# Defect-free atomic array formation using Hungarian matching algorithm

## TL;DR

This paper introduces a fast, optimal method using the Hungarian matching algorithm for defect-free atomic array formation, significantly improving success rates over heuristic approaches in cold atom experiments.

## Contribution

The paper demonstrates the application of the Hungarian matching algorithm for atom rearrangement, providing a rigorous and efficient solution to the combinatorial optimization problem in atomic lattice formation.

## Key findings

- Hungarian algorithm reduces collision paths during atom rearrangement.
- Over 50% higher success probability compared to heuristic methods.
- Experimental results align with theoretical analysis.

## Abstract

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.