Theoretical Study On Quantum Correlation And Criticality In Spin Chains And CQED Lattice Systems

Quantum information theory has received a lot of research interest due to its appli-cations that have significant advantage over traditional counterparts such as speeding up the search of unsorted lists or the factorization of large numbers. It is generally believed that quantum information theory can also give us a deep understanding of the fundamental limitation of classical computation tasks. However, one of the major obstacles to building a real-world quantum information device is that the system is always interacting with its envi-ronment to a certain extent, leading to a rapid destruction of quantum coherence. Therefore, a deep understanding of the mechanism for such decoherence effects is still needed and it is of great importance to prevent or minimize the decoherence induced by environmental noises on the practical realization of quantum information and computation. Quantum cor-relations such as entanglement and the newly-proposed quantum discord are believed to be the physical resource for many quantum information and computation tasks and has been extensively studied under many circumstances. On the other hand, quantum phase tran-sition (QPT) has attracted much attention in condensed matter physics and become a hot topic over the years. Traditional QPT approaches mainly focus on the identification of the order parameters and the pattern of symmetry breaking. The existence of a QPT strongly influences the behavior of many-body system near the critical point associated with the divergence of correlation length of two-point correlation functions and the vanishing of the gap in the exciton spectrum. QPTs, which happen at very low temperature, are purely driven by quantum fluctuations and are a qualitative change in the ground state properties of a quantum many-body system as some external parameters of the Hamiltonian is varied. In this thesis we will use many ideas from quantum information theory to study the quantum phase transition of many-body systems. We also extensive study the effect of environment decoherence on the qubit and its relationship to the quantum criticality of the environment, as well as the control method to suppress such decoherence effects. First, we study the dynamics of two initially correlated qubits coupled to their own separate spin baths modeled by a XY spin chain and find the explicit expression of the quantum discord for the system. A sudden transition is found to exist between classical and quantum decoherence by choosing certain initial states. We show that the sudden transition happens near the critical point, which provides a new way to characterize the quantum phase transition. The protection of quantum correlations against environmental noise and deco-herence is very important for the practical implementation of quantum information tasks. Therefore, we propose a scheme to prolong the transition time of the quantum discord by applying the bang-bang pulses. We then investigate the phenomenon of sudden transitions in geometric quantum correlation of two qubits in spin chain environments at finite temper-ature. It is shown that when only one qubit is coupled to the spin environment, the geometric discord exhibits a double sudden transition behavior, which is closely related to the quan-tum criticality of the spin chain environment. When two qubits are uniformly coupled to a common spin chain environment, the geometric discord is found to display a sudden tran-sition behavior where the system transits from pure classical decoherence to pure quantum decoherence. Moreover, an interesting scaling behavior is revealed for the frozen time, and we also present a scheme to prolong the time during which the discord remains constant by applying bang-bang pulses. Next, we investigate the influence of a flip operation of the central spin on the quantum criticality of a radical pair system by employing the spin echo and its product yield. It is found that with echo control on the central spin, the critical be-havior can be described by the product yield at very high temperatures. Moreover, we also study the short and long time behavior of the spin echo, and show that the decay factor of the short time evolution scales linearly. The long time evolution shows different statistics for varying chain lengths, temperature and external parameters of the Hamiltonian.Another topic of this thesis is to use an alternative approach to study the quantum phase transition in atom-field interaction lattice systems at finite temperature. As an illustrative example, we investigate the behaviors of the trace distance and quantum phase transition in a Jaynes-Cummings lattice at finite temperature. It is found that the trace distance can be used to describe the critical point of the quantum phase transition at finite low temperatures and the critical points are sensitive to the atom-field interaction strength and the detuning factor. For non-equilibrium states, we demonstrate that the time evolution of the trace dis-tance’s maximum value is also a good indicator of the critical points. Moreover, we show that the scaling behavior of derivative of the trace distance at the critical points and the scal-ing rule are dependent on the external parameters of the Hamiltonian. We then investigate the quantum phase transition of a superconducting circuit QED system at finite temperature by employing the trace distance. It is shown that the trace distance of the system’s Gibbs state and the product of its marginals exhibits a discontinuity at the critical point of a quan-tum phase transition even at finite temperature and for non-equilibrium states. The scaling behavior of derivative of the trace distance at the critical points is also found.