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Physical Review Letters

Is There an Aharonov-Bohm Effect for Neutrons?

Daniel M. Greenberger, D. K. Atwood, John Arthur, C. G. Shull, M. Schlenker

Published Sep 14, 1981• 26 citations
Publisher

Abstract

A neutron interferometer experiment testing the existence of an Aharonov-Bohm effect has been performed and no measurable phase shift has been found upon reversal of the enclosed magnetic flux. A positive result would have provided evidence for a breakdown in the standard minimal-coupling scheme for the electromagnetic interaction of a neutron. The sensitivity of the experiment sets the ratio of the Aharonov-Bohm effect for a neutron to that of a particle of charge $e$ to be less than 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}12}$.

DOI
10.1103/physrevlett.47.751

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A neutron interferometer experiment testing the existence of an Aharonov-Bohm effect has been performed and no measurable phase shift has been found upon reversal of the enclosed magnetic flux. A positive result would have provided evidence for a breakdown in the standard minimal-coupling scheme for the electromagnetic interaction of a neutron. The sensitivity of the experiment sets the ratio of the Aharonov-Bohm effect for a neutron to that of a particle of charge eee to be less than 5\ifmmode\times\else\texttimes\fi{}10\ensuremath−12{10}^{\ensuremath{-}12}10\ensuremath−12.
The special and unique techniques of neutron interferometry have been used to observe a number of topological effects. These include the quantum mechanical phase shift of a neutron due to the Earth's rotation (the quantum analog of the Michelson–Gale–Pearson experiment with light), the phase shift of a particle carrying a magnetic moment (a neutron) encircling a line charge (the Aharonov–Casher effect) and the scalar Aharonov–Bohm effect, observed with a pulsed magnetic field solenoid and time-of-flight neutron detection. On the occasion of the 50th anniversary of the Aharonov–Bohm paper, we provide an overview of the neutron interferometry technique and a description of these three historic experiments.
In the scalar Aharonov-Bohm effect, a charged particle (electron) interacts with the scalar electrostatic potential U in the field-free (i.e., force-free) region inside an electrostatic cylinder (Faraday cage). Using a perfect single-crystal neutron interferometer we have performed a ``dual'' scalar Aharonov-Bohm experiment by subjecting polarized thermal neutrons to a pulsed magnetic field. The pulsed magnetic field was spatially uniform, precluding any force on the neutrons. Aligning the direction of the pulsed magnetic field to the neutron magnetic moment also rules out any classical torque acting to change the neutron polarization. The observed phase shift is purely quantum mechanical in origin. A detailed description of the experiment, performed at the University of Missouri Research Reactor, and its interpretation is given in this paper.
This technical note gives a self-contained exposition of the Aharonov–Bohm effect, aimed at advanced undergraduate students. Starting from the role of electromagnetic potentials in classical electrodynamics, it introduces gauge freedom, the quantum Hamiltonian with minimal coupling, and the gauge covariance of the Schrödinger equation. It then derives the Aharonov–Bohm phase for both the time-dependent scalar configuration and the magnetic configuration, showing how a charged particle acquires an observable phase shift while travelling only through regions where the electromagnetic field vanishes. The final part reviews the experimental evidence, from the early electron-interference experiments of Chambers and of Möllenstedt and Bayh to the 1986 toroidal-magnet experiment of Tonomura and collaborators. In that experiment, superconducting shielding confined the magnetic flux completely and closed the leakage-field loophole, while flux quantization produced the characteristic half-fringe shift. The note is expository and pedagogical: it does not present original research results and has not been peer reviewed. Originally developed from study notes prepared for the PHYS02 scientific talk at Lady Margaret Hall, Oxford, in July 2026; an earlier version of the notes has been publicly available on GitHub since August 2026. Corrections and comments are more than welcome at giancarminesparso@gmail.com.
A phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space is known as the scalar Aharonov-Bohm (AB) effect. Unlike the more familiar AB effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. We have performed an analogous interferometric experiment with thermal neutrons subject to pulsed magnetic fields. The observations were carried out at the University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. The expected phase shifts have been observed to a high degree of accuracy. A detailed description of the experiment and its interpretation is given in this paper.
It has been suggested that the magnetic Aharonov-Bohm effect can be interpreted equally well as being due to a phase shift associated with an electron in an interferometer enclosing a magnetic flux, or as a phase shift associated with the electrons in the solenoid that generates the field. Here the Aharonov-Bohm effect is derived using second-quantized field theory to describe all the electrons as well as the electromagnetic field in a consistent way. The results are in agreement with the usual expression for the Aharonov-Bohm effect when the retardation of the electromagnetic field is negligible, but they predict the possibility of a fractional phase shift when retardation effects are significant.
The phase of the wave function of charged matter is sensitive to the value of the electric potential, even when the matter never enters any region with nonvanishing electromagnetic fields. Despite its fundamental character, this archetypal electric Aharonov-Bohm effect has evidently never been observed. We propose an experiment to detect the electric potential through its coupling to the superconducting order parameter. A potential difference between two superconductors will induce a relative phase shift that is observable via the DC Josephson effect even when no electromagnetic fields ever act on the superconductors, and even if the potential difference is later reduced to zero. This is a type of electromagnetic memory effect, and would directly demonstrate the physical significance of the electric potential.