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International Journal of Geometric Methods in Modern Physics

Geometric phases from neutron–mirror-neutron mixing in cold neutron interferometry

Antonio Capolupo, Gabriele Pisacane, Francesco Romeo, Aniello Quaranta

Published Jul 24, 2026• 0 citations
Publisher

Abstract

In this paper, we review how neutron–mirror-neutron mixing can induce a geometric phase for ordinary neutrons and how this phase can be accessed with a two-arm interferometer. By choosing different magnetic fields and suitable arm lengths, the dynamical phase difference can be canceled, so that the observed phase is directly related to the mixing. We summarize the main formulas and discuss representative regions of the neutron–mirror-neutron parameter space that can be explored with cold-neutron interferometry [A. Capolupo, G. Pisacane, A. Quaranta and F. Romeo, Phys. Dark Univ. 46 (2024) 101688].

DOI
10.1142/s0219887826400062

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In this paper, we review how neutron–mirror-neutron mixing can induce a geometric phase for ordinary neutrons and how this phase can be accessed with a two-arm interferometer. By choosing different magnetic fields and suitable arm lengths, the dynamical phase difference can be canceled, so that the observed phase is directly related to the mixing. We summarize the main formulas and discuss representative regions of the neutron–mirror-neutron parameter space that can be explored with cold-neutron interferometry [A. Capolupo, G. Pisacane, A. Quaranta and F. Romeo, Phys. Dark Univ. 46 (2024) 101688].
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.
We present results of the first experiment clearly demarcating geometric and dynamical phases. These two phases arise from two distinct physical operations, a rotation and a linear translation, respectively, performed on two identical spin flippers in a neutron interferometer. A reversal of the current in one flipper results in a pure geometric phase shift of \ensuremath{\pi} radians. This observation constitutes the first direct verification of Pauli anticommutation, implemented in neutron interferometry.
The object of this report is to review the recent results and some perspectives on cold neutron interferometry using multilayer neutron mirrors developed in KUR.The purposes of our research are to develop new experimental techniques, new devices for controlling neutron spin states for opening up a new world of physics.A multilayer neutron polarizes working under a very low external magnetic field (low field magnetic mirror), Funahashi's interferometer, a cold neutron spin echo instrument, a multilayer neutron spill splitter and a cold neutron pulser were developed.The equiv- alency of the quantum precession induced by the effective gap layer of the multilayer neutron spin splitter and Larmor precession of neutron spin in a magnetic field is established.This idea allows us to develop a cold neutron phase-spin-echo interferometer (a neutron spin interferometer).The neutron spin interferometer and a cold neutron pulser enabled us to carry out the delayed choice experiment for answering the question "how the neutron wave propagates after being split by the semitransparent mirror (wave splitter)".• These matters are reviewed in this paper.•
Abstract Advanced neutron interferometry includes the spinor properties of the neutrons. This makes it necessary to consider the influence of the mirrors on the spinor propagation. It is shown how the effect of an arbitrary mirror can be uniquely decomposed into a known kinematical part which is necessarily present, and a dynamical part which goes back to an interaction the neutron experiences in its rest‐space. For any particular realization of a mirror this dynamical part can be determined experimentally. An argument is given as to why it vanishes for the usual perfect‐crystal interferometer. The first relativistic approximations of the spinor reflection formula are discussed.
Neutron interferometer experiments have served as elegant demonstrations of the foundations of quantum mechanics. We show here two interferometer-experiments: one is the demonstration of a geometric phase in a split-beam experiment and the other is the measurement of off-diagonal geometric phase acquired in an evolution of a 1/2-spin system. The former was accomplished with the use of a two-loop neutron interferometer, where a reference beam can be added to the beam from one interference ioop. The combination of phase shifters and partial absorbers permitted the compensation of the dynamical phase and measurement of the geometric phase. The latter is investigated by means of a polarized neutron interferometer. Final counts with and without the polarization analysis enabled us to observe both the off-diagonal and diagonal geometric phases in two detectors. All experimental results show complete agreement with theoretical treatments.