Dynamics Of One Photon And Multiphoton Exchange Processes In Quantum Rabi Model

In recent years,with the improvement of various researches,the ultra-strong coupling between quantum bits and photons has been realized.In this case,the rotating-wave approximation(RWA)no longer works,and the dynamical behavior need to be described by the Rabi model.When the coupling between light and matter is enhanced,the interaction system has two-photon exchanges(a process of simultaneously absorbing and releasing two photons)in addition to the well-known process of single-photon exchange.The discovery of this phenomenon makes the intrinsic energy of interaction between light and matter more accurate,and the understanding of the physical mechanism about light-material interaction also be greatly enriched.In this paper,the analytical solutions of single-photon exchange and two-photon exchange in the quantum Rabi model are solved by using the transformed rotating-wave approximation(TRWA),which provides a theoretical basis for the energy spectrum.The results will helpful for the research of circuit quantum electrodynamics.The main research work of this paper is:1.Solve the Rabi model of single photon exchange process by the transformed rotating-wave approximation.Firstly,the system's Hamiltonian are transformed with two unitary operators.The transformed rotating-wave item is introduced in the transformation process,and the high-order approximation is adopted for the hyperbolic sine and hyperbolic cosine.Finally,the Hamiltonian form with similar structure under the rotating-wave approximation method is obtained.By solving the Hamiltonian eigenvalues,the energy level structure of the ground state and several excited states of the system is obtained.2.The quantum Rabi model for two-photon exchange process is solved.Firstly,the transformed rotating-wave approximation is used to preserve the transformed rotating-wave item.Then,selecting the appropriate transform parameters,the Hamiltonian matrix is diagonalized.Finally,the analytic solution of the Hamiltonian is realized,and the system energy spectrum is obtained.This thesis is devoted to the solution of Rabi model describes the strong interaction between quantum bits and the quantized light field.The obtained system energy spectrum is very important for understanding the structure of the quantum Rabi model and its symmetry information.This study can further provide atheoretical basis for the selection of the parameters in quantum light-matter ultra-strong or deep-strong coupling experiments.