Superfluid-Mott transitions and vortices in the Jaynes-Cummings-Hubbard lattices with time reversal symmetry breaking

We investigate the groundstate behaviour of Jaynes-Cummings-Hubbard lattices in the presence of a synthetic magnetic field, via a Gutzwiller ansatz. Specifically, we study the Mott-Superfluid transition, and the formation of vortex lattices in the superfluid regime. We find a suppression of the superfluid fraction due to the frustration induced by the incommensurate magnetic and spacial lattice lengths. We also predict the formation of regime.