Insulator to superfluid transition in coupled photonic cavities in two dimensions

A system of coupled photonic cavities on a two-dimensional square lattice is systematically investigated using the stochastic series expansion quantum Monte Carlo method. The ground state phase diagram contains insulating phases with integer polariton densities surrounded by a superfluid phase. The finite-size scaling of the superfluid density is used to determine the phase boundaries accurately. We find that the critical behavior is that of the generic, density-driven Mott-superfluid transition with dynamic exponent $z=2$, with no special multicritical points with $z=1$ at the tips of the insulating-phase lobes (as exist in the case of the Bose-Hubbard model). This demonstrates a limitation of the description of polaritons as structureless bosons.