Quantum fluids of light in all-optical scatterer lattices

One of the recently established paradigms in condensed matter physics is examining a system's behaviour in artificially constructed potentials, giving insight into physical phenomena of quantum fluids in hard-to-reach settings. A prominent example is the matter-wave scatterer lattice, also known as the barrier lattice or repulsive Dirac comb. There, high energy matter waves undergo transmission and reflection through narrow width barriers leading to stringent phase matching conditions with subsequent lattice band formation. It is one of the most well taught system in quantum mechanics but its realisation for macroscopic matter-wave fluids has remained elusive, in contrast to evanescently coupled lattice sites or waveguides. Here, we implement and study a system of exciton-polariton condensates in a non-Hermitian Lieb lattice of scatterer potentials by optically injecting incoherent exciton clouds which both emit, and interact with traveling polariton waves. By fine tuning the lattice parameters, we reveal a nonequilibrium phase transition between two distinct regimes of polariton condensation: a scatterer lattice of gain guided polaritons condensing on the lattice potential maxima, and trapped polaritons condensing in the lattice potential minima. The transition is characterised by multimodal condensation due to gain competition between the two regimes. Energy tomography on the polariton emission enables us to measure the intricate band structure of the optically induced lattices. Our results pave the way towards unexplored physics of non-Hermitian fluids in non-stationary mixtures of confined and freely expanding waves.