Free-Space Quantum Interface of a Single Atomic Tweezer Array with Light

We present a practical approach for interfacing light with a two-dimensional atomic tweezer array. Typical paraxial fields are poorly matched to the array's multi-diffraction-order radiation pattern, thus severely limiting the interface coupling efficiency. Instead, we propose to design a field mode that naturally couples to the array: it consists of a unique superposition of multiple beams corresponding to the array's diffraction orders. This composite mode can be generated from a single Gaussian beam using standard free-space optics, including spatial light modulators and a single objective lens. For a triangular array with lattice spacing about twice the wavelength, all diffraction angles remain below 35 degrees, making the scheme compatible with standard objectives of numerical aperture NA <= 0.7. Our analytical theory and scattering simulations reveal that the interface efficiency r(0) for quantum information tasks scales favorably with the array atom number N: reaching > 0.99 (> 0.9999) for N = 149 (N similar to 1000) and scaling as 1 - r(0) similar to 1/N for large N. The scheme is robust to optical imperfections and atomic-position errors, offering a viable path for quantum light-matter applications in current tweezer-array platforms.