We report on the engineering of a non-dispersive (flat) energy band in a geometrically frustrated lattice of micro-pillar optical cavities. By taking advantage of the non-hermitian nature of our system, we achieve bosonic condensation of exciton-polaritons into the flat band. Due to the infinite effective mass in such band, the condensate is highly sensitive to disorder and fragments into localized modes reflecting the elementary eigenstates produced by geometric frustration. This realization offers a novel approach to studying coherent phases of light and matter under the controlled interplay of frustration, interactions and dissipation.

We study the coherence and fluorescence properties of the coherently pumped and dissipative Jaynes-Cummings-Hubbard model describing polaritons in a coupled-cavity array. At weak hopping we find strong signatures of photon blockade similar to single-cavity systems. At strong hopping the state of the photons in the array depends on its size. While the photon blockade persists in a dimer consisting of two coupled cavities, a coherent state forms on an extended lattice, which can be described in terms of a semiclassical model.

We study the nonequilibrium steady state of the driven-dissipative Bose-Hubbard model with Kerr nonlinearity. Employing a mean-field decoupling for the intercavity hopping J, we find that the steep crossover between low and high photon-density states inherited from the single cavity transforms into a gas-liquid bistability at large cavity-coupling J. We formulate a van der Waals like gas-liquid phenomenology for this nonequilibrium setting and determine the relevant phase diagrams, including a new type of diagram where a lobe-shaped boundary separates smooth crossovers from sharp, hysteretic transitions. Calculating quantum trajectories for a one-dimensional system, we provide insights into the microscopic origin of the bistability.

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 correlations 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 nearestneighbor 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 study a dissipative Kerr-resonator subject to both single-and two-photon detuned drives. Beyond a critical detuning threshold, the Kerr resonator exhibits a semiclassical first-order dissipative phase transition between two different steady-states, that are characterized by a π phase switch of the cavity field. This transition is shown to persist deep into the quantum limit of low photon numbers. Remarkably, the detuning frequency at which this transition occurs depends almost-linearly on the amplitude of the single-photon drive. Based on this phase switching feature, we devise a sensitive quantum transducer that translates the observed frequency of the parametric quantum phase transition to the detected single-photon amplitude signal. The effects of noise and temperature on the corresponding sensing protocol are addressed and a realistic circuit-QED implementation is discussed.