Some Statistical Aspects for Non-linear Interaction Between Some Quantum Systems

Abstract

In this thesis, the interaction between a three-level atom and four systems of Ntwo-level atoms in di erent cases is studied. Besides, the atom is coupled with the systems by time-dependent coupling parameters. The analytical solution of this model is presented. further, the in uence of the Kerr-like medium on this model is introduced. The approximate solution of this system and the wave function are obtained, under a speci c conditions, and therefore the Schrodinger equation is solved. Finally, we consider our model, but in di erent interaction Hamiltonian. The exact solution for the wave function is obtained, by taking some special cases. We investigate some physical statistical properties of the three systems such as the atomic population inversion and the second-order correlation function. Then also the e ects of several parameters such as the numbers of two-level atoms of the four systems and the coupling parameters between spins on these statistical properties are studied. The analysis of results manifests that correlated behavior can be controlled by adjusting some parameters like the coupling parameters between spins. Also, it has been revealed that the atomic inversion and correlation function are greatly a ected by the Kerr medium.