Optical signatures of Mott-superfluid transition in nitrogen-vacancy centers coupled to photonic crystal cavities

We study the phenomenon of controllable localization-delocalization transition in a quantum many-body system composed of nitrogen-vacancy centers coupled to photonic crystal cavities, through tuning the different detunings and the relative amplitudes of two optical fields that drive two nondegenerate transitions of the $\Lambda $-type configuration. We not only characterize how dissipation affects the phase boundary using the mean-field quantum master equation, but also provide the possibility of observing this photonic quantum phase transition (QPT) by employing several experimentally observable quantities, such as mean intracavity photon number, density correlation function and emitted spectrum, exhibiting distinct optical signatures in different quantum phases. Such a spin-cavity system opens new perspectives in quantum simulation of condensed-matter and many-body physics in a well-controllable way.