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We investigate the interaction of weak light fields with two-dimensionallattices of atoms, in which two-photon coupling establishes conditions ofelectromagnetically induced transparency and excites high lying atomic Rydbergstates. This system features different interactions that act on disparatelength scales, from zero-range defect scattering of atomic excitations andfinite-range dipole exchange interactions to long-range Rydberg-stateinteractions that span the entire array. Analyzing their interplay, we identifyconditions that yield a nonlinear quantum mirror which coherently splitsincident fields into correlated photon-pairs in a single transverse mode, whiletransmitting single photons unaffected. Such strong photon-photon interactionsin the absence of otherwise detrimental photon losses in Rydberg-EIT arraysopens up a promising approach for the generation and manipulation of quantumlight, and the exploration of many-body phenomena with interacting photons.

Photon-photon interactions in Rydberg-atom arrays