We investigate the interaction of weak light fields with two-dimensional lattices of atoms, in which two-photon coupling establishes conditions of electromagnetically induced transparency and excites high lying atomic Rydberg states. This system features different interactions that act on disparate length scales, from zero-range defect scattering of atomic excitations and finite-range dipole exchange interactions to long-range Rydberg-state interactions that span the entire array. Analyzing their interplay, we identify conditions that yield a nonlinear quantum mirror which coherently splits incident fields into correlated photon-pairs in a single transverse mode, while transmitting single photons unaffected. Such strong photon-photon interactions in the absence of otherwise detrimental photon losses in Rydberg-EIT arrays opens up a promising approach for the generation and manipulation of quantum light, and the exploration of many-body phenomena with interacting photons.
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