Spectral Collapse in the two-photon quantum Rabi model

TL;DR

This paper investigates spectral collapse in the two-photon quantum Rabi model, revealing conditions under which the spectrum transitions from discrete to continuous and analyzing the role of parity and qubit frequency.

Contribution

It demonstrates spectral collapse in the two-photon quantum Rabi model, especially in the degenerate qubit regime, and shows how parity and qubit frequency influence this phenomenon.

Findings

Spectral collapse occurs in the degenerate qubit regime.

Eigenfunctions with well-defined parity can be constructed.

Qubit frequency does not affect the critical point of spectral collapse.

Abstract

Spectral collapse, the transition from discrete to continuous spectrum, is a characteristic in quantum Rabi models. We explore this phenomenon in the two-photon quantum Rabi model in optical phase space and find that, in the so-called degenerate qubit regime, the collapse is similar to that happening in the transition from a quantum harmonic to an inverted quadratic potential with the free-partical potential as transition point. In this regime, it is possible to construct Dirac-normalizable eigenfunctions for the model that show well defined parity. In the general model, we use parity to diagonalize the system in the qubit basis and numerically find that the qubit frequency does not change the critical point where spectral collapse occurs.