Superrandiant Quantum Phase Transition In The Open Dicke System

The Dicke model describes a system consisting of multiple two-level atoms interacting with a single-mode light field.The superradiation phenomenon of this model was first discovered by Dicke.Later,the model has been widely studied and applied by researchers.Experimentally,the superradiation quantum phase transition of Dicke model is also realized.However,a real physical system will interact with the environment,that is to say,the experimental implementation of the Dicke model of superradiation quantum phase transition involves the inter-action between the system and the environment.The experiment of traditional research of light field interacting with a two-level atom is only in the case of weak coupling.in recent years,the experiment can make the intensity of the interac-tion of light field with a two-level atom to achieve strong coupling.Therefore,studies on the open Dicke system in the region of the strong coupling character-istics of the output of the light are particularly important.In general,quantum open systems can be studied using standard master equations in weakly coupled regions.In the ultrastrong coupling region,the standard master equation can no longer describe the quantum open system,then the quantum Dressed mas-ter equation can be applied to any coupling strength region.In the ultrastrong coupling region,the traditional second-order correlation function is no longer ap-plicable to describe the statistical characteristics of the output light.According to the input-output theory,the improved second-order correlation function can be used to measure the statistical characteristics of the output light.At first,we calculate the eigenstates and eigenvalues of Dicke model by using the Fock state approximation method and the extended coherent state approximation method,and study the dynamical characteristics of the closed Dicke model.Finally,we numerically calculate the two-photon correlation functions of different coupling intensity regions,different atomic numbers,and different thermal reservoir tem-peratures to discuss the statistical characteristics of the output light of the open Dicke system.In the first chapter of this thesis,we introduce the statistical characteris-tics of light in quantum optics,quantum dissipation theory,and the research background and significance of superradiation quantum phase transition theory.In the second and third chapters,we mainly introduce the quantization of electromagnetic fields and the important model in the interaction between light and matter:Rabi model,Jaynes-Cummings model,and Dicke model.We mainly introduce the Dicke model,using the Fock state approximation and the extended coherent photonics states approximation to solve the eigenstates and eigenvalues of the Dicke model,and analyze the dynamical characteristics of the closed Dicke model.In chapter 4,we discuss the standard master equations commonly used in quantum open theory.The derivation process of the standard master equation is given.The standard master equation applies only when the coupling between the optical field and the two-level atom is weak.We also discuss the quantum dressed master equation applicable to the arbitrary coupling strength region.In chapter 5,we discuss the function which is used to measure the statis-tical characteristics of the output light quantum coherence.we first introduce the traditional definition of second-order correlation function and the traditional definition of input-output theory,the traditional definition of second-order corre-lation function and the traditional definition of input-output relationship is only for light field with a two-level atom coupling strength is weak.Therefore,we also discuss the improved second-order correlation functions and input-output theory.The improved situation is applicable to arbitrary coupling strength.In chapter 6,based on the discussion in chapter 5,we analyze the statistical characteristics of the output light of the open Dicke system,numerically solve the two-photon correlation functions of different coupling intensity regions,different atom numbers and different heat reservoir temperatures,and draw a conclusion.Finally,the conclusion and prospect are put forward in chapter 7.