Research On The Berry Phase Of An Atom-Kerr Medium Interacting System

In Cavity QED theory, J-C model is considered universally as the simplest and most effective model to completely solve the problems arise from the interactions between atom and light field. This model has been promoted by many scholars to explore new quantum effects, stimulated by its success. One of the ways is to consider the interactions between the field and medium, or among fields themselves, such as the cavity filled with Kerr medium. J-C model with Kerr medium has become one of the research topics of modern physics, and research finds that Kerr medium will have influences to the feature of light field and the dynamic behaviors of an atom. The Berry phase of this model has attracted attention from many researchers. Consider that in parameter space, a quantum system going through adiabatic evolution and in its eigenstate. When its wave function has gone through one period, a dynamic phase will be obtained, meanwhile, a geometric phase that reflects the topological properties of the states. The geometric phase is called the Berry phase. The exploration of Berry phase does not only make a breakthrough to the quantum adiabatic elimination of old theories, but also gives explanations to many physical phenomena. Berry phase has been experimentally proved, and is widely used in systems such as atomic physics, polarized light, etc. But there are still unsolved problems and experiments existed in the practical use of Berry phase, thus the study of the evolution features of Berry phase in all kinds of quantum systems becomes very important.In this paper, the theory and experimental detection of Berry phase is introduced in the first place. Meanwhile, the dynamic influences of Kerr medium are introduced as well. Moreover, the eigenenergy, eigenstates of single atom system and two-atom system are calculated. Then the Berry phases with arbitrary photon numbers after introducing the phase-shifting operator is calculated, and discuss and explain the eigenenergy E and Berry phase changing with the quantum number of the field, interaction between atom and field, the strength of Kerr medium. We find very interesting and plentiful changes of Berry phase with changing different parameters through its images.