Hidden Symmetry Operators Of Asymmetric Two-mode Quantum Rabi Model

The interaction between the light field and the two-level system is the most basic research object in quantum optics.Initially,researchers generally used jaynes-Cummings model(J-C model)to simulate and calculate this phenomenon,thus obtaining a series of important discoveries and calculation results.However,with the deepening of quantum optics research,the emergence of more quantum system modes and the conduct of experiments,J-C model has been unable to meet a series of influences caused by the increase of coupling strength,so it cannot accurately describe the dynamic process,so Rabi model and a series of derivative models are introduced.This paper mainly introduces the Rabi model of two-mode asymmetric quantum,and discusses its analytical solution,energy spectrum crossover and hidden symmetry,mainly including the following work:1.Bogoliubov transformation and SU(1,1)Lie algebra are used as methods to study,so as to obtain the energy spectrum by solving the G-function analytically,and compared with the numerical solution,it is found that the results are in good agreement.2.We also discussed the level crossing associated with hidden symmetry,in asymmetric two-mode quantum Rabi model,the level crossing usually occurs in the subspace of q value is different,and when there is a same q space,we find that under the condition of ò=2(?)(nb-na),still exists the phenomenon of level crossing,the intersection of(ò,g)level depends on recursive coefficient fna=0,wna=0,This condition is tested and verified at low energy level.3.In this paper,Bogoliubov transformation method is adopted to deduce the implicit symmetry operator J(0),J(1)of the Rabi model of asymmetric two-mode quantum.