The Dynamics And Quantum Phase Transition In Open And Periodically Driven Systems

Studying the dynamics of a quantum system is a vital issue in the field of quan-tum control which is based on quantum optics and condense matter physics. Because the dynamical characteristic of the quantum many body system directly depends on the quantum phase determined by the ground state structure, the study of the related quan-tum phase transition gives help in understanding the dynamical evolution behavior of the quantum system. On the other hand, periodic driving has become a widely used efficient control strategy, studying the impact of periodic driving on topological phases has been drawn much attention recently. Two main parts are discussed in this thesis, in the first part, we first discuss exact decoherence dynamics of an open two-level quantum system and its decoherence suppression behavior in some certain conditions. We then discuss the quantum phase transition in the open-two level system and explain its physical con-sequence. We also discuss the dynamics in a periodically driven open two-level system and propose an effective method to simulate quantum Zeno and anti-Zeno effect. In the second part, we mainly discuss the topological properties of a periodically driven quantum system. We discuss the novel physical properties in such system with no analogy in the static one. Specifically:In chapter Ⅱ, we discuss the exact decoherence dynamics of a two-level system in-teracting with a vacuum environment. We find that when the quantum system form a bound state with its interacting environment, decoherence of the quantum system would be suppressed. Here, a bound state is a superposition state of the system and its environ-ment in the single excitation space. We present a general condition of forming a bound state.In chapter Ⅲ, we discuss physics behind the formation of a bound state. We find that the formation of the bound state corresponds to the quantum phase transition in the system. At the critical point of forming bound state, the ground state’s property changes qualitatively. We calculate the quantities, such as the ground state energy, entanglement entropy and so on, and confirm that it is a first-order quantum phase transition. The dynamical consequence of such a quantum phase transition is the decoherence suppression of the two-level system. After taking partially the counter-rotating terms, we predict a potential quantum phase transition in the spin-boson model besides the well-known delocalized-localized quantum phase transition.In chapter VI, the dynamics of a periodically driven open two-level system is stud-ied. We find that, via properly modulating, we can control the decoherence dynamics of the quantum system. Specifically, we simulate a controllable dissipative channel for the quantum system using coupled cavities. Via tuning the energy level of the two-level system, we obtain a quantum zeno and anti-zeno-like dynamical behavior.In chapter V, we discuss the topological phases in the periodically driven one-dimension p-wave superconductor. We find that periodic driving changes not only the topological property of the system, but also the symmetries of the system, hence its class. We also discuss that periodic driving can induce long-range interaction in the system, which is a unique property of periodically driven system. As an example, we generated many Majorana modes in a single p-wave superconductor, which would give help in ex-perimentally identifying and detecting Majorana fermions.We hope that this thesis would give some help in understanding the dynamics and quantum phase transition in open and periodically driven quantum system.