  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.
