Berry's phase,density matrices and incompatible observables

Adiabatically time-varying parameter-dependent cyclic Hamiltonians are known to generate Berry's phase in state vectors in addition to the usual dynamical phase. Using the standard algorithm for collapse into a mixture following a quantum measurement process, we investigate the general nature of measurements in which the effects of Berry's phase, introduced at some intermediate stage of the measurement process, persist in the final collapsed density matrix. We find that it is possible to construct a sequence of a preparation followed by a measurement of an observable incompatible with the prepared state, where the collapsed density operator carries intermediate changes of phase in pure states; hence unitary time evolution alone is not essential for the observation of geometrical phases. This result confirms similar suggestions made by other investigators.