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Constructing Arbitrary Coherent Rearrangements in Optical Lattices

Alexander Roth1,2, Liyang Qiu1, Timon Hilker1,3, Titus Franz1,4, and Philipp M. Preiss1,4,*

  • *Contact author: philipp.preiss@mpq.mpg.de
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PRX Quantum 7, 043021 – Published 30 October, 2026

DOI: https://doi.org/10.1103/jsr3-2r5t

Abstract

Coherent control of motional degrees of freedom of ultracold atoms in optical lattices offers a promising route toward 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.

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Popular Summary

Ultracold atoms in optical lattices are one of the leading platforms for engineering synthetic quantum matter. However, a key limitation has been the lack of programmable local control over coherent particle motion. We address this by introducing a framework inspired by programmable optical networks and adapt it for optical lattices. Our scheme decomposes arbitrary single-particle unitaries into simple global tunneling pulses and local phase shifts. This method enables key applications, including the exact discrete Fourier transform for coherent momentum measurements and efficient sublinear atom rearrangements in 2D arrays. Ultimately, this provides a scalable route to genuine gate-based manipulation of motional states, crucial for advancing from global dynamics to universal control over lattice quantum matter.

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PRX Quantum 7, 043021– Published 30 October, 2026
  • Received 4 March 2026
  • Revised 11 August 2026
  • Accepted 8 September 2026
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