A Study On The Dynamical Process For Atom Interacting With The Kerr Medium

In the field of quantum optics, Kerr medium-material interaction is one of the useful systems in experimental and theoretical study. More specific effects could be brought about in such system. Meanwhile Kerr medium could act as the data bus in the study of quantum information. For the interaction system between atoms and Kerr medium, the degree of freedom of light field can be eliminated in a given condition. Therefore, the effective interaction only between atoms can be reached. For the achievement of effective Hamiltonian, the Fr(o|¨)hlich transformation is the more helpful. The result gotten by using Fr(o|¨)hlich transformation is similar to the one by perturbation theory. And rather, the orders of Fr(o|¨)hlich transformation is more clear. One optic-mechanical system can be equivalent to the interaction of Kerr medium with atoms.This paper studied the dynamical process of atom interacting with the Kerr medium. By using the Fr(o|¨)hlich transformation, the effective dynamics is derived by eliminating the degree of freedom of the cavity field. As the light field is detuning, it could be seen that spontaneous symmetry breaking occurring. The atomic entanglement is then analyzed. Also, we discuss the displacement of the steady state of the medium based on the theory of second order phase transition, and study the affect to the entanglement in detail.