The Study Of Geometric Phase In Open Systems

Geometric phase has been widely investigated, because it depends on the topo-logical characteristic of the quantum system. It played an important role in explainingor predicting new phenomena in the field of Condensed Matter Physics, MolecularPhysics and the other domain of physics. Geometric phase has great potential forapplication in Quantum information, so the study of geometric phase for open andnonlinear system has profound theoretical and important practical significance.The properties of the geometric phase in open and nonlinear system has beeninvestigated by using the quantum jump and unitary transformation methods in thisdissertation. Significant results are shown as follows:1. The geometric phase of a spinning quantum system interacting with a clas-sical magnetic field with a ?uctuating component is analyzed. Beyond the quantumMarkov approximation, the eigenvector and the corresponding geometric phase areobtained by employing the unitary transformation technique, and the effects of classi-cal ?uctuations on both geometric and dynamic phases is discussed. The results showthat the geometrical aspects of geometric phase can reduce the effect on geometricphase caused by the ?uctuations.2. The effect of decoherence on the geometric phase in the composite system isdiscussed. Based on the existence of interaction between the two spin-1/2 systems ofcomposite system, the corrections for geometric phase were discussed when one sub-system driven by a classical or quantum field subjecting to decoherence. The resultsshow that the corrections to the geometric phase is only of second order in the decay-ing rateλof the field when considering adiabatic evolutions, while the corrections tothe geometric phase is first order inλwhen considering nonadiabatic evolutions.3. The behavior of geometric phase in a generalized nonlinear two-level system was investigated. The effects of the nonlinear intensity-dependent atom-field couplingand the nonlinearity of the quantized field on the geometric phase were discussed. Theresults show that geometric phase changes bigger slowly as photon number increasesin the fixed atom–field coupling, and the vacuum field can introduce a correlation tothe geometric phase, and the fractional statistical phenomenon appeared in this systemif some case is considered.4. Based on the dispersive interactions, an effective two photons two-level atomcoupled to single quantized fields was considered, the geometric and dynamic phasewere obtained by using Invariant method. The results show that the geometric phasecan be effected by the Stark shift.In conclusion, this dissertation investigation may be helpful not only to under-stand better the characteristic of geometric phase in open and nonlinear systems,and to provide the theoretical foundation for the design of fault-tolerant quantumcalculation, but also to make an investigation on the application of geometric phase inquantum information and quantum calculation.