  An array of high-Q electromagnetic resonators coupled to qubits gives rise to
the Jaynes-Cummings-Hubbard model describing a superfluid to Mott insulator
transition of lattice polaritons. From mean-field and strong coupling
expansions, the critical properties of the model are expected to be identical
to the scalar Bose-Hubbard model. A recent Monte Carlo study of the superfluid
density on the square lattice suggested that this does not hold for the
fixed-density transition through the Mott lobe tip. Instead, mean-field
behavior with a dynamical critical exponent z=2 was found. We perform
large-scale quantum Monte Carlo simulations to investigate the critical
behavior of the superfluid density and the compressibility. We find z=1 at the
tip of the insulating lobe. Hence the transition falls in the 3D XY
universality class, analogous to the Bose-Hubbard model.
