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 three-dimensional $XY$ universality class, analogous to the Bose-Hubbard model.

• Received 4 June 2011

DOI:https://doi.org/10.1103/PhysRevA.84.041608