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.5 MoreReceived 10 August 2021Accepted 7 December 2021DOI:https://doi.org/10.1103/PRXQuantum.3.010316Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasBose-Einstein condensatesQuantum simulationSynthetic gauge fieldsPhysical SystemsUltracold gasesTechniquesAtom & ion coolingAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics
Highlights
Physical spaces with nontrivial geometries can give rise to novel phenomena difficult to attain in planar spaces
Bose-Einstein condensate (BEC) crystalline order and topological band structure emerge due to curving the Hall strip into a Hall cylinder and are intrinsic properties of a Hall cylinder, not relying on an extra real-space lattice potential
We observe topological band crossings protected by a nonsymmorphic symmetry, while Ref. [74] revealed a gapped topological band protected by a generalized inversion symmetry
Summary
Physical spaces with nontrivial geometries can give rise to novel phenomena difficult to attain in planar spaces. The microscopic mechanisms of how changing the geometry of the underlying space may give rise to distinct topological matter require further research Atomic quantum simulators, such as atoms in optical lattices [34–37] subject to additional ingredients like synthetic gauge fields [38–44], have been employed to explore topological quantum matter in planar spaces [45–48]. We observe a topological transition manifested as gap opening at band crossings and further manipulate the band structure and BEC’s transport via controlling the axial synthetic magnetic flux In striking contrast, these phenomena emerging on the Hall cylinder vanish when we unzip the cylinder into a planar Hall strip, illustrating the crucial and intriguing role of topology and geometries of spaces in novel topological quantum phenomena
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