General symmetry operators of the asymmetric quantum Rabi model

TL;DR

This paper develops a systematic method to derive symmetry operators in the asymmetric quantum Rabi model, revealing hidden symmetries linked to level crossings and extending understanding of its spectral properties.

Contribution

The authors introduce a hierarchical Bogoliubov operator approach to explicitly construct symmetry operators for arbitrary multiples in the asymmetric quantum Rabi model, unifying and extending previous results.

Findings

Derived symmetry operators for arbitrary multiples

Reproduced known symmetry operators for small multiples

Defined a general parity operator encompassing the symmetric case

Abstract

The true level crossing in the asymmetric quantum Rabi model without any obvious symmetry can be exhibited in the energy spectrum if the qubit bias is a multiple of the cavity frequency, which should imply the existence of the hidden symmetry. In this work, within a Bogoliubov operator approach, we can readily derive the symmetry operators associated with the hidden symmetry hierarchically for arbitrary multiples. The symmetry operators for small multiples in the literature can be extremely easily reproduced in our general scheme. In addition, a general parity operator is defined through the symmetry operator, which naturally includes the well-known parity operator of the symmetric model. We believe that the present approach can be straightforwardly extended to other asymmetric Rabi models to find the relevant symmetry operators.