Studies Of Quantum Information And Quantum Phase Transition In Decoherence Environment

Quantum information is a new inter-discipline about the quantum mechanics and infor-mation science. Over the last decades, quantum information made great breakthroughs in both theoretical and experimental researches, quantum information not only brings new vigor and vi-tality into traditionary information science, but also provides some new research ideas in optics, atomic and molecular physics as well as condensed matter physics. The quantum coherence and quantum correlation are important resources for realizing quantum information tasks, however, one of the major obstacles to building a real-world quantum information device is that the quan-tum system is always interacting with its surrounding environment to a certain extent, leading to the destructions of quantum coherence and quantum correlation. In this sense, it is necessary to investigate the dynamics of quantum coherence and quantum correlation in dissipative system, meanwhile, it is of importance to prevent or minimize the influences of environmental noises on quantum system. On the other hand, quantum phase transition has attracted much attention in condensed matter physics and becomes a hot topic over the years. Quantum phase transition, which originates from the pure quantum fluctuations at absolute zero or very low temperature, strongly influences the behavior of many-body system near the quantum critical points associated with the divergence of the correlation length of the correlation functions and the vanishing of the gap in the exciton spectrum. Traditional quantum phase transition approaches mainly focus on the identification of the order parameters and the pattern of symmetry breaking. Recently, quan-tum fidelity, trace distance and quantum correlation emerged from quantum information science have been used to characterize quantum phase transition and obtained many important results.In this paper, we investigate the quantum coherences, quantum correlations and quantum phase transitions in several quantum dissipative systems. First, we study the dynamics of quan-tum coherence and quantum correlation in a generalized spin-boson model. By making use of quantum master equation and a perturbation approach based on a unitary transformation, we obtain the exactly analytical expression of reduced density matrix for qubit. At high tempera- ture, we find the counter-rotating terms of spin-boson model is able to increase the decoher-ence rate for sub-Ohmic baths, however, for Ohmic and super-Ohmic baths, the counter-rotating terms trend to decrease the value of decoherence rate. At low temperature, we find the rotating wave approximation always plays a positive role in preserving the qubit’s quantum coherence regardless of sub-Ohmic, Ohmic and super-Ohmic baths. Next, we study the geometric quantum discord between a bare qubit and a spin-boson model with zero tunneling constant. It is found that the geometric quantum discord in this two-qubit system exhibits a phenomenon of dou-ble sudden transition. Moreover, we explore the possibility of protecting the geometric discord between the two qubits and prolonging the time during which the geometric discord remains constant by applying bang-bang pulses. We also explore the dynamics of quantum correlation in a two-qubit system consisting of identical spin-boson models. It is found that the behaviors of quantum discord with and without rotating wave approximation are similar in the weak-coupling regimes, however, the quantum discord beyond rotating wave approximation shows a quit differ-ent behavior compared with that with rotating wave approximation. Moreover, we investigate the multipartite entanglement dynamics of a many-body system consisting of N identical two-level atoms locally embedded in their own band-gap photonic crystals. It is shown that the tripartite en-tanglement of this photonic-crystal-system can be frozen in a stationary state and the four-partite entanglement exhibits a double sudden change phenomenon under certain suitable conditions. Next, we investigate the quantum phase transition of cavity-BEC system via the geometric phase and quantum Fisher information of an extra probe atom. We also find that the geometric quan-tum correlation between two probe atoms exhibits a double sudden transition phenomenon and show this double sudden transition phenomenon is closely associated with the quantum phase transition of the atomic ensemble. This result suggests that the double sudden transition can be employed to detect quantum phase transition. Furthermore, we propose a theoretical scheme to prolong the frozen time during which the geometric quantum correlation remains constant by applying time-dependent electromagnetic field.Finally, we investigate the Loschmidt echo of a quantum system where a central spin is symmetrically coupled to a compass spin-chain. It is found that the Loschmidt echo and its sta-tistical distribution are able to detect the quantum criticality of the compass spin-chain at low temperature. By applying a spin flip operation to reverse the central spin’s orientation, we find the controlled spin echo and its statistical distribution can effectively reveal quantum criticality at very high temperature. Moreover, we show that the geometric phase of a central spin can be used to indicate the quantum phase transition of a compass spin-chain and obeys scaling behav-ior in the vicinity of a quantum phase transition. We investigate the quantum phase transitions of spin-chain systems in one and two dimensions by employing trace distance and multipartite entanglement along with real-space quantum renormalization group method. As illustration ex-amples, a one-dimensional XY model, a one-dimensional XXZ model and a two-dimensional XY model are considered. It is shown that the quantum phase transitions of these spin-chain systems can be revealed by the singular behaviors of the first derivatives of renormalized trace distance and multipartite entanglement in the thermodynamics limit. Moreover, we find the renormalized trace distance and multipartite entanglement obey certain universal exponential-type scaling laws in the vicinity of the quantum critical points of these spin-chain systems.