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Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian

Nature Physics volume 13, pages 1195–1200 (2017)Cite this article

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Abstract

Ring exchange is an elementary interaction for modelling unconventional topological matter. Here, we report the observation of four-body ring-exchange interactions and the topological properties of anyonic excitations within an ultracold atom system. A minimum toric-code Hamiltonian, in which the ring exchange is the dominant term, was implemented in disconnected four-spin plaquette arrays formed by two orthogonal superlattices. The ring-exchange interactions were resolved from the dynamical evolutions of the spin orders in each plaquette, matching well with the predicted energy gaps between two anyonic excitations of the spin system. A braiding operation was applied to the spins in the plaquettes and an induced phase 1.00(3)π in the four-spin state was observed, confirming 1/2 mutual statistics. This work offers new prospects for the quantum simulation of topological phases by engineering many-body interactions.

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Figure 1: Experimental scheme and the ring-exchange process in disconnected four-site plaquettes.
Figure 2: Observation of four-body ring-exchange interactions.
Figure 3: Frequencies of the spin oscillations.
Figure 4: Coherent control of ring-exchange dynamics and braiding anyons in a minimal toric-code model.

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Acknowledgements

We thank A. J. Leggett, P. Zoller and B. Zhao for helpful discussions. This work was supported by the National Key R&D Program of China (2016YFA0301600), National Natural Science Foundation of China (91421305, 11521063), and the Chinese Academy of Sciences.

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Author notes

  1. Han-Ning Dai and Bing Yang: These authors contributed equally to this work.

Authors and Affiliations

  1. Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

    Han-Ning Dai, Bing Yang, Hui Sun, Yu-Ao Chen, Zhen-Sheng Yuan & Jian-Wei Pan

  2. Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany

    Han-Ning Dai, Bing Yang, Andreas Reingruber, Xiao-Fan Xu, Zhen-Sheng Yuan & Jian-Wei Pan

  3. CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

    Han-Ning Dai, Bing Yang, Hui Sun, Yu-Ao Chen, Zhen-Sheng Yuan & Jian-Wei Pan

  4. Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Erwin-Schroedinger-Strasse, Building 46, 67663 Kaiserslautern, Germany

    Andreas Reingruber

  5. CAS-Alibaba Quantum Computing Laboratory, Shanghai 201315, China

    Yu-Ao Chen, Zhen-Sheng Yuan & Jian-Wei Pan

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Contributions

Y.-A.C., Z.-S.Y. and J.-W.P. initiated and designed this research project. H.-N.D., B.Y., A.R., X.-F.X. and Z.-S.Y. set up the experiment. H.-N.D., B.Y., A.R. and H.S. performed the measurement and analysed the data. All authors contributed to manuscript preparation. Z.-S.Y. and J.-W.P. supervised the whole project.

Corresponding authors

Correspondence to Zhen-Sheng Yuan or Jian-Wei Pan.

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Dai, HN., Yang, B., Reingruber, A. et al. Four-body ring-exchange interactions and anyonic statistics within a minimal toric-code Hamiltonian. Nature Phys 13, 1195–1200 (2017). https://doi.org/10.1038/nphys4243

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