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, r0=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 r0, 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.