The effect of intersubsystem coupling on the geometric phase in a composite system driven by decohering quantized fields

We investigate the behaviour of the geometric phase of a bipartite system with intersubsystem coupling via a quantum jump approach, where one of the subsystems is driven by a one- or two-mode quantized field which is also subjected to decoherence. The results show that the first correction due to the decohering field is only quadratic in decaying rate lambda when the evolution of the system is adiabatic, and the lowest order correction is related to the first order in.l when the evolution of the system is non-adiabatic. Moreover, an interesting interpretation of this phenomenon is given.