Critical spectrum of the anisotropic two-photon quantum Rabi model

TL;DR

This paper analyzes the anisotropic two-photon quantum Rabi model, revealing spectral collapse, quantum phase transitions, and the existence of bound states using analytical methods, thus resolving longstanding issues in the model.

Contribution

It provides a rigorous analytical study of the spectral properties and phase transitions in the anisotropic two-photon quantum Rabi model, including conditions for spectral collapse and bound state existence.

Findings

Identification of doubly degenerate exceptional states

Derivation of conditions for spectral collapse and continuous spectrum

Discovery of bound state regimes dependent on anisotropy and atomic frequencies

Abstract

The anisotropic two-photon quantum Rabi model is studied using the Bogoliubov operator approach. The doubly degenerate exceptional states are identified through analytical methods. By adjusting the position of the last exceptional point belonging to two adjacent energy levels, we derive a condition for the absence of the discrete spectrum at the critical coupling where ``spectral collapse" occurs. In this special case, the spectrum becomes fully continuous above a threshold energy, with no bound states existing, whereas the ground state remains gapped in the general case. This also signals a quantum phase transition. More interestingly, we rigorously find that a finite number of bound states exist between two anisotropy dependent critical atomic frequencies, with infinitely many bound states beyond this frequency regime. In this manner, all issues in the two-photon quantum Rabi model are resolved.