الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
In this thesis, we examine some quantum models to study a quantum entropy for a non-linear interaction systems. In this regard, we discuss a system of a three-level atom interacting non-linearly with a single-mode of electromagnetic cavity quantized field. Under the timedependent coupling parameter and decay of the field in the presence of Kerr-like medium and Stark shift. We investigate this system by proposing convenient non-Hermition Hamiltonian. The wave function, the probability amplitude and expression of the reduced density operator of the atom are obtained when the atom is initially prepared in its uppermost state and the field is initially prepared in coherent state . The entanglement via concurrence, atomic inversion and Shannon entropy are studied under the effects of time-variation coupling parameter, damping of the field, Stark shift contribution and Kerr-like nonlinearity.
Also, we extend the previously cited treatments to study the problem of a four-level atom in ♦-configuration interacting with a single mode field, including acceptable kinds of nonlinearities of both the field and the intensity-dependent atom-field coupling. The evolution of the atom-field entanglement through the von Neumann entropy and the collapses-revivals phenomenon are investigated. A factorization of the initial density operator is assumed, considering the field to be initially in the coherent, pure chaotic and squeezed coherent states, while the atom initially in its uppermost excited state. The dynamical behavior of the atomic entropy and the time evolution of the photon number are analyzed. In particular, the effects of the mean photon number, field distributions, detuning, Kerr-like parameter and the intensity-dependent coupling functional on the entropy and the time evolution of photon number are examined.
Finally, the extension to the general formalism for ♦-type four-level atom interacting nonlinearly with a two-mode electromagnetic cavity field, in the presence of Kerr-like medium, the damping of the field and intensity coupling function is studied. The solution of the wave function of the system is given and consequently, the density matrix is obtained. The effects of detuning parameters, Kerr-like parameter, coupling and damping rate are discussed on atomic population inversion, Shannon information entropy, linear entropy and second order correlation function. Some of this results are new and published in international journals and conference.