NEUTRON INTERFEROMETRY AND ITS RELATION TO FUNDAMENTAL PHYSICS

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NEUTRON INTERFEROMETRY AND ITS RELATION TO FUNDAMENTAL PHYSICS

H. Rauch

To cite this version:

H. Rauch. NEUTRON INTERFEROMETRY AND ITS RELATION TO FUNDA-

MENTAL PHYSICS. Journal de Physique Colloques, 1984, 45 (C3), pp.C3-197-C3-207.

�10.1051/jphyscol:1984333�. �jpa-00224047�

JOURNAL DE PHYSIQUE

Colloque C3, suppl6ment au n03, Tome 45, mars 1984 page C3-197

NEUTRON INTERFEROMETRY AND ITS RELATION TO FUNDAMENTAL PHYSICS

H. Rauch

Atominstitut der Oesterreichischen Universitaeten, A-1020 Wien, Austria

RESUME

-

D i f f k r e n t e s l o i s fondamentales de l a mgcanique quantique ont 6 t 6 test6es d I ' a i d e d'un i n t e r f 6 r o m e t r e d neutrons, dans l e q u e l des ondes de m a t i e r e cohgrentes completement separees peuvent & r e influencees d'une maniere indgpendante. La v g r i f i c a t i o n e x p l i c i t e de l a symgtrie de 4 ~ des f o n c t i o n s d'onde s p i n o r i e l l e s , de l a l o i de s u p e r p o s i t i o n des spins

-

t a n t s t a t i q u e que dkpendante du temps

-

e t c e l l e de phenomenes v a r i e s l i e s d l a cohgrence des ondes de m a t i e r e sont a u t a n t d'exemples carac- t g r i s t i q u e s .

ABSTRACT

-

Various fundamental laws o f quantum mechanics have been t e s t e d by neutron i n t e r f e r o m e t r y , where w i d e l y separated coherent m a t t e r waves can be i n f l u e n c e d separately. The e x p l i c i t e v e r i f i c a t i o n o f the 4 ~ symmetry o f s p i n o r wave f u n c t i o n s , o f t h e s t a t i c and time dependent s p i n s u p e r p o s i t i o n law and o f various coherence phenomena o f m a t t e r waves are c h a r a c t e r i s t i c a l examples.

I

-

INTRODUCTION

Neutron i n t e r f e r o m e t r y most c l e a r l y demonstrates t h e wave p r o p e r t i e s o f t h e neutron, which e x i s t besides i t s p a r t i c l e p r o p e r t i e s mainly discussed d u r i n g t h i s workshop.

The advent o f p e r f e c t c r y s t a l neutron i n t e r f e r o m e t r y /1,2/ s t r o n g l y motivated r e l a t - ed measurements. W i t h i n t h i s macroscopic quantum device t h e neutron beam becomes s p l i t i n t o two w i d e l y separated coherent beams which can be i n f l u e n c e d separately.

Related measurements d e a l t w i t h t h e v e r i f i c a t i o n o f t h e 4~-symmetry o f s p i n o r wave f u n c t i o n s /3

-

5/, w i t h t h e i n f l u e n c e o f g r a v i t a t i o n a l f o r c e s /6

-

8/ and w i t h t h e coherence p r o p e r t i e s o f m a t t e r waves /9,10/. The r e s u l t s o f t h e f i r s t p e r i o d o f these measurements have been summarized i n the proceedings o f an I L L workshop h e l d i n 1978 /I I/ and more r e c e n t r e s u l t s have been reviewed i n v a r i o u s papers / I 2

-

141.

I n t h i s c o n t r i b u t i o n o n l y very r e c e n t r e s u l t s obtained mainly w i t h the j o i n t Dortmund-Grenoble-Wien i n t e r f e r o m e t e r set-up a t t h e I L L w i l l be discussed. The use o f p o l a r i z e d neutrons and o f a v i b r a t i n g i n t e r f e r o m e t e r p e r m i t new basic experiments concerning spin-superposition /15,16/ and coherence phenomena i n n o n i n e r t i a l systems /17/.

The f e a t u r e s o f the 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 a r e described by t h e dynamical d i f f r a c t i o n theory which gives the s o l u t i o n o f t h e Schrodinger-equation f o r a s t r i c t - l y p e r i o d i c a l p o t e n t i a l /18,19/. A m o n o l i t h i c c u t c r y s t a l ( F i g . 1 ) guarantees t h e coherence o f the s p a c i a l l a t t i c e arrangement over macroscopic distances. A d e t a i l e d t h e o r e t i c a l treatment o f such a system has been given i n /20,21/ and o n l y a few im- p o r t a n t r e s u l t s are needed here. The wave f u n c t i o n behind t h e i n t e r f e r o m e t e r i s com- posed o f wave f u n c t i o n s coming from beam path I and 11. For a p e r f e c t c r y s t a l i n i d e a l geometry and under t h e absence o f any d i s t u r b i n g i n t e r a c t i o n the f o l l o w i n g r e - l a t i o n s e x i s t

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984333

JOURNAL DE PHYSIQUE

Fig. 1: Sketch o f 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

Any k i n d o f i n t e r a c t i o n causes a t l e a s t a phase s h i f t ($:I +

"

e x p ( i f ) ) , which gives a pronounced modulation o f t h e beam

a

ZI+,,I~

(I + c o s n (21

The phase s h i f t f o r nuclear i n t e r a c t i o n reads as x = - ( 1 - n ) k D = - X N b c D

and f o r magnetic i n t e r a c t i o n ++ au

a = - +

-

2 w i t h a = $ i ~ d t : $ f % d s ti

where n i s t h e index o f r e f r a c t i o n , k = 2r/A i s t h e wave number o f neutrons having a wave l e n g t h A, D i s the thickness o f t h e sample, N i s t h e p a r t i c l e density, bc t h e coherent s c a t t e r i n g length,

d

denotes the P a u l i s p i n matrices, p t h e magnetic moment and v t h e v e l o c i t y o f the neutrons. a f o r m a l l y describes t h e Larmor precession angle around t h e magnetic f i e l d

$

along t h e neutron p a t h fds.

Various i m p e r f e c t i o n s o f t h e apparatus, o f t h e phase s h i f t e r and o f t h e beam i t s e l f can reduce t h e c a l c u l a t e d beam modulation. This may be accounted by a v i s i b i l i t y f u n c t i o n d e s c r i b i n g t h e mutual degree o f coherence

which can be determined from t h e i n t e n s i t i e s having b o t h beam path open and a l t e r n a - t i v e l y closed beam paths. I n t h e f o l l o w i n g s e c t i o n s o n l y t h e coherent p a r t o f t h e i n t e n s i t y w i l l be discussed.

I1

-

MEASUREMENT OF THE TRANSVERSAL COHERENCE R. 2

The l o n g i t u d i n a l coherence l e n g t h Ac = X / B A i s d e f i n e d i n t h e same sense than i n l i g h t o p t i c s and i s d i r e c t l y r e l a t e d t o t h e wave l e n g t h spread o f t h e beam. I n co- herence experiments i t causes a l o s s o f c o n t r a s t a t h i g h order, which has been v e r i - f i e d e x p e r i m e n t a l l y /9,10/.

In perfect crystal neutron interferometry the transversal coherence length can be much larger than the longitudinal one because i t i s caused by the mutual and multiple interference of the wave f i e l d s excited within the perfect c r y s t a l slab. This defines the wave function within the Borrmann fan whose width i s given as

at -

2 t . t g OB.

Within t h i s fan the wave function has a complicated amplitude and pkase s t r u c t u r e according t o the Pendelliisung phenomena in dynamical d i f f r a c t i o n theory /18,19/.

This feature manifests i t s e l f in a very narrow central peak of multiple Laue rocking curves /22,23/. The shape of t h i s central peak has been recently calculated f o r the t r i p l e Laue rocking curve /24/

and whose half width i s

which i s in the order of 0.001 sec of a r c . Inserting macroscopic s l i t s (Fig. 2) a broadening of the central peak can be observed, which allows the determination of

Fig. 2: Experimental arrangement and central peak without and with a d i f f r a c t i o n s l i t /25/.

the transversal coherence lengths, which was in t h i s case A, t 2. 6.5 mm /25/. The high angular resolution was achieved by using the small deflection a t prisms within the beams. Similar conclusions about the transversal coherence length can be drawn from the r e s u l t s of two p l a t e interferometry obtained by the M.I.T. group /26/.

I11

-

SPIN SUPERPOSITION

With the use of polarized incident neutrons inversion of the polarization direction i n one coherent beam and superposition of these beams a t the t h i r d crystal plate per- mits the measurement of the quantum mechanical spin superposition law on a macroscop- i c scale. When nuclear

( x )

and magnetic (a) phase s h i f t s a r e applied simultaneously the wave function propagates as /27,28/

C3-200 JOURNAL DE PHYSIQUE

which reduces f o r t h e s i t u a t i o n discussed above and shown i n Fig. 3 t o

Together w i t h t h e undisturbed wave f u n c t i o n o f beam I one o b t a i n s f o r t h e wave func- t i o n s behind the i n t e r f e r o m e t e r

- ^{I+> +}

^eix

^I+>

^{= l o ( l}

⁺

^{U) (10)}

which gives a f i n a l p o l a r i z a t i o n perpendicular t o both p o l a r i z a t i o n s t a t e s before s u p e r p o s i t i o n

V/Z-COIL ON-P C 5 1567

Fig. 3: Experimental arrangement and c h a r a c t e r i s t i c a l r e s u l t s o f t h e s p i n superposi- t i o n experiment /15/.

When a s t a t i c a/2 s p i n t u r n device i n the outgoing beam i s a c t i v a t e d t o r o t a t e t h e y - p o l a r i z a t i o n t o t h e z - d i r e c t i o n which i s the analyzer d i r e c t i o n t h e p o l a r i z a t i o n modulation according t o equation ( 1 1 ) can be observed /15,29/.

An a d d i t i o n a l Larmor precession occurs when the magnetic guide f i e l d Bo a c t s along t h e beam path. This phenomenon i s c l o s e l y r e l a t e d t o t h e s l i g h t d i f f e r e n c e o f t h e k-vectors o f t h e beams behind t h e s p i n r e v e r s a l system. Therefore t h i s experiment demonstrates n o t o n l y t h e quantum mechanical s p i n s u p e r p o s i t i o n behavior b u t a l s o t h a t waves having d i f f e r e n t k-vectors can c o h e r e n t l y o v e r l a p when t h e i r k - v e c t o r d i f f e r e n c e e x a c t l y f i t s t h e c o n d i t i o n f o r Larmor precession (Ak = 2 1 n ~ ~ ~ / . l i ~ k ) .

When a resonance s p i n f l i p p e r i s used i n s t e a d o f t h e s t a t i c f l i p p e r shwon i n Fig. 3 t h e p h y s i c a l s i t u a t i o n changes d r a s t i c a l l y . Now a time dependent i n t e r a c t i o n e x i s t s and t h e r e f o r e t h e time dependent Schrodinger equation has t o be used t o describe t h i s phenomenon. I n t h i s case t h e s p i n r e v e r s a l i s accompanied w i t h an exchange of a

photon having an energy fi = 2 ( p l B 0 between t h e neutron and t h e resonance f l i p p e r /30,31/. This changes t h e F o t a l and p o t e n t i a l energy b u t n o t t h e k i n e t i c energy and therefore n o t the k - v e c t o r o f the neutrons. The wave f u n c t i o n behind the resonance f l i p p e r reads as 1321

and t h e s u p e r p o s i t i o n w i t h t h e undisturbed wave f u n c t i o n o f beam I y i e l d s again a f i n a l p o l a r i z a t i o n i n t h e (xy)-plane which r o t a t e s i n t h i s plane i n phase w i t h t h e f l i p p e r f i e l d

This time dependent r o t a t i o n can be detected by a stroboscopic r e g i s t r a t i o n o f t h e neutrons synchronized w i t h t h e phase o f t h e f l i p p e r f i e l d .

HAGN W S H

POLARIZER MLHmlr.7 COIL

Fig. 4: Experimental arrangement and c h a r a c t e r i s t i c a l r e s u l t s o f t h e time dependent s p i n o r s u p e r p o s i t i o n experiment /16/.

- ,

_-m m ⁰

The parameters o f the experiment (Fig. 4) have been: guide f i e l d Bo 190 G , reso- nance frequency w f / 2 ~ = 55.4 kHz, l e n g t h o f t h e f l i p p e r c o i l 1 cm, i n t e r v a l between r e g i s t e r e d time cKannels 9.03 ms, widths o f time channels 4.51 ms, d i s t a n c e t o t h e d e t e c t o r 25 cm which avoids frame o v e r l a p f o r a neutron beam having a mean wave l e n g t h A. = 1.835

!

and a spread o f 6A/X0 = 0.015.

..'~.'~...,.." . . . ... ."..

^'

.

^'

- spin turn off

The experimental r e s u l t s a l s o agree w i t h t h e t h e o r e t i c a l p r e d i c t i o n s and demonstrate t h a t coherence can even be preserved when a r e a l energy exchange occurs /16/. One might argue t h a t besides the i n t e r f e r e n c e p a t t e r n t h e beam path can be detected by observing the added o r m i s s i n g photon o f t h e resonance c i r c u i t o r by measuring t h e change o f t h e k i n e t i c energy o f t h e neutron behind t h e guide f i e l d where t h e d i f f e r - e n t t o t a l energy i s due t o t h e l o n g i t u d i n a l Stern-Gerlach e f f e c t transformed t o a change o f t h e k i n e t i c energy o f t h e neutrons /33/. But we n o t e t h a t the d e t e c t i o n o f a s i n g l e photon t r a n s i t i o n simultaneously w i t h t h e i n t e r f e r e n c e p a t t e r n i s forbidden by t h e number phase u n c e r t a i n t y r e l a t i o n

C3-202 JOURNAL D E PHYSIQUE

since f o r t h e observation of t h e i n t e r f e r e n c e p a t t e r n the phase i n f o r m a t i o n must be a t l e a s t h a l f a period. This argumentation holds even when more e l a b o r a t e d formula- t i o n s o f the number-phase u n c e r t a i n t y r e l a t i o n s a r e used, which show t h a t coherent s t a t e s need n o t n e c e s s a r i l y minimize t h i s product /34,35/.

One now m i g h t t r y t o g e t t h e i n f o r m a t i o n about t h e path chosen by t h e neutron by measuring the change o f t h e k i n e t i c energy o f these neutrons which passed through t h e resonance f l i p p e r . The r e l a t e d d i f f e r e n c e i n the v e l o c i t y o f t h e neutrons i s

VB /mv /35/. I t can be measured by a t i m e - o f - f l i g h t system placed a t a

=

g

d i s ance R beyond the guide f i e l d r e g i o n when t h e w i d t h o f t h e i n c i d e n t beam i s s m a l l e r t h a n t h i s q u a n t i t y (Av < hvrf). I n o r d e r t o accumulate t h e neutrons w i t h t h e c o r r e c t p o l a r i z a t i o n phase i n t h e c o r r e c t time channels t h e i r widths have t o f u l f i l the c o n d i t i o n A t > AR/Av, whereas these t i m e channels have t o be A t < 2a/wrf t o ob- t a i n t h e i n t e r f e r e n c e p a t t e r n . This runs i n t o c o n f l i c t w i t h t h e momentum-position u n c e r t a i n t y r e l a t i o n AkAR > 1/2.

V

-

PHASE ECHO SYSTEMS

A t a workshop a t I L L h e l d i n 1979 we demonstrated t h a t t h e neutron i n t e r f e r o m e t e r makes phase echo systems f e a s i b l e /36/. This technique i s c l o s e l y r e l a t e d t o s p i n echo systems /37,38/. A dephasing caused by the d i s p e r s i v e a c t i o n o f a n u c l e a r ( x )

and/or a magnetic ( a ) phase s h i f t e r can be recovered by another phase s h i f t e r having an opposite a c t i o n on t h e phase. For a proper treatment one can consider t h e i n t e r - ferometer and the phase s h i f t e r as being p e r f e c t (equations ( 1 ) and ( 2 ) ) b u t one has t o i n c l u d e t h e i m p e r f e c t i o n o f t h e neutron beam. This can be done by d e s c r i b i n g i t i n t h e form o f a wave packet

which can be separated f o r t h e various d i r e c t i o n s . For a s t a t i o n a r y s i t u a t i o n and a Gaussian shaped packets centered around

XO

i t can be w r i t t e n as

where 6k i s t h e standard d e v i a t i o n o f the k - d i s t r i b u t i o n o f t h e beam, which can be obtained independently from a measurement o f t h e momentum d i s t r i b u t i o n o f t h e beam.

According t o the s t r u c t u r e o f equations ( 1 ) and ( 2 ) t h e r e s u l t f o r t h e i n t e n s i t y o r p o l a r i z a t i o n behind t h e i n t e r f e r o m e t e r i s t h e same when u s i n g t h e wave packet r e p r e - s e n t a t i o n s f o r $ o r by averaging t h e plane wave r e s u l t by t h e momentum d i s t r i b u t i o n f u n c t i o n /27/

+- 2

-

^{a ( k ) + -} 2 a ( k ) +

Po Jdk[A(k,ko)l C B s i n x ( k ) s i n T + B(P.B) s i n

7

For t h e simple case a ( k ) ⁵ 0 and u n p o l a r i z e d i n c i d e n t neutrons Pi : 0 we o b t a i n

which represents a r e d u c t i o n o f t h e v i s i b i l i t y a t h i g h orders m = D/Dk =.DNb /k which has been v e r i f i e d by experiments /9,10/ ( F i g . 5 ) . Analogous t o o p t ~ c s t k e long-

i t u d i n a l coherence l e n g t h i s d e f i n e d from t h ' s r e u c t i o n o f t h e v i s i b i l i t y f u n c t i o n

s . = P

o r from t h e momentum d i s t r i b u t i o n f u n c t i o n Ac h /6X = 2n/6k.

+ l rmAl

r l t m G c -

0 1000 b G

% 5 C 500

t

^n=O background

ii---

0 Q2l 2 75

-

^AD(cml

Fig. 5: Observed r e d u c t i o n o f the c o n t r a s t o f t h e i n t e r f e r e n c e p a t t e r n o f a h i g h l y monochromatic beam /9/.

The dephasing e f f e c t o r t h e v i s i b i l i t y f u n c t i o n D g o n l y depends on the n e t phase s h i f t between t h e two beams a t the p l a c e o f superposition. Therefore i t may happen t h a t the wave t r a i n s a t c e r t a i n p o s i t i o n s are l o n g i t u d i n a l l y wider separated than t h e i r coherence length. The complete c o n t r a s t can be recovered when by means o f a second phase s h i f t e r t h e s p i n echo c o n d i t i o n

x l r x z

=

xnet

= 0 i s f u l f i l l e d . There- f o r e a vanishing i n t e r f e r e n c e c o n t r a s t does n o t necessari y i n d i c a t e t h a t t h e beams have l o s t t h e i r coherence. This becomes even more e v i d e n t when a f o u r o r f i v e p l a t e i n t e r f e r o m e t e r i s considered (Fig. 6 ) . I n t h i s case no wave t r a i n o v e r l a p may e x i s t a t t h e t h i r d p l a t e b u t an i n t e r f e r e n c e depending on b o t h phase s h i f t s can be recover- ed afterwards. Recent c a l c u l a t i o n s on t h i s s u b j e c t /39/ y i e l d f o r t h e s i t u a t i o n shown

Fig. 6 : Scheme o f a f i v e p l a t e i n t e r f e r o m e t e r and t h e recovery o f an i n t e r f e r e n c e p a t t e r n .

i n Fig. 6 the i n t e n s i t y behind t h e f i f t h p l a t e

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i s t h e Laue-case p e r f e c t c r y s t a l r e f l e c t i v i t y /18,19/.

Returning t o t h e conventional t r i p l e Laue-case i n t e r f e r o m e t e r more complicated phase echo c o n d i t i o n s can be discussed. I n t h e case o f simultaneous nuclear and magnetic phase s h i f t s equation (17) can be w r i t t e n f o r u n p o l a r i z e d i n c i d e n t neutrons as

which shows t h a t a p a r t i a l compensation o f nuclear and magnetic phase s h i f t s can be achieved and a p a r t i a l recovery o f t h e i n t e r f e r e n c e s i g n a l can be observed (Fig. 7 ) .

+ F i g . 7: Sketch o f various phase echo systems.

Using p o l a r i z e d neutrons a complete phase echo svstem can be achieved even i n t h e case 0% simultaneous n u c l e a r and magnetic phase s h i f t . A d i f f e r e n t s i t u a t i o n e x i s t s when a complete o r p a r t i a l s p i n r e v e r s a l occurs and when t h e magnetic guide f i e l d extends t o t h e p l a c e o f s u p e r p o s i t i o n

(chapter 111). Thus the medium remains phase d i s p e r s i v e behind t h e s p i n t u r n device and t h e k-vectors o f t h e two beams become d i f f e r e n t due t o t h e Zeman s p l i t t i n g kot = k O ( l

;

pB0/2E) /31/. Therefore i n t h e s p i n s u p e r p o s i t i o n experiment o f chapter I 1 1 n o t o n l y I+z> and I - z > s t a t e s a r e superposed b u t a l s o s l i g h t l y d i f f e r e n t wave packets e x i s t a t t h e place o f super- p o s i t i o n

An i n f l u e n c e o f t h e s h i f t of t h e wave packets on t h e i n t e r f e r e n c e p a t t e r n appear o n l y when t h e Zeman s p l i t t i n g becomes com- parable t o 6k.

Pulsed beams o r a time dependent i n t e r a c - t i o n a r e described by t h e time dependent Schrodinger equation and a s p a c i a l spread- i n g of t h e wave packet occurs (e.g. /40/)

which i s known i n any t i m e - o f - f l i g h t experiment. The spreading phenomenon a l s o appears i n t h e case o f a time dependent i n t e r a c t i o n , which causes a c e r t a i n phase mark on t h e wave f u n c t i o n . A d d i t i o n a l l y , energy can be exchanged between t h e neutron and t h e apparatus which can separate t h e packets i n momentum and f o r o r d i n a r y space, b u t coherence phenomena can s t i l l be preserved and can be recovered afterwards by apply i n g an opposite i n t e r a c t i o n . The spreading o f t h e wave packet i s analogous t o time- o f - f l i g h t experiments. The phase focussing c o n d i t i o n s read as i n t h e s t a t i o n a r y case because the s p a c i a l s h i f t o f t h e wave packets (AX = (D/Dk)X) i s u s u a l l y s m a l l e r than 6 x ( t ) . Only i n h y p o t h e t i c a l cases where t h e c o n d i t i o n

i s f u l f i l l e d , t h e wave packets become separated i n space b u t they remain coherent.

The c o n s t r a i n t o f equation (23) has been e x t r a c t e d from equation (22) and t h e uncer- t a i n t y r e l a t i o n 6x(0)6k I 1/2. When i t i s f u l f i l l e d t h e i n d i v i d u a l packets have i n - formation about t h e beam path b u t no i n t e r f e r e n c e p a t t e r n appears. A d d i t i o n a l aspects a r i s e when a pulsed beam crosses a time dependent i n t e r a c t i o n r e g i o n which changes i t s p r o p e r t i e s considerably d u r i n g t h e passage o f the wave t r a i n . I n such cases the shape o f t h e wave packet can change d r a s t i c a l l y /41/.

V I

-

CONCLUDING REMARKS

Various a d d i t i o n a l p r o p e r t i e s o f t h e wave f u n c t i o n d e s c r i b i n g t h e neutron o f a c e r - t a i n beam become observable by neutron i n t e r f e r o m e t r y . A l l observed phenomena belong t o t h e s e l f - i n t e r f e r e n c e regime because t h e t i m e - o f - f l i g h t o f t h e neutrons through t h e i n t e r f e r o m e t e r i s orders o f magnitudes smaller than the mean i n t e r v a l o f two neutrons. Thus t h e statement i s allowed u s u a l l y t h a t t h e n e x t neutron i s n o t y e t born when a c e r t a i n neutron passes through t h e i n t e r f e r o m e t e r . But a l l neutron haveacommon h i s t o r y w i t h i n c e r t a i n c o n s t r a i n t s determined by the apparatus and determining t h e coherence p r o p e r t i e s . The question whether the wave f u n c t i o n describes a s i n g l e neutron o r a beam has t o be answered such t h a t i t describes a s i n g l e neutron o u t o f a c e r t a i n bedm. Therefore t h e wave packet r e p r e s e n t a t i o n c o n t a i n s parameters o f t h e p a r t i c l e and o f t h e beam which a r e d e f i n e d by t h e c o n s t r a i n t s o f t h e experimental arrangement.

The experimental r e s u l t s m a n i f e s t t h a t every neutron has a t t h e p l a c e o f superposi- t i o n i n f o r m a t i o n about t h e p h y s i c a l s i t u a t i o n i n both p o s s i b l e beam paths which uniquely determines i t s f u t u r e . There e x i s t s i t u a t i o n s where no i n t e r f e r e n c e p a t t e r n can be observed b u t t h e coherence p r o p e r t i e s a r e s t i l l preserved and i n t e r f e r e n c e phenomena can be recovered by applying phase echo methods. Even a f i n i t e change o f t h e energy need n o t destroy t h e coherence and need n o t n e c e s s a r i l y be a measuring process. Coherence i s preserved as l o n g as the wave f u n c t i o n i s known and incoherence appears as a l a c k o f i n f o r m a t i o n about i t . A l l experimental r e s u l t s a r e i n complete agreement w i t h t h e f o r m u l a t i o n o f quantum mechanics and should p r o v i d e h e l p towards a deeper understanding o f t h i s fundamental theory.

The experimental work on t h i s s u b j e c t has been supported by Fonds zur Forderung der Wissenschaftlichen Forschung ( p r o j e c t 4230). The cooperation and many h e l p f i l d i s - cussions w i t h G.Badurek, D.Petrascheck and J.Summhammer and w i t h i n the Dortmund- Wien interferometer crew a r e g r a t e f u l l y acknowledged.

C 3 - 2 0 6 J O U R N A L DE P H Y S I Q U E

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