Non-Markovian Decoherence And Disentanglement Dynamics Of Dissipation Two-state System

The quantum information science, a research field of great promise, including quantum control, quantum computation and quantum communication, is based on the coherence of the quantum instruments, those are destroied by the outer environment, especially, in the solid quantum instruments-quantum dot and superconductor. So the effect of the environment to the quantum system becomes a center topic, the key of which is to eliminate or suppress the dissipation effect on the quantum system imposed by its surrounding environment, such as decoherence and disentanglement.Many physicists have taken great progress in many aspects. Among these methods, it is surprising that few if any fundamental treatments of decoherence exist that include the dynamics of disentanglement with better than the Markovian approximation or phenomenological tradition. Although, the use of the Markovian approximation is justified in a large variety of quantum optical experiments where entanglement has been produced, one should notice that non-Markovian effects are important in describing some condensed-matter systems, such as the quantum dot qubits system. Therefore, it is desirable to study a non-Markovian effects of the decoherence and disentanglement in any viable realization of qubits. Thus in this thesis, we will made a detailed introduction of our method--perturbation based on unitary transformation, and apply it to several models to investigate the Non-Markovian decoherence and disentanglement dynamics of dissipation two-state system. The whole thesis is consisted of six chapters.In chapter one, we review the source of the decoherence dynamics of dissipation two-state system, the theoretical model---spin-boson model, the classical methods developed by the dynamics of dissipation quantum system---Markovian approximation. Then we introduced our approach in detail through solving the simple spin-boson model.In chapter two, we have studied the dynamics of charge qubit with the static bias by a perturbation treatment based on unitary transformations. The approach can be practiced for various forms of the spectral density and the usual Ohmic and piezoelectric spectra are used in our calculations. Analytical results of the quantum dynamics, described by the population inversion are obtained together with the damping rate and the oscillation frequency. We find that a weak coupling of the qubit to the environment leads to a higher coherence oscillation frequency and a longer coherence time. For a fixed tunneling between the double quantum dots, the finite bias enhances the oscillation frequency effectively but its effect on the damping rate is relatively small. This is a possible way to maintain quantum coherence.In chapter three, the dynamics of a driven spin-boson model is studied by means of the perturbation approach based on an unitary transformation. Analytical expressions for the population difference and the coherence of the two state system are obtained. The results show that for weak driving, the population difference displays damping coherent oscillation and/or damping quantum beat, depending on the initial preparation. The coherence exhibits damped oscillation with Rabi frequency. When driving is strong enough, the population difference exhibits undamped large-amplitude coherent oscillation. In addition, our theory leads to correct results in two limit cases: without dissipation and without driving field.In chapter four, we investigate the disentanglement dynamics of a two-qubit system in the non-Markovian approach. It is shown that only for weak coupling between the system and environment does an exponential decay of entanglement appear, for certain classes of two-qubit entangled states. When the coupling between qubit and the environment becomes stronger, entanglement sudden death always appears even if the dissipation environment is at zero temperature.In chapter five, the disentanglement of a pair of two identical qubits, sharing a dissipation environment, is investigated. We proposed a new analytical method to study the problem, which takes into account the counter-rotating term and leads to the non-Markovian treatment of the short-time dynamics. It is shown that when the qubits are sufficiently separated from each other, the model is equivalent to each subsystem interacts independently with the environment. The effects of the dissipation environment and the interqubit distance,on the time evolution of the concurrence for four bell states are examined in detail. And point out the new features appearing when the two qubits are close together.In chapter six,we give the main conclusions and prospect. This work was supported by the National Natural Science Foundation of China under contract Nos. 10474062 and 90503007,as well as the National Minister of Education Program for ChangJiang Scholars and Innovative Research Team in University of IRT0524.