الفهرس 
1.2.1.1 Some Properties of the Coherent StatesOnly 14 pages are availabe for public view
 |  | from | 197 |  |  |
| | | from | 197 | | |
Abstract
In this thesis, we study some quantum relativistic and quantum models under some effects such as isospin field, external magnetic field, phase damping, Kerr-like medium and Stark shift where we employ the solutions of
these models to study some of their statistical properties.
The 2+1 Dirac-Moshinsky oscillator coupled to an external isospin field
is mapped onto the Jaynes-Cummings model, which describes the interaction between two-level atom and a quantum single-mode field. The timedependent wave function and the density matrix are obtained in two cases.
In the first case, the quantum number state is considered, while in the second case, the coherent state is considered as an initial state. The effect
of both the detuning parameter and the coherence angle is studied on the
entanglement and on the population inversion. The results show that the
coherent state gives a better description than the number state for the entanglement and the population inversion.
The 2+1 Dirac-Moshinsky oscillator is mapped onto generalized JaynesCummings model, in which an external magnetic field is coupled to an
external isospin field. The basic equations of the model are solved analytically, where the coherent state is considered as an initial state. The results
show that the strength of the magnetic field and the coupling parameter of
the isospin field play important roles on some statistical properties such as
entanglement, population inversion and degree of coherence. It has been
shown that these parameters play a role in increasing the entanglement and show the revivals-collapses phenomenon.
Also, a system of a three-level atom in the three different configurations
(Ξ, ∨ and ∧ ) interacting nonlinearity with a two-mode of electromagnetic field, in the presence of Kerr-like medium and photon assisted atomic
phase damping included is studied. The explicit mathematical form for the
wave function is obtained and consequently, the density matrix is derived.
The effects of detuning parameters, Kerr-like medium and photon assisted
atomic phase damping parameters are discussed on atomic levels occupation and entanglement. The results show that the entanglement depends
on the detuning parameters, atomic phase damping and Kerr-like medium
parameters.
A three-level atom interacting nonlinearity with SU(1,1) quantum system
which is prepared in the Perelomov coherent state in the presence of photon assisted atomic phase damping is introduced. The time dependent
wave function is calculated by using the Schr¨odinger equation. The density matrix is obtained. The influences of damping, nonlinearity (Kerrlike medium), Perelomov coherent parameter and the Bargmann index k
on some nonclassical properties are investigated such as (revivals-collapses
phenomenon, entanglement, atomic variables squeezing, and Q-function).
Finally, The dynamics of purity, atomic Wherl density and second-order
correlation for a two-mode field cast through SU(1,1) operators interacting
with a three-level atom are investigated in the presence of Stark shift effect. An intensity-dependent atomic-field coupling is considered. Initially,
the SU(1,1) quantum system is in the Baraut-Girardello coherent state and
the atom is in superposition state. The time dependent wave function is
calculated using the Schr¨odinger equation. It is observed that the quantum
system is found highly sensitive to this environmental influence, where the
increasing of Stark effect leads to increase in the degree of purity.Some of these results in chapters (2-6) are new and published
1- ”Mapping of the 2+1 Dirac -Moshinsky Oscillator Coupled to an External Isospin Field onto the Jaynes-Cummtings Model” had been published
in J. Russ. Laser Res., 40, 132 (2019), Doi: 10.1007/s10946-019-09780-w.
2- ”Effect of an External Magnetic Field on Some Statistical Properties of
the 2+1 Dirac -Moshinsky Oscillator” had been published in J. Russ. Laser
Res., 43, 380 (2019), Doi: 10.1007/s10946-019-09808-1.
3-”A Study of a Nonlinear Interaction Between a Two-Mode Cavity Field
and a Three-Level Atom in Different Configurations with Damping”, had
been presented in ”4” CICs Multidisciplinary International Conference 2019-
2020, Egypt.
4-”A Study of a Nonlinear Interaction Between a Two-Mode Cavity Field
and a Three-Level Atom in Different Configurations with Damping” had
been accepted in Nonl Opt Quant Opt journal.
5- ”Interaction Between Su(1,1) Quantum System and a Three-Level Atom
in the Presence of the Stark Shift” under review in Scientific Reports journal.
6-”A Nonlinear Interaction Between SU(1,1) Quantum System and a ThreeLevel Atom in Different Configurations with Damping Term” under review
in Physica Scripta journal.