Using stored spin-polarized ultracold neutrons subjected to a temporally varying magnetic field, we have demonstrated a manifestation of Berry's phase. We verified several properties of Berry's phase which include its solid-angle dependency and additivity for multiple excursions along the same path in parameter space.
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.