On the Origin of the Hidden Symmetry in the Asymmetric Quantum Rabi Model

TL;DR

This paper uncovers the origin of hidden symmetry in the asymmetric quantum Rabi model, showing it arises from energy-level matching in an asymmetric double-well potential, especially in the strong-coupling regime where the two-level splitting greatly exceeds the mode frequency.

Contribution

It identifies the physical origin of the hidden symmetry using diagonalization methods and explores its implications for energy levels and phase transitions in the model.

Findings

Hidden symmetry results from energy-level matching in an asymmetric double-well potential.

Emergence of an excited-state quantum phase transition related to symmetry breaking and restoration.

Deeper understanding of the strong-coupling regime where the two-level splitting dominates.

Abstract

The introduction of an asymmetric term into the quantum Rabi model generally lifts energy-level degeneracies. However, when the asymmetry parameter takes specific multiples of the bosonic mode frequency, level degeneracies reappear$-$a phenomenon referred to as the hidden symmetry in the asymmetric quantum Rabi model. Identifying the origin of this hidden symmetry and its explicit operator form constitutes two central tasks in studying this system. Here, we investigate the origin of this hidden symmetry using the method of two successive diagonalizations, with a focus on physics in the regime where the ratio between the two-level splitting $\Delta$ and the mode frequency $\omega$ satisfies $\Delta/\omega \gg 1$. We find that the hidden symmetry stems from energy-level matching within the asymmetric double-well potential, a picture strongly supported by the wavefunctions of both the ground and excited states. Moreover, the emergence of an excited-state quantum phase transition is identified and qualitatively discussed, which arises from the breaking and restoration of this hidden symmetry across different coupling regimes. Our results provide deeper insight into the physics of the asymmetric quantum Rabi model, particularly in the previously less-explored strong-coupling regime where $\Delta/\omega \gg 1$.