Effect of decoherence on the Berry phase of a spin-half in a rotating magnetic field

We investigate the decoherence effect of a bosonic bath on the Berry phase of a spin-$\frac{1}{2}$ in a time-dependent magnetic field, without making the Markovian approximation. A two-cycle process resulting in a pure Berry phase is considered. The low-frequency quantum noise significantly affects the Berry phase. In the adiabatic limit, the high-frequency quantum noise only has a small effect. The result is also valid in some more general situations