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Moir\'e excitons promise a new platform with which to generate and manipulatehybrid quantum phases of light and matter in unprecedented regimes ofinteraction strength. We explore the properties in this regime, through studiesof a Bose-Hubbard model of excitons coupled to cavity photons. We show that thesteady states exhibit a rich phase diagram with pronounced bi-stabilitiesgoverned by multi-photon resonances reflecting the strong inter-excitoninteractions. In the presence of an incoherent pumping of excitons we find thatthe system can realise one- and multi-photon lasers.

Moir\'e-induced optical non-linearities: Single and multi-photon resonances