Study On The Dynamics Of Quantum Systems Without Rotating-wave Approximation And Markovian Approximation

Dynamics of atoms interacting with electromagnetic fields is a hot topic in theoretical study.The system formed by atoms and electromagnetic fields exhibits interesting phenomena.If the interactions between atoms and electromagnetic fields are weak enough,the model can be simplified by using the rotating-wave approximation and Markovian approximation.However,recent studies have shown that the rotating-wave approximation is valid only for weak interaction systems.For weak interaction systems,memory effects of environment can be ignored,the information and energy of the quantum system flow into the environment will be dissipated,the energy and information no longer returns to the quantum system again.In this case,the Markovian approximation can be employed.However,when the coupling strength of the quantum system and environment is strong,the memory effects of the environment can't be ignored,the Markovian approximation is not applicable.It is an urgent and realistic problem to deal with strong interaction systems without using the rotating-wave approximation and Markovian approximation.Tanimura used Hierarchy equations method to study the interactions of light field and individual qubit using the non-rotating-wave approximation and non-Markovian approximation.He pointed out that the non-Markovian process has important influence on the evolution of individual qubit.The main contents and conclusions of the present thesis are as follows:Firstly,the Jaynes-Cummings model formed by two-level atoms and fields with the non-rotating-wave terms is studied.The model is solved numerically.The results show that the non-rotating-wave terms have great influence on the dynamics of the present system.Secondly,Tanimura et al.studied the evolution of single qubit in the non-Markovian environment.In the present thesis,the interactions between qubits and environment is strong,therefore rotating-wave approximation and Markovian approximation cannot be applied.Hierarchy equations are carried out to study the evolution and the correlation of multi-body systems with strong interaction.The hierarchy equations are derived from the Hamiltonian of the system and environment without using the rotating-wave and Markovian approximation.Mathematically,they are formed by thousands or even tens of thousands of differential equations.The density matrix at any time can be obtained by solving the hierarchy equations with the help of the Runge-Kuta method.Thus we can investigate the dynamics of the system.We study the entanglement dynamics of two or three qubits interacting within a common bath by using the hierarchical equations method.With the exact hierarchy equations method used here,double excitations due to non-rotating-wave terms are found to have remarkable effects on the dynamics and the steady-state entanglement.Without using the rotating-wave approximation,the coupling spectrum of the system and the heat bath has a decisive influence on the entanglement of the two or three qubits.By adjusting the value of the spectrum,we can change entanglement behavior of the two or three qubits.We can also change the degree of stable entanglement of the qubits and realize the conversion between Markovian processes and non-Markovian processes.Then,we study the entanglement behavior of qubits with interaction.The interaction coefficient has an important influence on entanglement oscillation,stable entanglement value,death time of entanglement,disappear of entanglement and so on.