  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.
