Spectral collapse in two-mode two-photon Rabi model

Abstract

We have investigated the eigenenergy spectrum of the two-mode two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in an isotropic two-dimensional ”Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with an isotropic two-dimensional potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored straightforwardly.