  Deterministic loading of single atoms onto arbitrary two-dimensional lattice
points has recently been demonstrated, where by dynamically controlling the
optical-dipole potential, atoms from a probabilistically loaded lattice were
relocated to target lattice points to form a zero-entropy atomic lattice. In
this atom rearrangement, how to pair atoms with the target sites is a
combinatorial optimization problem: brute-force methods search all possible
combinations so the process is slow, while heuristic methods are time-efficient
but optimal solutions are not guaranteed. Here, we use the Hungarian matching
algorithm as a fast and rigorous alternative to this problem of defect-free
atomic lattice formation. Our approach utilizes an optimization cost function
that restricts collision-free guiding paths so that atom loss due to collision
is minimized during rearrangement. Experiments were performed with cold
rubidium atoms that were trapped and guided with holographically controlled
optical-dipole traps. The result of atom relocation from a partially filled
7-by-7 lattice to a 3-by-3 target lattice strongly agrees with the theoretical
analysis: using the Hungarian algorithm minimizes the collisional and
trespassing paths and results in improved performance, with over 50\% higher
success probability than the heuristic shortest-move method.

Atomic Physics