The Berry phase: a simple derivation and relation to the electric dipole moment experiments with ultracold neutrons

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 [omega]. The derivation is accomplished with the help of the exact solution of the Schr6dinger 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 [omega]. I also discuss the role of the Berry phase in the experimental search for an electric dipole moment of the neutron with ultracold neutrons. [DOI: 10.1119/1.2805237]