Spectral collapse in mixed Rabi model

In this paper we have conducted a simple variational study of the ground state of the mixed Rabi model, namely the variant of the Rabi model with both one-photon and two-photon couplings of light-matter interaction. We have shown how the spectral collapse occurs beyond the critical value of the two-photon coupling. Our analysis also indicates that the upper bound of the ground-state energy approaches negative infinity as the two-photon coupling strength increases towards the critical value. This special feature is clearly generated by the one-photon coupling and disappears in the absence of the one-photon process. Likewise, we have investigated the eigenenergy spectrum of the mixed Rabi model near the critical coupling. It is found that the energy spectrum essentially consists of a continuum and some discrete energy levels below it. Indeed, it is reminiscent of the incomplete spectral collapse of the two-photon Rabi model. (c) 2022 Elsevier B.V. All rights reserved.