Hidden symmetry and tunneling dynamics in asymmetric quantum Rabi models

The asymmetric quantum Rabi model (AQRM) has a broken Z2 symmetry, with generally a nondegenerate eigenvalue spectrum. In some special cases where the asymmetric parameter is a multiple of the cavity frequency, stable level crossings typical of the Z2-symmetric quantum Rabi model are recovered, however, without any obvious paritylike 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 tunneling dynamics in the displaced oscillator basis, a strong connection is found between the hidden symmetry and selective tunneling.