Universal approach for quantum interfaces with atomic arrays

We develop a general approach for the characterization of atom-array platforms as light-matter interfaces, focusing on their application in quantum memory and photonic entanglement generation. Our approach is based on the mapping of atom-array problems to a generic 1D model of light interacting with a collective dipole. We find that the efficiency of light-matter coupling, which in turn determines those of quantum memory and entanglement, is given by the 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 atomic arrays 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 array and illuminating beam and weak disorder in atomic positions. Our analytical results are verified numerically and reveal a key idea: efficiencies of quantum tasks are reduced by our approach to the classical calculation of a reflectivity. This provides a unified framework for the analysis of collective light-matter coupling in various relevant platforms such as optical lattices and tweezer arrays. Generalization to collective systems beyond arrays is discussed.