  We analyze equilibrium properties of coupled-doped cavities described by the
Jaynes-Cummings- Hubbard Hamiltonian. In particular, we characterize the
entanglement of the system in relation to the insulating-superfluid phase
transition. We point out the existence of a crossover inside the superfluid
phase of the system when the excitations change from polaritonic to purely
photonic. Using an ensemble statistical approach for small systems and
stochastic-mean-field theory for large systems we analyze static disorder of
the characteristic parameters of the system and explore the ground state
induced statistics. We report on a variety of glassy phases deriving from the
hybrid statistics of the system. On-site strong disorder induces insulating
behavior through two different mechanisms. For disorder in the light-matter
detuning, low energy cavities dominate the statistics allowing the excitations
to localize and bunch in such cavities. In the case of disorder in the light-
matter coupling, sites with strong coupling between light and matter become
very significant, which enhances the Mott-like insulating behavior. Inter-site
(hopping) disorder induces fluidity and the dominant sites are strongly coupled
to each other.
