Parity breaking and scaling behavior in light-matter interaction

The light-matter interaction described by the Rabi model and Jaynes-Cummings (JC) model under local bias fields is investigated by parity breaking as well as the scaling behavior of the ground state. We show that the parity breaking leads to different scaling behaviors in the two models, where the biased Rabi model demonstrates scaling invariance, but the biased JC model behaves in a cusp-like way. Our study helps further understand the rotating-wave approximation and could present more subtle physics than other characteristic parameters for the difference between the two models. More importantly, the scaling behavior is observable using currently available techniques in light-matter interaction.