الفهرس 
1 IntroductionOnly 14 pages are availabe for public view
 |  | from | 171 |  |  |
| | | from | 171 | | |
Abstract
Application of some quantum measures of information on three
di erent 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 e ect.
The time-dependent wave function and consequently the density
matrix are obtained from which we discussed the e ect of
Stark shift on di erent 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 e ective Hamiltonian
that describes two two-level atoms interacting with multiphoton
in the presence of nonlinear Stark shift. We then examine
the e ects 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 e ects 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. Di erent 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 e ective 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).