ELSEVIER Physica B 241 243 (1998) 117 120

A new experimental approach to observe neutron spinor behaviour

Peter Fischer a'*, Ferenc Mezei a, Alexander Ioffe a'b

Hahn-Meitner-lnstitut, Dpt NI, Glienicker Str. 100, 14109 Berlin, Germany b St. Petersburg Nuclear Physics Institute. Gatchina. Russian Federation

Abstract

The aim of the present experiment is to observe topological spinor wave function phase shifts due to adiabatically rotating magnetic fields. A complex magnetic field coil system, which allows us to adiabatically guide the neutron spins in both arms by rotating magnetic fields in opposite direction has been built around a skew symmetric neutron interferometer. Technical aspects of realizing strongly adiabatic field configurations within an interferometer are also discussed. ~(! 1998 Elsevier Science B.V. All rights reserved.

Keywords: Spin precession; Space rotation; lnterferometry

Since three decades the experimental observa- bility of the particular behaviour of spinors and the associated phase factors are discussed [1,2]. A half-integral spin particle achieves a sign reversal of the wave function produced by the operator for rotation through 2n radians:

R(~) = exp(--i~a/2) = 1 cos(~/2) - ai sin(~/2).

In 1975 this effect was observed for neutrons pre- cessing in a suitably chosen homogeneous magnetic field using a LLL-interferometer. Both teams [3,4] claimed a complete rotation symmetry demanded by the spinor character of the neutron wave func- tion.

After the performance of such experiments, Mezei [5] pointed out, that those experiments do

*Corresponding author. Fax: + 49 30 8062 2523; e-mail: fischer-p@hmi.de.

not provide a direct observation or a new consist- ency check of the spinor behaviour under space rotation, represented by the Larmor precession; in reality we were only concerned with the well- known classical Stern-Gerlach effect. As an alter- native, slowly rotating magnetic fields are stated to trap the precessing spin and turn it in space [6-8]. This is obviously an improvement on con- stant fields by showing manifest geometric rotation, and in part answers the complaint that the rotation is otherwise a calculated quantity [9]. The exact solutions of the equation of motion in the adiabatic limit show the same result [10]. The experimental realization of this approach is the subject of the present article.

A complex magnetic field setup has been built around a skew-symmetric LLL-interferometer (loaned from Vienna group) at the interferometer setup in H M I Berlin [11]. A vertical gradient field was produced by two identical devices in opposite

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118 P. Fischer et al. ,' P,kvsica B 241 243 (1998) 117 120

A

f

Single field vectors

rotated effective field vector

Back coil

~ . ~ f r o n t coil

" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V" V "~

Fig. l. Schematic view of the double-coil set-up with 180-rotation of the effective field vectors.

directions. At equal distance before and after the interferometer they provided a field gradient Bz = 1.7 G/mm. For experimental simplicity the two effective magnetic field vectors were rotated through angles of ~ in opposite senses, i.e. through a relative angle of 2re, by inserting two 25 mm long match-box-like side by side coils in the interfero- meter, producing opposite horizontal fields (Fig. 1).

The coils are wound with 110 turns of 0.4 mm diameter enamelled copper wire yielding a resist- ance of 1.7 f~ each. Both coils were placed in a com- mon copper-aluminium frame, which was well attached to a aluminium cooling cap. The gaps were smeared with thermoconductive paste to guarantee optimal contact; small plates of poly- foam and thin alu foil were wound over. Water cooled by a thermostat was flowing in a closed cycle, removed the heat and maintained the ambi- ent temperature.

To ensure whether adiabatic conditions are achieved, we measured the flipping ratio of a polar- ized beam [12] depending on coil current, using an external DC-flipper and a Heussler crystal as an analyzer. For the DC-flipper and coils switched off the gradient field should work as a Majorana-like

flipper. It means that the intensity should be min- imal, but for the DC-flipper switched on it changes to maximum. When the current in the coil is tuned the intensity rate Floff/Flon is turned upside down, thus rotating the spin z-component. One can see that adiabatical approximation is fulfilled for 1 > 0.6 A (Fig. 2). From different measurements we realized, that this strong condition is fulfilled only for a small beam cross section in the central part of the system (5 mm x 7 ram).

An accompanied simulation of the equation of motion of the spin dS/dt = 7 [ S × B ] was done, treating the Cartesian components as a system of coupled first-order linear differential equations. The calculation also gave us a final Sz-component of - 0.9 for l~on = 0.8 A.

Because in interferometry, one can measure only the s u m (A(~dy n ~-A(~)topol) of the dynamical and topological phase shifts introduced, we have to ensure that the dynamical phase shifts of path I and path II are almost cancelling each other, thus get- ting A~Ddy n = ¢ ~ y n - - ~bllyn <<~ A(/)topol. This was done by conducting runs for parallel and antiparallel coil fields in turn, instantly changing the field direction after a few intensity oscillations and reversed

P. Fischer et al. /Physica B 241 243 (1998) 117-120 119

1.0

o 0.8 n

13 0.6. ¢-

.o "~' 0 .4 -

0 .2 - 0

13.

o.o ¸

- - . . - - r a t i o

- - • - - r a t i o . r e v c u

o'.o 0'.5 1'o 1'5 2'0 current [ A ]

Fig. 2. Polarisation of a 5 x 7 mm 2 beam for clockwise and counterclockwise rotation due to the coil current.

again throughout the same run. The fitting procedure showed that there was no appreciable phase jump, i.e. change of dynamical phase in both cases.

The experiment was accomplished by measuring the interference pattern of an unpolarized beam successively for three different magnetic field con- figurations for the same current at each angular setting of the Si-phase-shifter: opposite coil fields (pos0), parallel ones (posl) and inverse opposite field directions (pos2). Additional measurements were performed with reverse current direction. Primarily, posl was thought to serve for zero-cur- rent measurement, but we experienced that the interferometer was 'heat shocked' when suddenly current was switched on and off. Thus, due to the constant current in the former case the thermal environment of the interferometer remained undis- turbed throughout each run. Although the results showed an evident phase shift of the antiparallel pos0 and pos2 compared to the single done zero- current measurement, we, however, recognized a time-dependent drift of the intrinsic phase qSo, even for small currents which made us lose reproducibility.

Due to the extreme temperature sensitivity of the interferometer crystal, it is quite a challenge to

work with a heat-producing device inside it. In our case we assume that the instability of the intrinsic phase was caused by temperature gradients due to the power of up to 14 W. Certain limitations can be mentioned here to explain this crucial fact. Be- cause of the short wavelength of 2 A we need a big value of the path integral to guarantee adiabatic approximation. Therefore, the whole path of the interferometer was occupied by the isolated double-coil gadget leaving only 4 m m space to- wards the lamellae. Moreover, the cooling had to be done from the top, since the heat at the bot tom part, which was close to basement, was slowly led off. Thus, recalling that the watermnvironment temperature difference was up to 5 ° , we believe that a nonvanishing gradient is responsible for the drift of the intrinsic phase, knowing that its constancy is a much stronger condition than to make an inter- ferometer work. We try to overcome these short- comings by means of a longer wavelength and a longer crystal.

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120 P. PTscher et aL / Physica B 241 243 (1998) 117-120

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