t h i s switched a f t e r passage o f t h e neutron through t h e double s l i t .

Another v e r s i o n o f the delayed choice experiment w i t h a d o u b l e - s l i t setup u t i l i z i n g p o l a r i z e d l i g h t has been proposed 1121. Such an experiment i m p l i e s a very r a p i d s w i t c h i n g o f p o l a r i z e r s . Along the l i n e s o f the r e c e n t s p i n s u p e r p o s i t i o n experiment /8/ one c o u l d i n p r i n c i p l e perform an analogous experiment u s i n g a conventional t h r e e - c r y s t a l i n t e r f e r o m e t e r . I n such an experiment the two o p p o s i t e l y p o l a r i z e d i n t e r f e r o - meter beams w i l l be superimposed i n the same way as i n t h e s p i n s u p e r p o s i t i o n e x p e r i - ment. Measuring now t h e p o l a r i z a t i o n component o f the beam p a r a l l e l t o the z-axis would g i v e i n f o r m a t i o n about t h e path taken i n s i d e t h e i n t e r f e r o m e t e r , w h i l e t h e i n t e r f e r e n c e phenomenon i s r e f l e c t e d i n t h e f a c t , t h a t t h e s u p e r p o s i t i o n o f +z and -z s t a t e s p o i n t s i n a d i r e c t i o n normal t o t h e z-axis. I t i s c l e a r , t h a t t h i s c o u l d e a s i l y be made i n t o a delayed choice experiment by t i m i n g a s p i n - t u r n c o i l i n f r o n t o f t h e analyzer. T h i s experiment i s a l s o a good example o f t h e r e l a t i o n between t h e complementarity o f t h e p a t h i n f o r m a t i o n and t h e i n t e r f e r e n c e p a t t e r n on t h e one hand and the complementarity o f o t h e r q u a n t i t i e s , here t h e s p i n d i r e c t i o n s , on t h e o t h e r hand.

This work was supported by t h e U.S. Department o f Energy, M a t e r i a l s Science D i v i s i o n g r a n t No. DE-AC02-76ER03342.AOIO. I wish t o acknowledge u s e f u l discussions w i t h Profs Y. Aharonov, H.J.Bernstein, D.Greenberger, M.A.Horne, H.Rauch and C.G.Shul1.

References

/I/ AHARONOV Y., 8OHM D., Phys. Rev. 115 (1959) 485.

/2/ BAYH W., Z. Physik 169 (1962) 4 9 2 ,

/3/ TONOMURA A. e t a l . ,Phys. Rev. L e t t . 48 (1982) 1443.

/4/ ZEILINGER A., L e t t . Nuovo C i m . 25 (1979) 333.

/5/ AHARONOV Y., presented a t " I n t - S y m p . on Foundations o f Quantum Mechanics", Tokyo, August 1983, i n press a t Japanese Physical Society.

/6/ BERNSTEIN H.J., ZEILINGER A., Phys. L e t t . 75A (1980) 169.

171 RAUCH H., ZEILINGER A., BADUREK G., W I L F I N ~ . , BAUSPIESS w., BONSE u.,

Phys. L e t t . 54A (1975) 425.

/8/ SUMMHAMMER JTBADUREK G., RAUCH H., KISCHKO U., ZEILINGER A., Phys. Rev. A27

(1983) 2523.

/9/ ZEILINGER A., GKHLER R., SHULL C.G., TREIMER W., i n "Neutron S c a t t e r i n g " , J.Faber (Ed.), AIP Conf. Series 89 (1982) 93.

/10/ JAMMER M., "The Philosophy o f Quantum Mechanics", John Wiley, New York, 1974.

/I!/ WHEELER J.A., i n "Mathematical Foundations o f Quantum Theory", A.P.Marlow ( ~ d . ) , Academic Press, New York, 1978, p. 9.

/12/ BARTELL L.S., Phys. Rev. D21 (1980) 1698.