الفهرس 
Chapter 1Only 14 pages are availabe for public view
 |  | from | 87 |  |  |
| | | from | 87 | | |
Abstract
In this dissertation, we have studied the effects of Kerr-like medium and Stark shift on atomic inversion, phase properties, quantum entropy, and entanglement through the interaction between an atomic system described by a two-level atom and a three-level atom with a quantized radiation field, which has one mode and two modes.The Jaynes-Cummings model (JCM), described by a two-level atom interacting with a one-mode coherent cavity field, is considered and studied for the atomic inversion, which shows the difference between the probabilities of finding the atom in its excited state and ground state. Also, the JC model of cascade-type coupled to a one-mode coherent cavity field and the phase properties for this system are analyzed under the consideration of the Kerr medium parameter (χ/λ).Then, we studied the effect of the Kerr medium and Stark shift on the time evolution of the quantum field entropy for the bimodal field interacting with an effective two-level atom via the Raman transition. We may summarize the results of the thesis as follows:Chapter one serves as a general introduction to quantum optics. Also, it introduces some early work that studied quantum entropy, entanglement, and other useful concepts for our work.In chapter two, we have considered the JC model described by a two-level atom interacting with a single-mode cavity field. The atom and the field are prepared in the excited and coherent states, respectively. We have studied the influence of average photon number n ̅ on the time evolution of the atomic inversion W(t) as a phenomenon of collapses and revivals. We found that, by increasing the value of n ̅, the amplitudes of the revival intervals decrease during the considered time, which means that the interaction becomes weak. Moreover, we have extended the JC model to solve a three-level atom (cascade-type) interacting with a single mode of electromagnetic field in a cavity filled with a nonlinear Kerr medium. The atom and the field are prepared in the excited and coherent states, respectively. We have studied the influence of the Kerr medium parameter (χ/λ) on the time evolution of the Pancharatnam phase _t (t). We found that, by increasing the value of (χ/λ), the phase jumps became sharper and the chaotic behavior became more observable as time passed.In chapter three, we have studied the system described by an effective two-level atom prepared initially in the excited state interacting with a two-mode cavity field through a multi-photon process in the presence of the Kerr medium and Stark shift, taking into account the coupling parameter λ between the atom and the field, which modulated to be time-dependent.λ(t)=λcos(vt). The cavity field is initially prepared in a coherent state. Under certain approximations similar to those of the rotating-wave approximation, the quantum field entropy calculation is introduced, and its time evolution is discussed in a comparison with the atomic inversion behavior. When all parameters are equal to zero, the field entropy evolves the phenomenon of collapses and revivals with more oscillations and a lower value of the amplitude during the considered time. Also, by increasing the value of the Kerr medium parameter (χ/λ) in the absence of Stark shift, we found that the oscillation number decreased and the field entropy reached its maximum value faster within the time evolution process. The influence of the Stark shift parameter on the evolution of field entropy and atomic inversion is displayed in the absence of the Kerr medium. When we consider the case in which the two levels have different Stark shifts (l < 1), the maximum value of field entropy decreases. Also, we observed that when the Stark shift parameter is equal to 1,(l = 1), the field entropy evolution is almost similar to the case in which all parameters are equal to zero. In the case of l = 2, the maximum value of field entropy increases compared to the case in which l = 1. It is shown that the time-dependent parameter plays an important role in the dynamics of the system. By increasing the value of the parameter (ν/λ), the oscillation amplitude decreases more and more within the time evolution process. It is shown that the time-dependent parameter plays an important role in the dynamics of the system. The oscillation amplitude decreases as soon as the value of the parameter (ν/λ) increases during the considered time. This implies that, when the nonlinear interaction of the Kerr medium with the field mode is very weak, the entanglement degree between the field and the atom is unreduced. Finally, some statistical features of our atomic system are calculated and discussed.Chapter four serves as a general conclusion and summary of our work.