Theoretical Research Of Entanglement Dynamics In Open Quantum Systems

Quantum information, as a multivariate and intersecting field of quantum mechanics, information and computer science, is carrying people's dream of crossing the limit of classical information. Now it's rapid development has deeply revolutionized the traditional areas of communications and computer. Meanwhile the great successes of quantum information both in theoretical and experimentally areas, in turn, enriches the profound meaning of quantum mechanics. As we know, the quantum property of microscopy systems is extremely fragile in the real conditions, their internal coherence or entanglement can be easily destroyed by the complex environment. This is the main obstacle for quantum information processing. Thus, it is of great realistic significance to suppress decoherence and protect quantum prop-erty. From the theoretical point of view, the study of the dynamical evolution of an open quantum system will contribute to understanding the mechanism of decoherence. From the perspective of reality, it is not always true that the environment has negative impact on the system, the memory effect is the key factor for protecting the quantum property under some circumstances. In open quantum systems, therefore, the non-Markovian memory effect is the main concerns of this thesis. Based on the exact decoherence dynamics of realistic physical settings, we explore a universal scheme for protecting quantum coherence via spacial structures of the environment.In the thesis, we first overview the history of quantum mechanics, from the aspect of the issue of quantum-to-classical transition. The necessity for the study of open quantum systems is discussed, and the research status of this field is reviewed. Then in Chapter ?, we introduce the Feynman-Vernon influence functional theory, which is also the basis of this thesis. Chapter ? and the following chapters show the main research works of the thesis. Started with the model of effective fermions, we establish the exact entanglement dynam-ics for the fermionic systems in bosonic environment, and design a decoherence suppression scheme for the fermions. In Chapter ?, we apply the decoherence suppression scheme to some practical systems. In quantum dot nanostructures, which have excellent integratabil-ity, controllability and well stability, by calculating the exact reduced density matrix and analyzing the nonequilibrium Green's function, we find that the key point for generating maximum steady state fermionic entanglement is the memory effect. In Chapter V, we turn our attention to the continuous variable systems, and investigate the interplay between the non-Markovianity and the radiation pressure effect in optomechanical systems. To this end, by utilizing the exact perturbation formal solutions that effectively take into account the environment's memory effect, we extend the basic theory of optomechanics that based on Born-Markov approximation to the non-Markovian region. In Chapter VI, by utilizing the equivalence between the Heisenberg picture and the Schrodinger picture, we theoretically reconstruct the wave function and the density matrix of x-x coupled oscillators.The research of this thesis plays an active role for understanding the entanglement evolution in open quantum systems. From discrete variable systems to continuous variable systems, the research technique of the thesis could be applied to a wider range of physical systems in the future.