The Dynamics And Bound State In Open Quantum System

Microscopic system inevitably interacts with its environment and becomes an open system. The decoherence of the open quantum system induced by this inter-action is a major reason for the dramatic differences of the quantum-mechanical phenomena in microscopic world from the classical ones in macroscopic world. It is also a crucial point of the incessant debates on the basic explanations of quan-tum theory. Recently, the renewed interest in decoherence of the open system originates from the recognition that the decoherence is one of the main obstacles to the practical realization of quantum information processing. Therefore, how to evaluate the destructive effects of decoherence on quantum information processing and how to design efficient strategy to suppress these unwanted effects are impor-tant problems in the field of quantum control. In this thesis, we propose a method to understand the decoherence dynamics of open quantum system by studying the energy spectrum of the composite system consisted of the quantum system and its environment. We find that, with the formation of a localized bound state in the composite system, the decoherence of the open system shows a substantial difference. We will focus on several models in open quantum system to reveal this conclusion. Through theoretical derivations and numerical calculations, the firm correspondence between different characteristics of the decoherence dynamics and the possibility of forming the bound state will be established.First, we will study the sub-Ohmic spin-boson model. Under the rotating-wave approximation, it is found that, with the increase of the coupling strength between the system and the environment, the decoherence of the system shows a counterintuitive slowdown behavior, which we call as anomalous decoherence. Further study on the energy spectrum of the composite system reveals that the anomalous decoherence is a dynamical consequence of a novel quantum phase transition (QPT) induced by the formation of a bound state of the composite system. Then we extend our results to the case without the rotating-wave ap-proximation. Using the perturbation approach based on unitary transformation, We find that the bound state still exists, and the formation of the bound state leads also to a novel QPT, which is different from the conventional delocalized-localized one in the spin-boson model. Due to this novel QPT, the nonequilibrium dynamics of the spin system shows the similar anomalous behavior as the case un-der the rotating wave approximation. Our dynamical results are compatible with the well-known coherent-incoherent transition in this model. It demonstrates that the previously well-known coherent-incoherent transition is essentially caused by the intrinsic QPT of the model, which greatly enriches our understanding to this model.Next, we will study an extended inhomogeneous Dicke model, in which both the excitation energies of the two-level atoms and the coupling strength between the atoms and the cavity field depend on the individual atoms. Our study on the dynamics of the cavity field shows that with the change of inhomogeneity, the nonequilibrium dynamics show rich behaviors, for example, an exponential decaying to zero, a damped oscillation to a finite value, or even a lossless periodic oscillation. Further study reveals that these behaviors correspond respectively to no bound state, one bound state, and two bound states are formed in the composite system. We also show that the formation of the bound state can also lead to the superradiant QPT. At last, a method to evaluate the long-time steady-state behavior is proposed according to our bound state theory, which fits well with the numerical simulation. Our results suggest a scheme to realize the superradiant QPT and different dynamical behaviors by manipulating the inhomogeneities of the Dicke model.At last, we will study the quantum speed limit time and the non-Markovianity in a damped multimode J-C model. The quantum speed limit time is defined as the minimal time of a microscopic system under the external disturbances which is needed to evolve between two distinguishable states. Previous studies show that non-Markovian effect in the open quantum system is responsible for the quantum speedup. We find here that both the quantum speedup and the non-Markovianity originate from the formation of a bound state of the composite system. This gives a mechanism explanation to the physical reason of quantum speedup and non-Markovianity. An experimentally accessible scheme in cavity quantum electrodynamics (QED) platform is proposed for potentially testifying our prediction. Our results suggest a way to describe the physical mechanism of quantum speedup by studying the energy spectrum of the composite system, and would expectedly enrich the related research methods and research results.In this thesis, some interesting results are obtained. We hope these results can contribute to the understanding of open quantum system dynamics.