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Sorting atoms stochastically loaded in optical tweezer arrays via anauxiliary mobile tweezer is an efficient approach to preparingintermediate-scale defect-free atom arrays in arbitrary geometries. However,high filling fraction of atom-by-atom assemblers is impeded by redundantsorting moves with imperfect atom transport, especially for scaling the systemsize to larger atom numbers. Here, we propose a new sorting algorithm(heuristic cluster algorithm, HCA) which provides near-fewest moves in ourtailored atom assembler scheme and experimentally demonstrate a $5\times6$defect-free atom array with 98.4(7)$\%$ filling fraction for one rearrangementcycle. The feature of HCA that the number of moves $N_{m}\approx N$ ($N$ is thenumber of defect sites to be filled) makes the filling fraction uniform as thesize of atom assembler enlarged. Our method is essential to scale hundreds ofassembled atoms for bottom-up quantum computation, quantum simulation andprecision measurement.

Efficient preparation of 2D defect-free atom arrays with near-fewest sorting-atom moves