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Physics-Uspekhi

The neutron Berry phase

V. K. Ignatovich

Published Jun 8, 2013• 4 citations
Publisher

Abstract

The neutron Berry phase is found from an exact analytic solution of the Schrödinger equation in a constant magnetic field and a perpendicular radiofrequency field rotating with an angular frequency . The solution is found for arbitrary values of , , and . The Berry phase is shown to be a linear approximation of the exact value in the parameter when this parameter is small.

DOI
10.3367/ufne.0183.201306e.0631

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The neutron Berry phase is found from an exact analytic solution of the Schrödinger equation in a constant magnetic field and a perpendicular radiofrequency field rotating with an angular frequency . The solution is found for arbitrary values of , , and . The Berry phase is shown to be a linear approximation of the exact value in the parameter when this parameter is small.
I derive the effective phase of the spin precession for a neutral particle with spin 1∕2 moving in a superposition of constant and radio frequency fields. The fields are perpendicular to each other at all times, and the radio frequency field is slowly rotating with angular speed ω. The derivation is accomplished with the help of the exact solution of the Schrödinger equation. I show that the geometrical (or Berry) phase is the linear term in the power series expansion of the effective phase in terms of ω. I also discuss the role of the Berry phase in the experimental search for an electric dipole moment of the neutron with ultracold neutrons.
In connection with Bitter–Dubbers experiment, an exact solution for the quantum dynamics of neutrons in magnetic field which is harmonically inhomogeneous (helical) and changes harmonically with time is obtained by invoking a time-dependent transformation with spin–space coupling. It predicts that a beam of neutrons with monotonous momentum will be split into two beams by the magnetic field. As its limiting case, the Berry's geometric phase in moving reference frame appears while the field is very strong.