Quantum Phase Transitions And Dynamics Of Several Spin-Boson Interacting Systems

In this Ph.D thesis, the quantum properties of a few spin-boson interacting systems without the rotating wave approximation in the strong coupling regime are studied. Some effective analytic and numerical methods are developed and applied to study energy spectrum, quantum phase transitions and dynamical properties of these systems, such as effects of CRTs on the vacuum rabi splitting effect for a two-level systems (TLS) interacting with single quantized field ( Rabi model), multi-body entanglement of TLSs coupling to single quantized field (Dicke model), ground state phase transition of one-dimensional Dicke lattice and Zeno-anti-Zeno transition in a TLS interacting with its environment. The main progress has been achieved in the following1. We propose a first-order correction to the rotating wave approximation(RWA) by considering the leading terms of the CRTs and derive a simple analytical results for the eigenenergies and eigenfunctions of Rabi model, which we denote as correction to RWA (CRWA). Excellent agreement with numerical exact results is achieved up to the coupling regime accessible in the modern experimental setups. The Rabi splitting effect is re-studied using CRWA. A novel correction on intensities of two leading transition processes is observed compared to RWA results. Finally, the absence of the collapse in the dynamics of atomic population inversion in the strong coupling regime is explained by CRWA results thanks to the oscillations resulting from the transitions through leading CRTs covered by this framework.2. The finite N-Dicke model of arbitrary number of two-level atoms is solved analytically in a unified way within extended coherent states. The G-function, which is only energy de-pendent function is derived and exact full eigenspectrum is obtained by searching the root of the G-function. The level distribution controlled by the pole structure of the G-functions suggests non-integrability for N> 1 model at any finite coupling in the sense of recent criteria found in the literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite N-Dicke model is presented using the obtained exact solutions3. The quantum phase transition of the Dicke-Hubbard model is studied by using matrix prod-uct state method combined with optional basis and displaced Fock state. The phase dia-gram describing coherent-incoherent transition is obtained. A novel phenomena which is quite different from that under RWA are observed due to the breakdown of U(1) symme-try through introducing CRTs. Cooperative effect of collective excitations, originated from superreliance effect, to the coherent photonic phase is further observed. Finally, the tem-poral and spacial correlation properties of light in both coherent and incoherent phase are studied. The nonequilibrium steady state phase transition of the dissipative Dicke-Hubbard model is further studied under mean-field theory. A coherent-incoherent phase transition is observed,similar to the quantum phase transition,where the coherent phase demonstrates an isolated-island pattern in the phase diagram.4. We study the quantum Zeno-anti Zeno transition of an open quantum system through a two level atom interacting with its environment. By applying a numerically exact method based on the matrix product state, the previous picture for the quantum Zeno-anti Zeno transition has been modified. We further remove the previous assumption that the state is projected on the initial qubit and state of the environment remains unchanged in the repetitive measure-ments. This leads to a net evolution of the environment,rendering a system-environment correlation exect in the repetitive measurement process. A significant decay rate of the sys-tem's survival probability is observed due to this correction.