Quantum Non-Markovianity And Quantum Correlation Of Open Systems

Any quantum systems inevitably interact with their surrounding environ-ments, therefore the quantum systems are open. The study of features of the dynamics of open quantum systems, such as the decoherence, the dissipation of energy, and the quantum correlation, is of central importance in many applica-tions of quantum mechanics. Usually, in the theoretical research of open quantum systems, environments are treated as Markovian ones without memory. However, environment often exhibits memory effects, the evolution of many important phys-ical systems must be described by using quantum non-Markovian process. In this thesis, we mainly investigate the quantum non-Markovianity and the dynamical characteristics of quantum correlations of open systems.The first chapter is mainly contributed to the introduction of some basic theories of open quantum systems.In chapter 2, from a Lindblad-like master equation, we have studied the ef-fect of Lamb shift on the non-Markovian dynamics. We found that Lamb shift can induce a non-uniform rotation of the Bloch sphere, but does not affect the non-Markovianity of the open system dynamics. We also, for the general non-Markovian master equation, obtained the necessary and sufficient conditions for the backflow of information, found the optimal initial-state pairs that maximize the backflow of information, and found the sudden change of the non-Markovianity. We tried from the evolution of Bloch sphere to figure out the non-Markovianity of quantum process, and used it to predict successfully and explain intuitively the obtained results.In chapter 3, we have investigated the non-Markovian dynamics of quantum correlation for two qubits embedded in respectively independent reserviors. We have found that non-Markovian effect can lead to quantum correlation oscilla-tions which can further interfere to form correlation quantum beats. We made a physically reasonable explanation for this phenomenon. This kind of quantum interference may be used to detect the difference between the qubit-transition frequencies or to indicate the difference between the local non-Markovian environ-ments. The quantum correlations can be preserved by the effective suppression of the spontaneous emission. Good monochromaticity of cavity mode, and large frequency detuning between qubit and cavity mode can help to protect quantum correlations.In chapter 4, based on independent-reservior model, we have studied the dy-namics of two correlations (measurement-induced nonlocality and geometric dis-cord) between two spins in independent (flat and Lorentzian) reservoirs. Research shows that the measurement-induced nonlocality of different partitions is identi-cal for the two types of initial states (one-and two-excitation states), while the geometric discord depends on the initial state. It also shows that all the correla-tions initially stored in the two spins transfor to reservoirs at the end of evolution. There is no sudden death of correlations for the spin system in the transferring process, and for Lorentzian reservior, oscillation appears which is the symbol of non-Markovian effect. At the same time, correlated quantum beat phenomenon is also observed.In chapter 5, for independent-reservior model, we have studied the influence of the coupling strength between the two qubits, and the initial phase of two-qubit entangled state on the quantum discord dynamics under two different decoherent channels. The results show, when the interaction between the two qubits is zero, quantum discord exhibits monotonically decay and is independent of the initial phase; While when the interaction between the two qubits is not zero, with the interaction strength between the two qubits increasing, quantum discord dynam-ics displays oscilations and revivals more quickly. The larger the initial phase, the larger the oscillation amplitude of the quantum discord is. Comparing the quantum doscord with the corresponding entanglement under the same decoher-ent channels, we find that quantum discord disappears slower and thus more robust than entanglement.The sixth chapter is a brief summary and outlook of this thesis.