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

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