The Study Of Geometric Phase In Composite Systems

Base on the investigations before, here we study the geometric phase in compositequantum systems. Firstly, the Berry phase in a composite system constituted of two coupled spin-1/2systems with one driven subsystem has been studied. We studied the coupling effect tothe Berry phase of the system, and we also investigate the relation between the subsystemand the whole system. The results could provide us a new way to control the Berry phase,which might aid in finding some applications in quantum computation. Secondly, based on the discovery of the vacuum induced Berry phase by I. Fuentes-Guridi et al[Phys. Rev. Lett. 89, 220404(2002)], we generalize the study to the casewith quantized fields, and investigate the quantized fields and vacuum effect to the Berryphase of the composite system, as well as the relation between the subsystem and thewhole system. The results show the effect of the quantized fields different from the case ofsemiclassical and also show that the intersubsystem coupling would diminish these phasesand make the observation of the field quantization effect diffcult except some specificangles. Finally, beyond the quantum Markov approximation, we calculate the geometricphase of a two-level system driven by a quantized magnetic field subjected to phasedephasing. The phase reduces to the standard geometric phase in the weak coupling limitand it involves the phase information of the environment in general. In contrast with thegeometric phase in dissipative systems, the geometric phase acquired by the system canbe observed on a long time scale. We also show that with the system decohering to itspointer states, the geometric phase factor tends to a sum over the phase factors pertainingto the pointer states.