The quantum Rabi model (QRM) is the simplest as well as the most important model to describe the interaction between light and matter. The QRM has parity symmetry, which admits level crossings in its eigenspectrum. In the asymmetric version of the QRM (AQRM), this parity symmetry is broken. As a result, the eigenvalue spectrum of the AQRM is generally non-degenerate. In some special cases where the asymmetric parameter is a multiple of the light frequency, the stable level crossings are recovered, still without any obvious symmetry. This unknown parity-like "symmetry" is thus referred to as hidden symmetry in the literature.

This talk will be split into two parts. Firstly, I will show that this hidden symmetry is not limited to the AQRM, but exists in various related light-matter interacting models with an asymmetric term. Conditions under which the hidden symmetry exists in these models are determined. I will discuss these conditions in detail. By investigating tunnelling dynamics in the displaced oscillator basis, we find a strong connection between the hidden symmetry and selective tunnelling. In the second part, I will discuss the challenges and potential applications regarding this hidden symmetry. Considerable effort has been devoted by many researchers to developing approximation schemes for the light-matter interaction models. Unfortunately, current approximating approaches are not accurate enough to reproduce the hidden symmetry in the AQRM. To address this problem, we have been working on developing a precise description of the AQRM eigenspectrum. I will report our progress in this project.

This talk is partly based on a joint work with Devid Ferri and Murray Batchelor, arXiv:2006.08913.

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