Parity breaking and scaling behavior in light-matter interaction

The light-matter interaction described by Rabi model and Jaynes-Cummings (JC) model is investigated by parity breaking as well as the scaling behavior of ground-state population-inversion expectation. We show that the parity breaking leads to different scaling behaviors in the two models, where the Rabi model demonstrates scaling invariance, but the JC model behaves in cusp-like way. Our study helps further understanding rotating-wave approximation and could present more subtle physics than any other characteristic parameter for the difference between the two models. More importantly, our results could be straightforwardly applied to the understanding of quantum phase transitions in spin-boson model. Furthermore, the scaling behavior is observable using currently available techniques in light-matter interaction.