Equilibrium and disorder-induced behavior in quantum light-matter systems

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.