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arXiv:2602.14549 · Physical Review Letters

Realization of a Synthetic Hall Torus with a Topological Charge Pump in a Spinor Bose-Einstein Condensate

T. -H. Chien, S. -C. Wu, Y. -H. Su, L. -R. Liu, N. -C. Chiu, M. Sarkar, Q. D. Zhou, Y. -J. Lin

Published Sep 28, 2026• 0 citations
arXivHTMLPDF

Abstract

We report the first experimental realization of a synthetic Hall torus using a spinor Bose-Einstein condensate confined in a ring-shaped trap with in situ imaging. By cyclically coupling three hyperfine spin states via Raman and microwave fields, we impose a periodic boundary condition in the synthetic dimension, which, together with a real-space ring trap, realizes a toroidal geometry with synthetic magnetic flux penetrating the surface. This flux induces azimuthal density modulations whose periodicity is uniquely determined by the quantized toroidal flux, a hallmark of the Hall torus. We then implement a topological charge pump by adiabatically varying an axial flux through the torus, inducing quantized azimuthal transport of the atoms. We further investigate the onset of these modulations as the system transitions from cylindrical to toroidal topology. Our results establish a versatile platform for exploring quantum Hall physics and topological phenomena in synthetic curved spaces.

DOI
10.1103/xzzd-glq5

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Synthetic spaces allow physicists to bypass constraints imposed by certain physical laws in experiments. Here, we show that a synthetic torus, which consists of a ring trap in the real space and internal states of ultracold atoms cyclically coupled by Laguerre-Gaussian Raman beams, could be threaded by a net effective magnetic flux through its surface-an impossible mission in the real space. Such a synthetic Hall torus gives rise to a periodic lattice in real dimensions, in which the periodicity of the density modulation of atoms fractionalizes that of the Hamiltonian. Correspondingly, the energy spectrum is featured by multiple bands grouping into clusters with nonsymmorphic-symmetry-protected band crossings in each cluster, leading to swaps of wave packets in Bloch oscillations. Our scheme allows physicists to glue two synthetic Hall tori such that localization may emerge in a quasicrystalline lattice. If the Laguerre-Gaussian Raman beams and ring traps were replaced by linear Raman beams and ordinary traps, a synthetic Hall cylinder could be realized and deliver many of the aforementioned phenomena.
The interplay between matter particles and gauge fields in physical spaces with nontrivial geometries can lead to novel topological quantum matter.However, detailed microscopic mechanisms are often obscure, and unconventional spaces are generally challenging to construct in solids.Highly controllable atomic systems can quantum simulate such physics, even those inaccessible in other platforms.Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux.We observe a symmetry-protected topological band structure emerging on this Hall cylinder but disappearing in the planar counterpart.BEC's transport observed as Bloch oscillations in the band structure is analogous to traveling on a Möbius strip in the momentum space, revealing topological band crossings protected by a nonsymmorphic symmetry.We demonstrate that breaking this symmetry induces a topological transition manifested as gap opening at band crossings, and further manipulate the band structure and BEC's transport by controlling the axial synthetic magnetic flux.Our work opens the door for using atomic quantum simulators to explore intriguing topological phenomena intrinsic in unconventional spaces.
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Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion-a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system.
The quantum Hall effect occurring in two-dimensional electron gases was first explained by Laughlin, who developed a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a quantum Hall cylinder periodically driven by an axial magnetic field, resulting in the quantized motion of electrons. We realize this milestone experiment with an ultracold gas of dysprosium atoms, the cyclic dimension being encoded in the electronic spin and the axial field controlled by the phases of laser-induced spin-orbit couplings. Our experiment provides a straightforward manifestation of the nontrivial topology of quantum Hall insulators, and could be generalized to strongly correlated topological systems.