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We develop a general approach for the characterization of atom-arrayplatforms as light-matter interfaces, focusing on their application in quantummemory and photonic entanglement generation. Our approach is based on themapping of atom-array problems to a generic 1D model of light interacting witha collective dipole. We find that the efficiency of light-matter coupling,which in turn determines those of quantum memory and entanglement, is given bythe on-resonance reflectivity of the 1D scattering problem, $r_0=C/(1+C)$,where $C$ is a cooperativity parameter of the model. For 2D and 3D atomicarrays in free space, we derive the mapping parameter $C$ and hence $r_0$,while accounting for realistic effects such as the finite sizes of the arrayand illuminating beam and weak disorder in atomic positions. Our analyticalresults are verified numerically and reveal a key idea: efficiencies of quantumtasks are reduced by our approach to the classical calculation of areflectivity. This provides a unified framework for the analysis of collectivelight-matter coupling in various relevant platforms such as optical latticesand tweezer arrays. Generalization to collective systems beyond arrays isdiscussed.

Universal approach for quantum interfaces with atomic arrays