Theoretical Study On Quantum Phase Transition And Topological Properties Of Cavity QED System

Condensed matter physics has been developing for more than half a century,and has made many breathtaking achievements.In recent years,quantum Hall effect has been extended to quantum spin Hall system,three-dimensional topological insulator and strongly correlated electronic system.Strongly correlated multibody system is one of the most important models in condensed matter physics.However,its microscopic properties are difficult to obtain experimentally.Therefore,scholars choose to use artificial models to simulate the related problems in condensed matter physics and have made important breakthroughs in experiments,such as Josephson junction and cold atom experiment bound by optical lattice.There are still some limitations in the observation of smaller scale quantum phenomena,because of the smaller lattice distance of the experimental model and the shorter coherence time.Therefore,a great deal of work has been focused on the simulation of quantum multi-reflection phenomena using coupled cavity array system.In the first chapter,the development of quantum information,theoretical basis of quantum optics,hot issues in quantum information field,and the cavity QED system are introduced.The second chapter introduces the research methods and related theories in this paper.The first part is the adiabatic rejection theory.In the second and third part of this chapter,BH Hamiltonian and quantum phase transition are studied respectively.In the fourth part,the quantum Hall effect and the topological properties are introduced.Chapter 3 is the key chapter of this paper and the main achievement of postgraduate study.Mott-insulation-superfluid phase transition and topological properties with coupled-cavity frequency conversion system.For the two-mode coupled optical cavity system,there is a three-level atom in each cavity.Under the condition of large detuning,the Hamiltonian of system is obtained by adiabatic elimination theory.The Hamiltonian is used to analyzed the phase transition process and topological properties of system,and a model for simulating the topological properties of the system is obtained.Chapter 4 summarizes the research results.In the effective Hamiltonian of the system,the frequency conversion between two-mode optical fields has the nonlinear effect in BH Hamiltonian,and can guide the quantum information process through the parameters of the control system.Alsocan get an effective model which can simulate the topological properties through the BogoliubovValatin transformation.