The Study Of Dynamics Properties In The Mode-mode Competition J-C Model And The Nonlinearity J-C Model

The interaction of the field and the atom, which can exhibit the non-classical effects such as collapses-revivals of the atomic inversion, the squeezing of the field and the atom, the anti-bunching and the sub-Poissonian distribution of the photon and so on, is the main content in quantum optics field. The Jaynes-Cummings (J-C) model which describes the interaction of a single two-level atom with a single mode field is the basic theoretical model. In the rotating wave approximation, J-C model can not only be solved exactly, but also reveal the mechanism of the quantum properties of the interaciton of the atom with the field. So considerable attention has been devoted to the study of the quantum properties of the mode-mode competition J-C model and the nonlinearity J-C model which are the two important extensions to the J-C model. In this paper, the dynamics behavior of the atom in the mode-mode competition J-C model and the quantum information entropy squeezing of the field in the nonlinearity J-C model are studied, and a series of significant results are obtained.In chapter 1, a simple history overview is presented of the mode-mode competition J-C model and the nonlinearity J-C model, firstly. Secondly, the competing three-photon and one-photon J-C model has been generalized into the competing K-photon and l-photon (k l) model, which is an effective work of ours, and the time evolution operator of the system is obtained, then one of the basic work model is established. Besides, with the Hamiltonian of the interaction between the field and the atom with Kerr medium, the evolution operator and the reduced density operator of the field are derived, then the other basic work model is obtained.In chapter 2, the dynamical properties of-the atom in the generalized mode-mode competition J-C model are studied by means of fully quantum theory. We discuss the influences of the relative coupling strength between the atom and the two-mode field and the initial state of the system on the atomic dynamics. We show that the presence of the mode-mode competition can result in quite periodical collapses-revivals of the atomic inversion, the increase of the relative coupling strength can lead to the fractional revivals and the increase of the initial photon number of the system can lead to the collapses-revivals phenomenon and prolong the revival time of the atomic inversion.In chapter 3, the entropy squeezing properties of the field in the nonlinearity J-C modelare studied by means of quantum information entropy, and the influences of the nonlinearity interaction of the Kerr medium with the field and the initial state of atom on the field entropy squeezing are discussed. It shows that the nonlinear interaction of the Kerr Medium can lead to an increase in the squeezing depth. On the other hand, the squeezing time and the squeezing depth of the entropy of the field increase with the increase of the atomic distribution angle.In chapter 4, summary of the thesis and prospect of our work are given in brief.