Universal Approach for Quantum Interfaces with Atomic Arrays

We develop a general framework for the analysis of two-sided quantum interfaces, composed of collections of atoms interacting with paraxial light. Accounting for photon-mediated dipole-dipole interactions, our approach is based on the mapping of collective atom-photon interfaces onto a generic one-dimensional model of light scattering, characterized by a reflectivity parameter $r_0$. This entails two key practical advantages: (i) the efficiency of the quantum interface in performing various quantum tasks, such as quantum memory or entanglement generation, is universally given by $r_0$ and is hence reduced to a measurement or classical calculation of a reflectivity; (ii) the efficiency can be greatly enhanced by a properly designed photon mode that spatially matches a collective-dipole eigenmode of the atoms. We demonstrate our approach for realistic cases of finite-size atomic arrays, partially filled arrays, and circular arrays. This provides a unified approach for treating collective light-matter coupling in various platforms, such as optical lattices and optical tweezers.