Study On The Steady State Correlation And Many-body Localized Correlation Distribution In Multipartite Dynamical Systems

Quantum correlation in multipartite systems is a kind of crucial non-classical resource and has been applied in many tasks of quantum information processing.In comparison to bipartite quantum correlation,multipartite quantum correlation is more important,since it plays a key role in complex quantum network communication,scaling quantum speed-up computation and can be utilized to characterize quantum phases and novel quantum phenomena in the field of condensed matter physics.However,due to the inevitable environment noises,quantum correlations in practical quantum systems may decay or disappear,which results in the destructive influence on the quantum information processing.Therefore,it becomes a frontier problem in quantum information field to study the dynamical properties of quantum correlation and its effective quantum modulation.In 2004,Yu and Eberly proved that the entanglement in two 2-level atoms can be disappeared in finite time under local dissipative environments.Therefore,it is a key issue in the quantum state engineering that how to modulate the entanglement in the steady states.In2011,Kastoryano et al presented that the entanglement in two atoms can be modulated to the maximally entangled state via optical cavity couplings.It is desirable and necessary to further study the modulation of multipartite quantum correlation in the steady state of many atom systems.On the other hand,the thermalizing procedure of many body quantum systems is also a typical dynamics.In 1958,Anderson first found that the disorder environment can be used to localize the electronic state in the thermalizing procedure,which is referred as Anderson localization.Along with the fast development in the field,in 2018,Wang et al pointed out that the initial quantum correlation can be maintained in the phase of many-body localization.In order to study the localization phenomenon in multipartite systems,we need to further analyze the dynamical quantum correlation distribution in the thermalizing quantum systems.In this thesis,we have studied the tripartite quantum correlation modulation in the steady-state in three 2-level atoms,and investigate multipartite quantum correlation distribution in the localization phases of thermalizing multipartite systems.The thesis is composed of three chapters.In Chapter one,we introduced the multipartite quantum correlation based quantum entanglement distribution,steady state correlation in the dissipative dynamics,and many-body localization phenomenon,and so on.In Chapter two,we studied the correlation dynamics in three atoms,and found that the tripartite quantum evolution can be modulated by the initial state and the coupling between individual atoms.Under the non-Markov environment,the tripartite quantum correlation will disappear in finite time,but we can realize the effective steady state modulation by adding the laser pump on individual atoms which results in the steady tripartite quantum correlation in the dissipative dynamics.In Chapter three,we studied the quantum correlation distribution in the evolved state of a one-dimensional disordered XXZ spin chain,where the dynamical properties of quantum correlation distribution are quite different in the thermalization phase and the localization phase in the thermalizing procedure.We find that the initial quantum correlation can be localized on the spins on both ends and the transferred correlation can be localized on the central spins.At the end of this thesis,we summarize our main results on the multipartite steady-state correlation in the dissipative dynamics and the quantum correlation distribution in the thermalizing procedure of the disordered spin chain.