Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Spin Precession During Interferometry of Fermions and the Phase Factor Associated with Rotations Through 2π Radians

Herbert Joseph Bernstein

Published Jun 12, 1967• 89 citations
Publisher

Abstract

A proposed experiment which combines spin precession and two-slit interferometry of unpolarized neutrons is analyzed. The analysis elucidates the connection with a possible observation of the phase factor (-1) associated with the rotation of a half-integral spin particle through $2\ensuremath{\pi}$ radians.

DOI
10.1103/physrevlett.18.1102

Related papers

Proposed neutron interferometer observation of the sign change of a spinor due to 2π precession

Michael A. Home

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.

Cambridge University Press eBooks•Feb 26, 1993•0 citations

Observation of 2π Rotations by Fresnel Diffraction of Neutrons

A. G. Klein, G. I. Opat

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.

Physical Review Letters•Aug 2, 1976•104 citations

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

S. A. Werner, R. Colella, A. W. Overhauser +1 more

We have directly observed the sign reversal of the wave function of a fermion produced by its precession of 2π radians in a magnetic field using a neutron interferometer.Received 27 August 1975DOI:https://doi.org/10.1103/PhysRevLett.35.1053©1975 American Physical Society

Physical Review Letters•Oct 20, 1975•313 citations

Direct observation of fermion spin superposition by neutron interferometry

Johann Summhammer, G. Badurek, H. Rauch +2 more

The coherent superposition of oppositely polarized neutron beams of equal amplitude results in a final beam polarization perpendicular to the polarization of both initial beams. This polarization can be rotated by purely scalar interaction applied to the beams before superposition, which is equivalent to an additional Larmor precession applied to the beam after superposition. We have directly observed these effects in an experiment performed using the perfect-crystal neutron interferometer at the high-flux reactor at Grenoble. This paper gives the experimental results and discusses their theoretical foundation.

Physical Review A•May 1, 1983•137 citations

Observability of 2π rotations: A proposed experiment

A. G. Klein, G. I. Opat

Rotations by $2\ensuremath{\pi}$ radians of spin-\textonehalf{} systems are predicted to give rise to factors of -1 in the wave function. We propose an experiment involving Fresnel diffraction of thermal neutrons to test this proposition.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 1, 1975•31 citations

Observation of geometric and dynamical phases by neutron interferometry

Brendan E. Allman, Helmut Kaiser, S. A. Werner +3 more

The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.

Physical Review A•Dec 1, 1997•44 citations
A proposed experiment which combines spin precession and two-slit interferometry of unpolarized neutrons is analyzed. The analysis elucidates the connection with a possible observation of the phase factor (-1) associated with the rotation of a half-integral spin particle through 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.
The coherent superposition of oppositely polarized neutron beams of equal amplitude results in a final beam polarization perpendicular to the polarization of both initial beams. This polarization can be rotated by purely scalar interaction applied to the beams before superposition, which is equivalent to an additional Larmor precession applied to the beam after superposition. We have directly observed these effects in an experiment performed using the perfect-crystal neutron interferometer at the high-flux reactor at Grenoble. This paper gives the experimental results and discusses their theoretical foundation.
The total phase acquired during an evolution of a quantal system has two components: the usual dynamical phase, $\ensuremath{-}1/\ensuremath{\Elzxh}\ensuremath{\int}H(t)dt,$ given by the integrated expectation value of the Hamiltonian, and a geometric phase ${\ensuremath{\Phi}}_{G}(C)$ which depends only on the geometry of the curve traced in ray space. We have performed an interference experiment using polarized neutrons which clearly demarcates the separate contributions of the dynamical and geometric phases to the total. In the experiment, the two phases arise from two distinct physical operations, a translation and a rotation of a spin flipper within the interferometer, respectively. This work also constitutes the first direct observation of the Pauli anticommutation; a purely geometric phase shift of \ensuremath{\pi} radians appears after a reversal of the current in one of the spin flippers. The experiment was carried out at the 10 MW University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. A detailed description of the experiment and its interpretation is given in this paper.