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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mn>35</a:mn> <a:mo>∘</a:mo> </a:msup> </a:math> , making the scheme compatible with standard objectives of numerical aperture <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>NA</c:mi> <c:mo>≤</c:mo> <c:mn>0.7</c:mn> </c:math> . Our analytical theory and scattering simulations reveal that the interface efficiency <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>r</e:mi> <e:mn>0</e:mn> </e:msub> </e:math> for quantum information tasks scales favorably with the array atom number <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>N</g:mi> </g:math> : reaching <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo>&gt;</i:mo> <i:mn>0.99</i:mn> </i:math> ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mo>&gt;</k:mo> <k:mn>0.9999</k:mn> </k:math> ) for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>N</m:mi> <m:mo>=</m:mo> <m:mn>149</m:mn> </m:math> ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>N</o:mi> <o:mo>∼</o:mo> <o:mn>1000</o:mn> </o:math> ) and scaling as <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mn>1</q:mn> <q:mo>−</q:mo> <q:msub> <q:mi>r</q:mi> <q:mn>0</q:mn> </q:msub> <q:mo>∼</q:mo> <q:mn>1</q:mn> <q:mo>/</q:mo> <q:mi>N</q:mi> </q:math> for large <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi>N</s:mi> </s:math> . 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.