Dynamics Of Atoms Interacting With Optical Field Under The Non-markovian Approximation

Dynamics of atoms interacting with electricity magnetic is a hot topic in theoreticalstudy, especially study of atomic dynamics such as the phenomenon of atomic collapseand revival or correlation of atoms. It is an important resource in the quantuminformation processing. The main contents and conclusions are as follows:1A new method to solve the Jaynes-Cummings model has been investigated. Thephenomenon of atomic collapse and revival predicted by Jaynes-Cummings model isdemonstrated. Solutions are consistent with previous such as using the operator method.Furthermore, the Jaynes-Cummings Hamiltonian including anti-rotating wave term isalso solved precisely using this new way and results agree experiments. Essences of theanti-rotating wave term are revealed. We discuss the relations of the phenomenon ofatomic collapse and revival with the average photons number, the light field phase angle,the resonant frequency and the size of coupling constant. The discussions may make usselect suitable conditions to carry out experiment well and this method may be appliedon quantum electrodynamics.2We present a detailed microscopic derivation of non-Markovian master equationfor a qubit interacting with a general reservoir. The master equation is derived by theNakajima-Zwanzig and the time convolutionless projection operator technique.Dynamical behaviour of a qubit in a reservoir can be solved exactly and also found bymeans of two variants of projector operator techniques. The comparisons of dynamicalbehavior of a qubit between non-Markovian and Markovian solutions are discussed. Thediscussion indicates the validity of non-Markovian deduced by above two projectionoperator techniques in different coupling regimes of a qubit coupling to a reservoir. Italso points out that the Markovian master equation may not precisely describe thedynamics of an open quantum system. The solution may be effective for many qubitsinteracting with a heat reservoir.3. A general expression of quantum discord and classical correlation for two-bodyX structure density matrix was derived. Then, the dissipative dynamics of non-coupledtwo qubits independently interacting with their reservoir was solved by thenon-Markovian master equation in a single excitation state. Under the detuning spectraldensity, the quantum discord dynamics was discussed and compared in differentcoupling regime. The results showed that this expression was employed to anytwo-body physical system having X structure density matrix, and we further confirmthe two variants of master equations were exploited in different coupled regimes in thedescription of quantum correlation dynamics. It is convenient to calculate the quantumdiscord and classical correlation of X structure state for later study and provide certainreference about which kind of master equation used in different coupling areas. 4. The quantum discord dynamics of two non-coupled two-level atomsindependently interacting with their reservoir, was studied in two kinds ofnon-Markovian conditions namely an off-resonant case with atomic transition frequencyand a photonic band gap. In the first case, the phenomenon of the quantum discord lossand the oscillator behavior of the quantum discord can be occurred by changing thedetuning quantity and reducing the spectral coupling width for any initial Bell state. Forthe second condition, the trapping phenomenon of the quantum discord can be presentedby adjusting the width of gap that is the quantum discord of two atoms keeps a nonzeroconstant in long time.