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

摘要

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 Schrodinger 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. (c) 2008 American Association of Physics Teachers.