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

Sorting atoms stochastically loaded in optical tweezer array via an auxiliary mobile tweezer is an efficient approach to prepare defect-free atom arrays of arbitrary geometries. However, high filling fraction of atom-by-atom assemblers is impeded by redundant sorting moves with imperfections during atom transport, especially for scaling the system size to larger atom numbers. Here, we propose a new sorting algorithm (heuristic cluster algorithm) which provides near-fewest moves in tailored our atom assembler scheme and experimentally demonstrate a 5*6 defect-free atom array with 98.4% filling fraction for one rearrangement cycle. Furthermore, the novel feature of this algorithm makes the filling fraction high and uniform as the size of atom assembler enlarged. Our approach is essential to scale hundreds of assembled atoms for bottom-up quantum computation, quantum simulation and precision measurement.