Symmetry operators of the asymmetric two-photon quantum Rabi model

TL;DR

This paper introduces a Bogoliubov operator approach to identify symmetry operators in the asymmetric two-photon quantum Rabi model, revealing hidden symmetries linked to observed level crossings.

Contribution

The work develops a hierarchical method to derive symmetry operators in asymmetric Rabi models, including explicit Lie algebra structures at low biases.

Findings

Explicit symmetry operators derived for the asymmetric tpQRM.

Identification of hidden symmetries associated with level crossings.

Potential extension of the method to other asymmetric Rabi models.

Abstract

The true level crossings in a subspace of the asymmetric two-photon quantum Rabi model (tpQRM) have been observed when the bias parameter of qubit is an even multiple of the renormalized cavity frequency. Generally, such level crossings imply the existence of the hidden symmetry because the bias term breaks the obvious symmetry exactly. In this work, we propose a Bogoliubov operator approach (BOA) for the asymmetric tpQRM to derive the symmetry operators associated with the hidden symmetry hierarchically. The explicit symmetry operators consisting of Lie algebra at low biases can be easily obtained in our general scheme. We believe the present approach can be extended for other asymmetric Rabi models to find the relevant hidden symmetry.