A collaboration of the Simon and Schuster groups at the University of Chicago MRSEC have realized a photonic strongly interacting Mott insulator using a 1D lattice of superconducting qubits (see figure). A key difference between photonic and electronicmaterials is that photon number is not conserved. We have developed dissipative stabilization protocols which can stabilize incompressible phases, including the Mott insulator.