Study Of The Dynamics For The Cavity-damped Jaynes-cummings Model With Kerr Medium

Jaynes-Cummmings model is a single two-level atom interacts with a single mode of the electromagnetic radiation field.Experimental achievements with Rydberg atoms explain the revival of interests in the JCM and its various generalizations.Two of the important generalizations are the JCM with cavity camping and JCM with Kerr medium. It is of interest to generalize JCM with both cavity damping and Kerr medium.To our knowledge,there is only one such generalizations in literature.The purpose of the present paper is to study the dynamics of the cavity-damped Jaynes-Cummings model with Kerr medium.For a system with three components,A,B and C(for our case,A is a atom,B is a field and C is environment(or dissipative cavity),Olaya-Castro etal showed that the intrinsic entanglement,M_A,B=S_A+S_B-S_A,B is a good quantity to describe the entanglement between A and B,where S_A,S_B and S_A,B are the linear entropies for the component A,B and subsystem A and B,respectively.In this paper,instead of using linear entropy of atom(field),we will use the intrinsic entanglement of atom and field to describe the entanglement between field and atom.This thesis study the intrinsic entanglement between the atom and the field of the standard JCM and the intensity-dependent coupling JCM.The result shows Kerr medium affects the period of the intrinsic entanglement.The nonlinear of Kerr-medium is from the refractive index changing with the light intensity.Kerr-medium has the nonlinear effect because of its different refractive index. Currently,people widely focus on studying that influences of linear entropies evolution in the J-C model with Kerr medium inside a phase damping cavity.We have discussed that the standard J-C model and the intensity-dependent coupling J-C model are in Kerr-medium inside a phase damping cavity,and Kerr-medium influences the linear entropies and the intrinsic entanglement evolution of the two J-C model.The same way,In the rotating-wave approximation,we can get the effective Hamiltonian of the system.By solution density of the matrix element we can get the reduced density operator of atom and field.So we have the linear entropies and the intrinsic entanglement of atom and field.