Berry's phase with quantized field driving: effects of inter-subsystem coupling

The effect of inter-subsystem couplings on the Berry phase of a composite system as well as that of its subsystem is investigated in this paper. We analyze two coupled spin-$\frac 1 2 $ particles with one driven by a quantized field as an example, the pure state geometric phase of the composite system as well as the mixed state geometric phase for the subsystem is calculated and discussed.