  We explore the phase diagram of the dissipative Rabi-Hubbard model, as could
be realized by a Raman-pumping scheme applied to a coupled cavity array. There
exist various exotic attractors, including ferroelectric, antiferroelectric,
and inccomensurate fixed points, as well as regions of persistent oscillations.
Many of these features can be understood analytically by truncating to the two
lowest lying states of the Rabi model on each site. We also show that these
features survive beyond mean-field, using Matrix Product Operator simulations.
