Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models

TL;DR

This paper explores hidden symmetries in asymmetric quantum Rabi models and related systems, revealing their connection to tunnelling dynamics and conditions for their existence beyond traditional symmetry assumptions.

Contribution

It demonstrates the presence of hidden symmetry in various light-matter models with asymmetry and links it to tunnelling phenomena, expanding understanding of symmetry in quantum systems.

Findings

Hidden symmetry exists in multiple asymmetric light-matter models.

Conditions for the existence of hidden symmetry are identified.

Hidden symmetry is strongly connected to selective tunnelling phenomena.

Abstract

The asymmetric quantum Rabi model (AQRM) has a broken $\mathbb{Z}_2$ symmetry, with generally a non-degenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the $\mathbb{Z}_2$-symmetric quantum Rabi model are recovered, however, without any obvious parity-like symmetry. This unknown "symmetry" has thus been referred to as hidden symmetry in the literature. Here we show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interaction models with an asymmetric qubit bias term. Conditions under which the hidden symmetry exists in these models are determined and discussed. By investigating tunnelling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunnelling.