  We investigate the decoherence effect of a bosonic bath on the Berry phase of
a spin-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.
