Hidden symmetry in the biased Dicke model

Abstract

The symmetry operators generating the hidden ${\mathbb{Z}}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) at bias $\epsilon \in \frac{1}{2}\mathbb{Z}$ have recently been constructed by V. V. Mangazeev et al. [J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to determine symmetry operators for the $N$-qubit generalisation of the AQRM, also known as the biased Dicke model, at special biases. We also prove for general $N$ that the symmetry operators, which commute with the Hamiltonian of the biased Dicke model, generate a ${\mathbb{Z}}_2$ symmetry.

arXiv comment15 pages, 1 figure, minor changes

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• Symmetry operators of the asymmetric two-photon quantum Rabi model
• Anisotropic Rabi model with two-photon relaxation
• Quantum Multicritical Behavior for Coupled Optical Cavities with Driven Laser Fields
• Enhanced charging in open Rabi and Dicke quantum batteries