Unified approach to the nonlinear Rabi models

An analytical approach is proposed to study the two-photon, two-mode and intensity-dependent Rabi models. By virtue of the su(1, 1) Lie algebra, all of them can be unified to the same Hamiltonian with Z(2) symmetry. There exist exact isolated solutions, which are located at the level crossings between different parities and correspond to eigenstates with finite dimension. Beyond the exact 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 expansion coefficients of the eigenstates present an exponential decay behavior. The decay rate decreases with increasing coupling strength. When the coupling strength tends to the spectral collapse point g -> omega/2, the decay rate tends to zero which prevents the convergence of the wave functions. This work paves a way for the analysis of novel physics in nonlinear quantum optics.

Automated summary

An analytical approach is proposed to study the two-photon, two-mode, and intensity-dependent Rabi models and unify them with Z(2) symmetry. Exact isolated solutions and regular spectrum are found, showing the characteristics and decay behavior of eigenstates. This work paves the way for the analysis of novel physics in nonlinear quantum optics.