A unified approach to the nonlinear Rabi models

Abstract

An analytical approach is proposed and applied to study the two-photon, two-mode and intensitydependent Rabi models. By virtue of the su(1,1) Lie algebra, all of them can be unified to the same Hamiltonian with Z2 symmetry. There exist some exact isolated solutions which correspond to eigenstates with finite dimensions. Beyond the isolated solutions, the regular spectrum can be achieved by finding the roots of the G-function. The corresponding eigenstates are of infinite dimension. It is noteworthy that the coefficients of the eigenstates present an exponential decay behavior. The decay rates decrease with the increase of the coupling strength. When the coupling strength tends to the spectral collapse point g → ω/2, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of the novel physics in nonlinear quantum optics.