Constructing Arbitrary Coherent Rearrangements in Optical Lattices

TL;DR

This paper presents a method for arbitrary coherent rearrangement of ultracold atoms in optical lattices, enabling programmable quantum dynamics through systematic unitary transformations using tunneling and phase shifts.

Contribution

It introduces a scheme inspired by linear optics to construct any single-particle unitary in optical lattices, scalable to two dimensions for efficient atom rearrangement.

Findings

Successfully constructs arbitrary unitaries using tunneling and phase shifts.

Demonstrates scheme's robustness against noise and crosstalk.

Enables scalable, high-density atom rearrangement in 2D lattices.

Abstract

Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route towards programmable quantum dynamics with massive particles. We propose and analyze a scheme for implementing coherent rearrangement of ultracold atoms, corresponding to arbitrary unitary transformations on single-particle motional states. Exploiting an analogy between dynamics in optical superlattices and discrete linear optics, we employ the Clements scheme to systematically construct any global $N$-dimensional single-particle unitary from tunneling and phase shifts in arrays of double wells. Tunneling is controlled globally, while local operations are achieved through site-resolved potential shifts. We numerically investigate the susceptibility of the scheme to intensity noise and addressing crosstalk. We identify key subroutines enabled by this unitary construction, including the Discrete Fourier Transform and the implementation of non-native Hamiltonians. Extending the scheme to two dimensions enables all-to-all atomic rearrangement with a circuit depth that scales sublinearly with the atom number, providing a high-density and highly scalable approach to atom rearrangement.