Decoherence Dynamics Of Open Quantum Systems

This thesis is contributed to the study of decoherence dynamics of dissipative qubit system. We mainly concentrate on the profound impact of the formation of a bound state between the qubit and its local environment on the decoherence behavior of the reduced qubit system under the non-Markovian dynamics.Firstly, we evaluate exactly the non-Markovian effect on the decoherence dynamics of a single qubit interacting with a dissipative vacuum reservoir. We find that the quantum coherence of the qubit can be partially trapped in the steady state when the non-Markovian memory effect of the reservoir is taken into account. Our analysis shows that it is the formation of a bound state between the qubit and its reservoir that results in this residual coherence in the steady state under the non-Markovian dynamics. A physical condition for the formation of the bound state is given explicitly. Our results suggest a potential way to decoherence control by modifying the system-reservoir interaction and the spectrum of the reservoir to the non-Markovian regime in the scenario of reservoir engineering.Secondly, We study the entanglement dynamics of two qubits locally interact-ing with their reservoirs and explore the entanglement preservation under the non-Markovian dynamics. We show that the existence of a bound state of the qubit and its reservoir and the non-Markovian effect are two essential ingredients and their inter-play plays a crucial role to preserve the entanglement in the steady state. When the non-Markovian effect is neglected, the entanglement sudden death is reproduced. On the other hand, when the non-Markovian is significantly strong but the bound state is absent, the phenomenon of the entanglement sudden death and its revival is recovered. Our formulation presents for the first time a unified picture about the entanglement preservation and provides a clear clue on how to preserve the entanglement in quantum information processing.Finally, in order to obtain a thorough understanding of the entanglement dynam-ics, we study the entanglement distribution of a two-qubit system, each of which is embedded into its local reservoir, among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. Different to the result that the entan- glement of the qubits is transferred entirely to the reservoirs under the Markovian dynamics, we find that the entanglement can be stably distributed among all compo-nents under the non-Mar kovian dynamics, and particularly it also satisfies an identity firstly given by Yonac, Yu and Eberly [J. Phys. B 40, S45 (2007)] for a double J-C model without decoherence. While the explicit distribution of the entanglement is de-pendent of the detail of the model, even the approximation used, the identity remains unchanged. Our unified treatment includes the previous results in the literature as special cases. The result reveals the profound nature of the entanglement and should have significant implications for quantum information processing.This thesis may give a clear clue of decoherence dynamics under different approx-imations and how to preserve quantum coherence in the steady state.