The Kerr Interaction Of A Four-level Atomic System In The N Configuration

In this paper,we firstly introduce the methods for the research of Multi-level atomic systems interacting with electromagnetic fields,which is consisting of adiabatic approximation and Non-adiabatic approximation.We have noticed that when there was time-dependent Hamiltion of the system,the evolution of Hamiltion with time would last long enough,while the coupling between system and fields can't be negligible.So we could just treat this situation in non-adiabatic approximation method.Then, by the means of non- adiabatic approximation we simplified the four-level atomic system in N configuration coupling with three electromagnetic fields into a three-level system. Further more, we derive the form of the self-kerr and cross-kerr interaction in the system we got through non-degenerate perturbation theory. In order to find out the determinants of the form of kerr effect,we finally calculated the microscopic expression of electrical susceptibility accompanies the self-kerr and cross-kerr responses of atomic system through Semiclassical density matrix theory.