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arXiv:2602.21108 · Physical Review A

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

David G. Reid, Holly A. J. Middleton-Spencer, Grazia Gabriella Salerno, Nathan Goldman, Hannah M. Price

Published Sep 16, 2026• 0 citations
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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.

DOI
10.1103/k33y-s9n9

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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.
Synthetic dimension is a potent tool in quantum simulation of topological phases of matter. Here we propose and demonstrate a scheme to simulate an anisotropic Harper-Hofstadter model with controllable magnetic flux on a two-leg ladder using the spin and motional states of a single trapped ion. We verify the successful simulation of this model by comparing the measured dynamics with theoretical predictions under various coupling strength and magnetic flux, and we observe the chiral motion of wave packets on the ladder as evidence of the topological chiral edge modes. We develop a quench path to adiabatically prepare the ground states for varying magnetic flux and coupling strength, and we measure the chiral current on the ladder for the prepared ground states, which allows us to probe the quantum phase transition between the Meissner phase and the vortex phase. Our work demonstrates the trapped ion as a powerful quantum simulation platform for topological quantum matter.
We study two-component bosons on the Harper-Hofstadter model with two legs. The synthetic magnetic fields for the two types of bosons point to either the same direction or opposite directions. The bosons have hardcore intraspecies interaction such that there can be no more than one boson of the same type on each lattice site. For certain filling factors in the absence of interspecies interaction, each component realizes a vortex Mott insulator with rung current or a Meissner superfluid without rung current. The system undergoes phase transitions to other phases as interspecies interaction is turned on, which are characterized numerically using the density matrix renormalization group method and supplemented with analytical studies when possible. The vortex Mott insulator transits to a gapped Meissner phase without rung current and the Meissner superfluid transits to a gapped vortex phase with rung current. In both cases, we observe gapped spin density wave states that break certain Z2{\mathbb{Z}}_{2}Z2​ symmetries.
We propose and study systems of coupled atomic wires in a perpendicular synthetic magnetic field as a platform to realize exotic phases of quantum matter. This includes (fractional) quantum Hall states in arrays of many wires inspired by the pioneering work [C. L. Kane et al., Phys. Rev. Lett. 88, 036401 (2002)], as well as Meissner phases and vortex phases in double wires. With one continuous and one discrete spatial dimension, the proposed setup naturally complements recently realized discrete counterparts, i.e., the Harper-Hofstadter model and the two-leg flux ladder, respectively. We present both an in-depth theoretical study and a detailed experimental proposal to make the unique properties of the semicontinuous Harper-Hofstadter model accessible with cold-atom experiments. For the minimal setup of a double wire, we explore how a subwavelength spacing of the wires can be implemented. This construction increases the relevant energy scales by at least an order of magnitude compared to ordinary optical lattices, thus rendering subtle many-body phenomena such as Lifshitz transitions in Fermi gases observable in an experimentally realistic parameter regime. For arrays of many wires, we discuss the emergence of Chern bands with readily tunable flatness of the dispersion and show how fractional quantum Hall states can be stabilized in such systems. Using for the creation of optical potentials Laguerre-Gauss beams that carry orbital angular momentum, we detail how the coupled atomic wire setups can be realized in nonplanar geometries such as cylinders, disks, and tori.
Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long-range dipolar interactions on a two-leg ladder. We focus on the limit where the number of particles per site is large and the interactions are weak. Using two complementary variational approaches, we find rich physics driven by the long-range forces. Generically, long-range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. For example, nearest-neighbor interactions produce an interleg charge density wave phase, where the total density remains uniform but the density on each leg of the ladder is modulating in space, out of phase with one another. Next-nearest-neighbor interactions lead to a fully modulated biased ladder phase, where all of the particles are on one leg of the ladder. This state simultaneously breaks Z2{Z}_{2}Z2​ reflection symmetry and U(1)\mathrm{U}(1)U(1) translation symmetry. For values of the flux near $\ensuremath{\phi}=\ensuremath{\pi}$, we find a switching effect for arbitrarily weak interactions, where the density is modulated but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Remarkably, varying the rung to ladder hopping produces a cascade of first-order transitions between modulated density wave states with different wave vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak rung hopping. We discuss the experimental consequences of our work and draw connections between our work and recent experiments on cold atoms in synthetic dimensions.
Abstract Periodically driven quantum systems can realize phases of matter that do not appear in time-independent Hamiltonians. One application is the engineering of synthetic gauge fields, which enables the study of topological many-body physics with neutral atom quantum simulators. Here we realize the strongly interacting Mott–Meissner phase—a state combining interaction-induced localization with chiral currents induced by an artificial magnetic field—in large-scale bosonic flux ladders with 48 sites at half-filling using a neutral atom quantum simulator. By combining quantum gas microscopy with local basis rotations, we reveal the emerging equilibrium particle currents with local resolution across large systems. We find chiral currents exhibiting a characteristic interaction scaling, providing direct experimental evidence of the interacting Mott–Meissner phase. Moreover, we benchmark density correlations with numerical simulations and find that the effective temperature of the system is on the order of the tunnel coupling. These results establish the feasibility of scaling periodically driven quantum systems to large, strongly correlated phases, enabling further studies of topological quantum matter with single-atom resolution and control.
We introduce a simple scheme to implement synthetic dimensions in ultracold atomic gases, which only requires two basic and ubiquitous ingredients: the harmonic trap, which confines the atoms, combined with a periodic shaking. In our approach, standard harmonic oscillator eigenstates are reinterpreted as lattice sites along a synthetic dimension, while the coupling between these lattice sites is controlled by the applied time modulation. The phase of this modulation enters as a complex hopping phase, leading straightforwardly to an artificial magnetic field upon adding a second dimension. We show that this artificial gauge field has important consequences, such as the counterintuitive reduction of average energy under resonant driving, or the realization of quantum Hall physics. Our approach offers significant advantages over previous implementations of synthetic dimensions, providing an intriguing route towards higher-dimensional topological physics and strongly-correlated states.