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Title:  Analytical treatment of quantized electromagnetic field (Mathematical and physical aspects) 
Authors:  Mohammad Sebaweh Mahmoud Abdalla AlGwaiz, Mohammad Abd AlRahman ElQersh, Mohammad Mahmoud Mohammad Nassar Khalil 
Keywords:  Electromagnetic field Coupling parameters Squeezing Wigner function Hamiltonian model Heisenberg picture Qfunction 
تاريخ النشر:  2008 
Abstract:  In this thesis we have introduced and studied the problem of three mutually time
dependent coupled oscillators. The system consists of three different electromagnetic
fields injected within a cavity with unequal frequencies. As a result of the interaction
between the fields, the cavity material changes and the system acquires the time through
the coupling parameters. The problem has been handled from different points of view,
for example, in chapter two we have considered a particular form for the third coupling
parameter to connect up the other two couplings and field frequencies. The wave function
in the SchrÄodinger picture and in the coherent states are calculated besides the Green's
function and the Wigner function. Also, the phenomenon of squeezing is discussed in
detail, where we have used different kinds of squeezing. For example, the normal squeez
ing for different initial states, as well as the principal squeezing are considered. It has
been shown that when the system is initially in even coherent states collapse and revival
phenomenon can be seen.
In chapter three we have considered the same problem, however, with a restriction
on the third field frequency. Contrary to the previous chapter we have assumed that
the third field frequency contains beside the other two field frequencies all the coupling
parameters of the system. The main concentration was on the nonclassical properties
as well as on the transition amplitude of the system. Therefore we have calculated the
dynamical quantities using the solution of the equations of motion in the Heisenberg
picture. Also the Wigner function is calculated via the wave function in the coherent
states. The phenomenon of squeezing is discussed where the normal squeezing and the
amplitude squared squeezing are involved. The transition amplitude between different
states are also considered and a complete section is devoted to this purpose. We have
shown that the rate of exchange of the energy between the states is always sensitive to
the variations in the initial mean photon numbers in addition to the field frequencies and the coupling parameters.
In the fourth chapter the problem has been reformulated and the rotatingwave
approximation is applied by discarding the nonconservative terms from the Hamiltonian
of the model. The problem is converted into parametric amplifier and frequency converter
models coupled to each other through a timedependent coupling parameter. In this case
the timedependence is apparent and our consideration is extended to discuss the effect
of the pump phase on the whole system. Due to the difficulty on obtaining the wave
function in both the number states and the coherent states, our starting point was the
solution of the equations of motion in the Heisenberg picture. The nonclassical properties
have been examined by discussing the squeezing phenomenon and the photon bunching
and antibunching through the correlation function. In addition we have also considered
the quasiprobability distribution functions Wigner and Qfunction as well as the phase
distribution. For a large value of the coupling parameter which is responsible for the
parametric amplifier, the system gets very sensitive to any variation in the pump phase.
In the chapter five we have turned our attention to consider the problem of the time
dependent frequency converter model. The Hamiltonian model we have considered in this
case consists of an arbitrary timedependent coupling and pump phase in addition to an
external random force. The wave function is calculated in both coherent and number state
representations. Discussions related to the nonclassical properties are given. Also we have
managed to get the connection between the integrability condition and the random force
to reduce the noise in the system. 
Description:  This study has been conducted & submitted in Partial fulfillment of requirements for the Degree of Doctor of Philosophy in Applied Mathematics, College of Science, King Saud University, May 2008. 
URI:  http://hdl.handle.net/123456789/8825 
يظهر في المجموعات:  College of Science

جميع جميع الابحاث محمية بموجب حقوق الطباعة، جميع الحقوق محفوظة.
