Excitons in a semiconductor monolayer form a collective resonance that can reflect resonant light with extraordinarily high efficiency. Here, we investigate the nonlinear optical properties of such atomistically thin mirrors and show that finite-range interactions between excitons can lead to the generation of highly non-classical light. We describe two scenarios, in which optical nonlinearities arise either from direct photon coupling to excitons in excited Rydberg states or from resonant two-photon excitation of Rydberg excitons with finite-range interactions. The latter case yields conditions of electromagnetically induced transparency and thereby provides an efficient mechanism for single-photon switching between high transmission and reflectance of the monolayer, with a tunable dynamical timescale of the emerging photon-photon interactions. Remarkably, it turns out that the resulting high degree of photon correlations remains virtually unaffected by Rydberg-state decoherence, in excess of non-radiative decoherence observed for ground-state excitons in two-dimensional semiconductors. This robustness to imperfections suggests a promising new approach to quantum photonics at the level of individual photons.
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