Degenerate Perturbation Method To Solve The Rabi Model

In recent decades, with the technology of laser cooling and trapping of neutral atoms matures, cavity quantum electrodynamics rapid developments. Cavity quantum electrodynamics main studies the interaction of electromagnetic fields and material in a cavity. Cavity quantum electrodynamics finds many new physical phenomena, such as, the collapse and recovery phenomena of the atoms、 Rabi oscillations in the strong coupling condition and Casimer effects. In cavity quantum electrodynamics, the simplest and most classic model is a model of the interaction of laser and a two-level atom. This paper main researches the interaction of a single-mode field with a two-level atom, i.e. Rabi model. In this paper we propose a new method to solve the energy spectrum and wave function of the Rabi model. This paper consists of three parts:A brief review of the development of quantum electrodynamics, introducing the development and the application of cavity quantum electrodynamics, describing the interaction of cavity with atoms, discussing the semi-classical theory and the quantum theory of the interaction of the cavity with a two-level atom, and thus we propose the Rabi model.In the circuit QED system, we derive the Hamiltonian of the Rabi model, starting from the superconducting charge qubit, a brief introduction to the work principle of the superconducting charge qubit, and derivation of the Hamiltonian of superconducting charge qubit and superconducting transmission line resonator, analysis of the situation of the superconducting charge qubit and superconducting transmission line resonator coupling, then we derive the Hamiltonian of the Rabi model.In the light of the feature of the energy degeneracy, this paper proposes the degenerate perturbation method to solve the Rabi model and after derivation we obtain the energy spectrums and wave functions of the Rabi model. The derived energy spectrums agree well with the direct numerical simulation in a certain range of the experimental parameters. This method has a guiding sense to solve the energy levels of the Rabi model, and is benefit for further considering the application of the Rabi model.