Solution of the two-mode quantum Rabi model using extended squeezed states

TL;DR

This paper introduces an exact solution for the two-mode quantum Rabi model using extended squeezed states, deriving G-functions to analyze its spectrum and spectral collapse phenomena.

Contribution

It provides the first derivation of G-functions for the two-mode quantum Rabi model, revealing spectral properties and conditions for degeneracies.

Findings

G-functions share structure with one- and two-photon Rabi models

Spectrum determined by zeros of G-functions

Spectral collapse occurs at critical coupling

Abstract

The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive $G$-functions for each Bargmann index $q$% . They share a common structure with the $G$-function of the one-photon and two-photon quantum Rabi models. The regular spectrum is given by zeros of the $G$-function while the conditions for the presence of doubly degenerate (exceptional) eigenvalues are obtained in closed form through the lifting property. The simple singularity structure of the $G$-function allows to draw conclusions about the distribution of eigenvalues along the real axis and to understand the spectral collapse phenomenon when the coupling reaches a critical value.