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Abstract Application of some quantum measures of information on three dierent quantum systems is studied. A non-linear Tavis Cummings model is studied, especially, two two-level atoms interacting with two modes of radiation eld with Stark shift eect. The time-dependent wave function and consequently the density matrix are obtained from which we discussed the eect of Stark shift on dierent statistical aspects for this system, for example, atomic inversion, entanglement, squeezing phenomena, degree of coherence and Q function are investigated. It is observed that the Stark shift parameter plays an important role on the evolution of these aspects. When Stark shift parameter moves away from 1, the atomic inversion is shifted upwards, entanglement decreases and more squeezing occur. Also, a system of two three-level atoms interacting with two modes of an electromagnetic eld in a trap is studied, An adiabatic elimination scheme is used to derive an eective Hamiltonian that describes two two-level atoms interacting with multiphoton in the presence of nonlinear Stark shift. We then examine the eects of the Stark shift parameter, initial eld state and multiplicity parameters on entanglement, phase properties and photon number distribution of this system. It has been shown vii that the system is sensitive to any change of the Stark parameter, initial eld state and multiplicity parameters. Also the numerical results show that the behaviour of AWD is similar to the von Neumann entropy, and the phase probability distribution represents the RCP. Finally, we solve a system of a type three-level atom interacting with one mode eld in presence of Kerr-like medium and photon assisted atomic phase damping. Then, the eects of the Kerr-like medium and the phase damping on some non-classical properties of this system such as atomic levels occupation, entanglement, atomic dipole squeezing through angular momentum operators and Q-PD functions (specially Q function) are studied. The results indicate that the Kerr medium plays a role contrary to that due to the phase damping except on the degree of entanglement, where, by increasing values of these parameters, the states of atom and eld begin to be separable. Dierent quadratures of the atomic variables squeezing are considered. Some of these results in chapters (2,3,4) are new and published 1- ”Application of some quantum measures of information to non-linear interaction of two two-level atoms and two modes of radiation eld”, had been presented in International Conference for Mathematics and Applications (ICMA15) 27-29 DEC. 2015, Cairo, Egypt. 2- ”Entanglement and Phase Properties of the nonlinear interaction between an eective two two-level atoms and two modes”, had been presented in One-Day Conference in Mathematics and its Applications, (14 April 2016) Assiut, Egypt 3- ”Some statistical properties for a non-linear Tavis Cummings model”, had been published in Appl. Math. Inf. Sci.11, No.1, 147-154 (2017). |