Polariton lattices for quantum simulation

Coupled micropillars etched in semiconductor microcavities are an excellent platform to engineer the properties of exciton-polaritons. Thanks to the direct optical access characteristic of polaritons, these etched structures can be used to simulate various solid-state hamiltonians. Here we will show a hexagonal structure in which we engineer a spin-orbit coupling for polaritons. The coupling is evidenced via the spontaneous formation of polarization vortices when polaritons condense. When extended to a honeycomb lattice we report the direct observation of Dirac cones and a non-dispersive band, i.e., a flatband. Our structure is thus very promising for the study of anomalous transport and disorder in massless particles, and the strongly correlated phases expected in flatbands.