We study the interplay of geometric frustration and interactions in a non-equilibrium photonic lattice system exhibiting a polariton flat band as described by a variant of the Jaynes-Cummings-Hubbard model. We show how to engineer strong photonic cor
relations in such a driven, dissipative system by quenching the kinetic energy through frustration. This produces an incompressible state of photons characterized by short-ranged crystalline order with period doubling. The latter manifests itself in strong spatial correlations, i.e., on-site and nearest-neighbor anti-bunching combined with extended density-wave oscillations at larger distances. We propose a state-of-the-art circuit QED realization of our system, which is tunable in situ.
We investigate the single-photon transport properties of a one-dimensional coupled cavity array (CCA) containing a single qubit in its central site by coupling the CCA to two transmission lines supporting propagating bosonic modes with linear dispers
ion. We find that even in the nominally weak light-matter coupling regime, the transmission through a long array exhibits two ultra-narrow resonances corresponding to long-lived self-protected polaritonic states localized around the site containing the qubit. The lifetime of these states is found to increase exponentially with the number of array sites in sharp distinction to the polaritonic Bloch modes of the cavity array.
