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Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms

Nature Physics volume 11, pages 162166 (2015) | Download Citation

Abstract

Sixty years ago, Karplus and Luttinger pointed out that quantum particles moving on a lattice could acquire an anomalous transverse velocity in response to a force, providing an explanation for the unusual Hall effect in ferromagnetic metals1. A striking manifestation of this transverse transport was then revealed in the quantum Hall effect2 where the plateaux depicted by the Hall conductivity were attributed to a topological invariant characterizing the Bloch bands: the Chern number3. Until now, topological transport associated with non-zero Chern numbers has only been observed in electronic systems2,4,5. Here we use the transverse deflection of an atomic cloud in response to an optical gradient to measure the Chern number of artificially generated Hofstadter bands6. These topological bands are very flat and thus constitute good candidates for the realization of fractional Chern insulators7. Combining these deflection measurements with the determination of the band populations, we obtain an experimental value for the Chern number of the lowest band νexp = 0.99(5). This first Chern-number measurement in a non-electronic system is facilitated by an all-optical artificial gauge field scheme, generating uniform flux in optical superlattices.

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Acknowledgements

We acknowledge fruitful discussions with J. Dalibard and also with A. Dauphin, P. Gaspard, F. Gerbier, F. Grusdt, I. Carusotto, T. Ozawa and H. Price. This work was supported by NIM, the EU (UQUAM, SIQS) and EPSRC Grant No. EP/K030094/1. M.Aidelsburger was further supported by the Deutsche Telekom Stiftung, M.L. by ExQM and N.G. by the Université Libre de Bruxelles and the FRS-FNRS (Belgium).

Author information

Author notes

    • J. T. Barreiro

    Present address: Department of Physics, University of California, San Diego, California 92093, USA.

Affiliations

  1. Fakultät für Physik, Ludwig-Maximilians-Universität, Schellingstrasse 4, 80799 München, Germany

    • M. Aidelsburger
    • , M. Lohse
    • , C. Schweizer
    • , M. Atala
    • , J. T. Barreiro
    •  & I. Bloch
  2. Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany

    • M. Aidelsburger
    • , M. Lohse
    • , C. Schweizer
    • , M. Atala
    • , J. T. Barreiro
    •  & I. Bloch
  3. Collège de France, 11 place Marcelin Berthelot & Laboratoire Kastler Brossel, CNRS, UPMC, ENS, 24 rue Lhomond 75005 Paris, France

    • S. Nascimbène
    •  & N. Goldman
  4. T. C. M. Group, Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, UK

    • N. R. Cooper
  5. Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (U.L.B.), B-1050 Brussels, Belgium

    • N. Goldman

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Contributions

M.Aidelsburger, M.L. and C.S. performed the experiment. All authors contributed to the design of the experiment, the theoretical and data analysis, and to the writing of the paper. I.B. and N.G. supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to M. Aidelsburger.

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DOI

https://doi.org/10.1038/nphys3171

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