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

TL;DR

This paper investigates how long-range, inhomogeneous interactions in a hybrid Harper-Hofstadter system with a synthetic harmonic trap dimension influence quantum phases, revealing novel states like the 'Meissner stripe' in finite systems.

Contribution

It provides the first numerical analysis of interaction effects in a hybrid Harper-Hofstadter system with a synthetic harmonic trap dimension, uncovering new quantum phases.

Findings

Identification of vortex and Meissner phases in a hybrid two-legged ladder.

Observation of a 'Meissner stripe' state with counter-propagating currents.

Discovery of unusual ground states in a 2D Harper-Hofstadter model with interactions.

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, inter-particle 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 2D 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 counter-propagating Meissner-like 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.