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Moir\'e lattices formed from semiconductor bilayers host tightly localisedexcitons that can simultaneously couple strongly to light and possess largeelectric dipole moments. This facilitates the realization of new forms ofpolaritons that are very strongly interacting and that have been predicted tolead to strong optical nonlinearities controlled by multi-photon resonances.Here, we investigate the role of the non-local component of the exciton-exciton(dipolar) interactions on the optical response of these strongly-interactingmoir\'e exciton-polaritons under conditions of strong optical driving. We findthat the non-local interactions can strongly influence the steady-stateproperties leading to multi-stabilities with broken translational symmetry andpronounced distortions of the multi-photon resonances. We develop aself-consistent approach to describe the steady-state solution of moir\'eexcitons coupled to a cavity field, treating the long-range interaction betweenthe excitons and the photon field at the semi-classical level.

Optical non-linearities and spontaneous translational symmetry breaking in driven-dissipative moir\'e exciton-polaritons