The hidden symmetry of the asymmetric quantum Rabi model

TL;DR

This paper uncovers a hidden symmetry in the asymmetric quantum Rabi model by explicitly constructing commuting operators at special bias values, explaining observed level crossings in its spectrum.

Contribution

It explicitly constructs operators that reveal the hidden symmetry in the AQRM at specific bias values, advancing understanding of its spectral properties.

Findings

Identifies the origin of level crossings in AQRM.

Constructs explicit operators commuting with the Hamiltonian.

Applicable to related light-matter interaction models.

Abstract

The asymmetric quantum Rabi model (AQRM) exhibits level crossings in the eigenspectrum for the values $\epsilon\in\frac{1}{2}\mathbb{Z}$ of the bias parameter $\epsilon$. Such level crossings are expected to be associated with some hidden symmetry of the model. The origin of this hidden symmetry is established by finding the operators which commute with the AQRM hamiltonian at these special values. The construction is given explicitly for the first several cases and can be applied to other related light-matter interaction models for which similar level crossings have been observed in the presence of a bias term.