  We theoretically investigate the strange phenomenon of attraction between the
cavity mode and the exciton mode that has been experimentally observed in a
photonic crystal cavity. Our results within the Lindblad master equation
approach successfully explain why the apparent cavity-to-exciton spectral
shifting occurs, and how this phenomenon is a manifestation of a dynamical
phase transition in the system. Moreover, our findings are in good qualitative
agreement with pioneer experimental results as well as support the hypothesis
that an intermediate coupling regime exists in the cavity quantum
electrodynamics. In fact, this new quantum regime exhibits phenomenology from
both weak and strong coupling regimes simultaneously.
