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.