Analytical Solutions Of Rabi Model With Two Quantum Qubits

The process of interactions between light and two-level system is a fundamental research target in quantum optics.It was simulated by the Jaynes-Cummings model(J-C model)previously,whereby an amount of important achievements,such as nuclear magnetic resonance,were obtained.However,with the development of quantum system-based experiments and the increasing coupling strength,J-C model has been unable to describe the dynamics of the system accurately.So,it becomes particularly essential to deal with Rabi model and its derivative models.This dissertation introduces two analytical calculating procedure of two-qubit Rabi model with single or double photon exchanging process,and including the following aspects:1.By using Generalized Rotating-Wave Approximation(GRWA)method,the Rabi model of two identical qubits in two-photon exchange was solved analytically.In the process of solving the problem,three main approximate methods were used to transform the Hamiltonian into diagonal blocks in the odd and even subspaces.The analytical expressions of the energy spectrum and eigenstates under super strong coupling were obtained,and the mean photon number was calculated.Comparing with the results of rotating wave approximation,reasons of the differences between the analytical solutions and the numerical simulation were examined.In addition,taking an arbitrary squeezed state as the initial state,the dynamic evolution of the mean value of the total angular momentum in the Z direction by time was calculated,and it was found that the method in this dissertation can describe the dynamic evolution in a certain time.2.Using Transformed Wave approximation(TRWA)method,the analytical solution process of the Rabi model with two qubits with single photon exchange was calculated comprehensively,and the theoretical expressions of energy spectrum and eigenstates were obtained.The theoretical results can not only give the energy spectrum of low energy levels precisely,but also agree well with the results of numerical simulation in high energy levels.The theoretical expression of the ground state wave function was used to calculate the particle number distribution and the results were also in good agreement with the numerical simulation.In this paper,two different models and their respective methods of solving were presented.Conditional constraints and approximate methods to transform the Hamiltonian into a solvable diagonal block matrix in state spaces or subspaces,and the Hamiltonian can be solved by mathematical methods analytically.The results in this paper can provide a theoretical basis for the development of quantum optics.