The Study Of Geometric Phase In Anisotropic Rabi Model

Phase factor is one of the most basic concepts in quantum mechanics and all interference phenomena originated from phase factor.The concept of phase factor play an important role in quantum mechanics as well as probability amplitude.However,in the early years,people paid more attention on probability amplitude.With the deep development of quantum mechanics,the geometric phase played more and more important role in quantum physics,such as in the field of quantum computation,quantum communication and so on.The Rabi model,which describes the two-level atoms interacting with a radiation field,is very important in the study of light and matter interaction.Such model can be realized in various physical systems,such as Ion trap,Cavity quantum electrodynamics,etc.As is known to all,the rotating wave approximation is no longer valid in the strong coupling regimes.In the strong,or ultrastrong coupling regimes,the research of the Rabi model is particularly important.On the other hand,the anisotropic Rabi model as the generalization of isotropic Rabi model,plays an important role in different physical situations,such as quantum optics,solid state physics,mesoscopic physics and so on.There were series of research works on the Berry phase of the Jaynes-Cummings model and Rabi model.Based on these research works,we studied the geometric phase of anisotropic Rabi model and multi-qubit anisotropic Rabi model in this thesis.Our works on this topic not only enriched the theory of the geometric phase,but also provide more sufficient evidence about the existence of Berry phase in the quantum Rabi model.In this paper,we first introduced the symmetry and important application of anisotropic Rabi model in the physical system.Then,we studied the geometric phase of the anisotropic Rabi model and multi-qubit anisotropic Rabi model,theoretically and numerically.Finally,we do an matlab simulation on our results.