Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model

TL;DR

This paper reveals hidden symmetries in the asymmetric two-photon quantum Rabi model by analyzing level crossings and degeneracies, highlighting differences from the one-photon case and uncovering new spectral properties.

Contribution

It uncovers the existence of hidden symmetries in the asymmetric two-photon QRM through analysis of level crossings and degeneracies, expanding understanding of spectral structures.

Findings

Double degeneracy indicates hidden symmetry in the model.

Number of crossing points is comparable to the one-photon QRM.

Bias parameters for level crossings differ from the one-photon case.

Abstract

In this paper, we uncover the elusive level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Due to the absence of any explicit symmetry in the subspace, this double degeneracy implies the existence of the hidden symmetry. The non-degenerate exceptional points are also given completely. It is found that the number of the doubly degenerate crossing points in the asymmetric tpQRM is comparable to that in asymmetric one-photon QRM in terms of the same order of the constrained conditions. The bias parameter required for occurrence of level crossings in the asymmetric tpQRM is characteristically different from that at a multiple of the cavity frequency in the asymmetric one-photon QRM, suggesting the different hidden symmetries in the two asymmetric QRMs.