  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.
