Emergent Finite Frequency Criticality of Driven-Dissipative Correlated Lattice Bosons

We study dynamical and steady-state dissipative quantum phase transitions of a driven Bose Hubbard model between an incoherent Mott-like insulating phase and a non-equilibrium superfluid. We highlight the crucial role of pumping scheme and the unique features that emerge in the driven- dissipative case as compared to the well known equilibrium quantum criticality. These results might be relevant for the upcoming generation of circuit QED arrays experiments aiming at realizing Mott Insulator of Polaritons and its transition into a nonequilibrium superfluid.