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Phases of interacting bosons in a hybrid Harper-Hofstadter system with a synthetic dimension of harmonic trap states

David G. Reid1, Holly A. J. Middleton-Spencer1, Grazia Salerno2,3, Nathan Goldman4,5,6, and Hannah M. Price1

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Phys. Rev. A 114, 043308 – Published 16 October, 2026

DOI: https://doi.org/10.1103/k33y-s9n9

Abstract

Synthetic dimensions are a powerful tool for engineering desired quantum systems, based on coupling together sets of states and reinterpreting these as lattice sites along an artificial dimension. Recently, a synthetic dimension of harmonic trap states has been successfully implemented in an ultracold-atom experiment, opening the way for future realizations in this platform of topological lattice models, such as hybrid Harper-Hofstadter (HH) systems, which have one real and one synthetic dimension. However, unlike conventional systems, interparticle interactions along a synthetic dimension of harmonic trap states are inhomogeneous, long ranged and non-state-preserving. Therefore, this setup provides a natural platform for the exploration of the interplay between long-range interactions (including correlated pair tunneling) and magnetic effects. In this paper, we set out to numerically study the effect of such interactions on both a hybrid two-legged HH ladder and a two-dimensional HH model. In the former, we find variants of vortex and Meissner phases familiar from conventional models, while in the latter, we observe the emergence, in small finite systems, of unusual ground states, including a “Meissner stripe” state, which combines counterpropagating Meissner-type currents with strong density variations. This opens up interesting questions, including about the nature of strongly correlated states that would emerge in such a platform.

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Phys. Rev. A 114, 043308– Published 16 October, 2026
  • Received 18 March 2026
  • Accepted 16 September 2026
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