Theoretical Research On Photon Statistics Driven By Quantum Phase Transition

The interaction between light and matter is one of the most foundmental processes in nature,which forms the basis for our understanding of various physical phenomena.Jaynes-Cummings(JC)model and Rabi model are the core models in describing the interaction of two-level systems with light fields.We firstly study the basic cavity quantum electrodynamic system formed by the interaction of a single-mode electromagnetic resonator and a two-level system.In recent years,a new platform for quantum simulation has emerged,which is used to realize the model which consists of a single cavity quantum electrodynamic system with the interaction of an atomic system and a light field in lattice.At present,there have been some researchers using the JC lattice model to study the phase transition from the Mott insulating phase to the superfluid phase.We will proceed to consider some properties of the phase transition issues of these lattice models in this thesis.In this thesis,we use the mean field approximation and an iterative method.Starting from the basic JC model and Rabi model,we study the two photon statistical behaviors of the JC lattice model and the Rabi lattice model: The quantum phase transition of Mott insulator phase to superfluid phase and the behavior of light bunchingantibunching,and consider the effect of Kerr nonlinear on quantum phase transition and photon statistical characteristics.Subsequently,we study the influence of the rotating wave term on the Rabi lattice model,as well as the steady-state solution of the Rabi lattice model in the open system.The thesis is mainly divided into the following chapters:In chapter 1,we briefly introduce the research background of JC model,Rabi model,and mean field theory.We obtain the analytical solution of the JC model and the numerical solution of the two types of models,and then obtain their energy spectrum based on the numerical solutions.At the same time,we solve the simple model using the mean field theory with only light fields,which lays the foundation for the JC lattice model and the Rabi lattice model in the next chapter.In chapter 2,we study the JC lattice model and the Rabi lattice model.We have studied the quantum phase transition of the Mott insulator phase-superfluid phase and the light bunching-antibunching behavior of the two models.The results show that the increase of the two-level atom and photon interaction strength and photon in the Rabi lattice model and the increase of the photon transition intensity between the lattice points will cause the lattice system to transform from the Mott insulator phase to the superfluid phase,and at the same time,the photon statistical behavior will change from bunching to anti-bunching.In chapter 3,we use the method introduced in the second chapter to study the influence of the Kerr nonlinear term on the quantum phase transition and photon statistical behavior of the JC lattice model and the Rabi lattice model.We find that the Kerr nonlinear term has an restrained effect on the superfluid phase.The JC lattice model does not have the transition from bunching to anti-bunching,while for the Rabi lattice model,the Kerr nonlinear intensity has a tendency to the generation of photon anti-bunching.This shows that the Kerr nonlinear term can produce effective photon-photon repulsion between photons.In Chapter 4,we study the phase transitions of the Rabi lattice model without rotating-wave terms and the anisotropic Rabi lattice model.This part is the expansion of the Rabi lattice model,and we use it to study the influence of the rotating-wave term on the Rabi lattice model.In the last Chapter,we study the steady-state solution of the Rabi lattice model in the open system.We use the density operator to characterize the state of the system,convert the density operator of the Hamiltonian from the Schr(?)dinger picture to the interaction picture,then take the Born approximation and Markov approximation,and finally return to the Schr(?)dinger picture.Finally,we get the steady-state solution of the Rabi lattice model in the open system.We extend the Rabi lattice model from a closed system to an open system,laying a solid foundation for our future research on quantum phase transitions of the Rabi lattice model.