Entanglement Dynamics Of J-c Model Undergoing Two-photo Transition In Dissipative Cavity With An Additional Kerr Medium

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 interesting to generalize JCM with both cavity damping and Kerr medium.To our knowledge,there is only one such generalizations in literature.In order to investigate the effect of dissipative or kerr medium on the entanglement between atom and field,all of them used linear entropy theory.The linear entropy of the system is a quantity to describe the entanglement between the system(field plus atom) and environment(dissipative cavity),and the linear entropy of the field(atom) is used to describe the entanglement between field(atom) and atom(field) plus the environment.Therefore,it is not perfect to use the linear entropy of the field(atom) to describe the entanglement between field(atom) and atom(field).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(dissipative cavity),Olaya-Castro etal showed that the intrinsic entanglement, 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 thesis,we use the quantum system of J-C model undergoing two-photo transition in a dissipative cavity with an additional kerr medium to investigate the entanglement between atom and field,entanglement between atom and environment and entanglement between field and environment through this theory.It is shown:kerr medium not only change the period and amplitude of E_a,f,E_a,e and E_f,e,but also restrains the intrinsic entanglement between atom and field.Many physical problems in various fields such as cosmology,quantum optics, particle physics,quantum measurement,quantum computation,and quantum information theory,are related to solving the master equation.So it is importance to find a convenience method to solve the master equation.Of course,some well-known methods have been developed,either exactly,or approximately.C-number equivalent is one method,superoperator of Lie algebras is another method.In this thesis,we studied the effect of dissipation on a macroscopic superposition of quantum states and get the same result:a superposition of two states is reduced to a mixture at a rate proportional to the separation between the two states.