Research On PT Symmetry Rabi Model And Nonlinear Photonic Graphene

In the past two decades,the study of parity-and time-reversal(PT)symmetric quantum mechanics has attracted much attention,because it changed people’s views on non-Hermitian quantum mechanics.The traditional quantum mechanics told us only the Hermitian systems had real eigenvalues,which corresponded to observed physical quantities.The PT-symmetric quantum mechanics makes one realize that non-Hermitian quantum systems can have real eigenvalues and extends the Hamiltonians of observable physical systems from the real domain to the complex domain,which has a great contribution to the development of quantum mechanics.The Rabi model is one of the most basic models in quantum optics.Although that model has been studied in detail,it is mainly focused on the Hermitian systems.The in-depth research on the non-Hermitian Rabi models is necessary.Therefore,the Rabi model with PT-symmetry is studied in this thesis,which is a special non-Hermitian two-level system.The first part of this thesis mainly investigated the analytical solutions for generalized PT-symmetric Rabi models.Firstly,we briefly described the properties of PT-symmetric quantum systems and how to implement PT-symmetric quantum systems based on optical systems.Then we gave out the generalized PT-symmetric Rabi model and used three kinds of confluent Heun functions to solve the analytical solutions of the generalized PT-symmetric Rabi models driven by external fields with monochromatic periodic,linear,and parabolic forms,respectively.The related research has an important significance for understanding the properties of the PT-symmetric Rabi models.In this thesis,the nonlinear photonic graphene filled with Rydberg atoms is also studied.Thouless,Haldane,and Kosterlitz won the Nobel Prize in Physics 2016 for the discoveries of the topological phase and topological phase transitions of matter.Topological photonics mainly concentrates on the global properties of the photon wave functions of the periodic optical structures in the dispersive region,and discovers new photon states and corresponding potential applications.The current researches mainly focuse on linear systems.When nonlinear effects are introduced into topological photonics,the systems may appear noval phenomena.There is a long-range dipole-dipole interaction between Rydberg atoms,which can be used to construct tunable and nonlocal linear and nonlinear optical effects by filling the Rydberg atoms into different regions.The second part of this paper investigated the topological properties of the photonic states in periodic optical systems with nonlocal linear and nonlinear optical effects.This will promote the study of the topological properties of nonlinear periodic optical systems.