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arXiv:1809.02122 · PRX Quantum

Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder

Chuan-Hsun Li, Yangqian Yan, Shih‐Wen Feng, Sayan Choudhury, David Blasing, Qi Zhou, Yong P. Chen

Published Jan 31, 2022• 37 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/prxquantum.3.010316

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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.
Interplay between matter and fields in physical spaces with nontrivial geometries gives rise to many exotic quantum phenomena. However, their realizations are often impeded by experimental constraints. Here, we realize a Bose-Einstein condensate (BEC) on a synthetic cylindrical surface subject to a net radial synthetic magnetic flux, topologically equivalent to a two-dimensional (2D) Hall ribbon with two edges connected. This cylindrical surface comprises a real spatial dimension and a curved synthetic dimension formed by cyclically-coupled spin states. The BEC on such a Hall cylinder has counterintuitive properties unattainable by its counterparts in 2D planes. We observe Bloch oscillations of the BEC with doubled periodicity of the band structure, analogous to traveling on a Mobius strip, reflecting the BEC's emergent crystalline order with nonsymmorphic symmetry-protected band crossings. We further demonstrate such topological operations as gapping the band crossings and unzipping the cylinder. Our work opens the door to engineering synthetic curved spaces and observing intriguing quantum phenomena inherent to the topology of spaces.
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.
Quantum anomalies arise when symmetries of a classical theory cannot be preserved upon quantization, leading to unconventional topological responses. A prominent example is the parity anomaly of a single two-dimensional Dirac fermion, which enforces a half-quantized Hall response. Anomaly inflow mechanism allows this effect to be observed at the surfaces of three-dimensional topological insulators, however, its realization in a genuinely two-dimensional system has remained elusive. Here we report the observation of a parity-anomalous Hall response at the critical point of a quantum Hall topological phase transition in a synthetic two-dimensional system of ultracold dysprosium atoms. By coupling a continuous spatial dimension to a finite synthetic dimension encoded in atomic spin states, we engineer tunable Chern bands with C = 0 and 1. At the transition, the bulk gap closes at a single Dirac point, where we observe a robust half-quantized Hall drift despite strong non-adiabatic excitations. We show that this response originates from the global structure of the band topology, is protected by an emergent parity symmetry at criticality, and disappears when parity is explicitly broken. Our work establishes synthetic quantum systems as a powerful platform to probe quantum anomalies and their interplay with topology and non-equilibrium dynamics.
Abstract Topological superfluidity is an important concept in electronic materials as well as ultracold atomic gases1. However, although progress has been made by hybridizing superconductors with topological substrates, the search for a material—natural or artificial—that intrinsically exhibits topological superfluidity has been ongoing since the discovery of the superfluid 3He-A phase2. Here we report evidence for a globally chiral atomic superfluid, induced by interaction-driven time-reversal symmetry breaking in the second Bloch band of an optical lattice with hexagonal boron nitride geometry. This realizes a long-lived Bose–Einstein condensate of 87Rb atoms beyond present limits to orbitally featureless scenarios in the lowest Bloch band. Time-of-flight and band mapping measurements reveal that the local phases and orbital rotations of atoms are spontaneously ordered into a vortex array, showing evidence of the emergence of global angular momentum across the entire lattice. A phenomenological effective model is used to capture the dynamics of Bogoliubov quasi-particle excitations above the ground state, which are shown to exhibit a topological band structure. The observed bosonic phase is expected to exhibit phenomena that are conceptually distinct from, but related to, the quantum anomalous Hall effect3–7 in electronic condensed matter.
By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, physical observables strongly depend on the axial magnetic flux, providing us a sensitive means to probe either the transition or the axial flux using one another. In the irrational limit, physical observables are no longer affected by the axial flux, signifying a scheme to suppress decoherence induced by fluctuations of the axial flux.
We show that by modifying the setup of the recent experiment that creates a "Dirac string" one can engineer a quasi-2D spinor Bose-Einstein condensate on a cylindrical surface, with a synthetic magnetic field normal to the surface. Because of the muticonnectivity of the surface, there are two types of vortices (called A and B) with the same vorticity. This is very different from the planar case, which only has one kind of vortex for fixed circulation. As the strength of the synthetic gauge field increases, the ground states will form a necklace of alternating AB vortices surrounding the lateral midpoint of the cylinder, and will split into two A and B necklaces at higher synthetic gauge fields. The fact that even the basic vortex structure of a Bose-Einstein condensate is altered in a cylindrical surface implies that richer phenomena are in store for quantum gases in other curved surfaces.