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Physical Review Letters

Observation of 2π Rotations by Fresnel Diffraction of Neutrons

A. G. Klein, G. I. Opat

Published Aug 2, 1976• 104 citations
Publisher

Abstract

We report on the first observation of Fresnel diffraction of a beam of unpolarized slow neutrons by individual ferromagnetic domain boundaries. The observed occurrence of destructive interference in the experiment demonstrates that the phase of a spinor wave function changes by a factor of - 1 when the particle described by that wave function is rotated by an odd multiple of $2\ensuremath{\pi}$ radians.

DOI
10.1103/physrevlett.37.238

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Observation of the Phase Shift of a Neutron Due to Precession in a Magnetic Field

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Physical Review Letters•Oct 20, 1975•313 citations
We report on the first observation of Fresnel diffraction of a beam of unpolarized slow neutrons by individual ferromagnetic domain boundaries. The observed occurrence of destructive interference in the experiment demonstrates that the phase of a spinor wave function changes by a factor of - 1 when the particle described by that wave function is rotated by an odd multiple of 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ radians.
If a spin-½ particle is placed in a constant uniform magnetic field for a time t during which, classically, the Larmor precession angle would be θ, then according to quantum mechanics the components of the spin part of the wave function undergo phase changes of ±θ/2. Hence, corresponding to a classical precession of 2π radians, there is a sign change of the spinor, whatever the initial polarization may be. Bernstein pointed out that this sign change can be observed by coherently splitting a fermion beam, subjecting one part to the magnetic field, and coherently recombining the parts. Evidently, the same interference effect can be achieved by subjecting the two parts of the beam to fields which would classically cause precessions of π radians in opposite senses. He noted advantages in studying neutral rather than charged particles, and outlined a proposal for an interferometry experiment with neutrons. The recent invention and application of a remarkable single-crystal neutron interferometer greatly increases the feasibility of observing the sign change. In the experiment of Ref. 3 a neutron beam is split, and the two parts follow paths of different elevations. The interference of the recombined parts exhibits the effect of gravitational potential difference between the two elevations. In the experiment which we propose, the paths could be kept at the same elevation, but phase differences would be produced by appropriate magnetic fields.
A series of experiments is reviewed on precision measurements of the diffraction of slow neutrons paralleling those with light: diffraction at an absorbing edge, at an absorbing wire, and at single- and double-slit assemblies. Besides their educational value, the experimental results also provide precise confirmations of the theoretical predictions as calculated via a Fresnel–Kirchhoff approach. The intensity in all these experiments was so low that the formation of the interference patterns individual neutron by individual neutron could easily be observed. The experiments are presented and analyzed in a way suitable for undergraduate teaching.