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Observation of dynamical vortices after quenches in a system with topology

Nature Physics volume 14, pages 265–268 (2018)Cite this article

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Abstract

Topological phases constitute an exotic form of matter characterized by non-local properties rather than local order parameters1. The paradigmatic Haldane model on a hexagonal lattice features such topological phases distinguished by an integer topological invariant known as the first Chern number2. Recently, the identification of non-equilibrium signatures of topology in the dynamics of such systems has attracted particular attention3,4,5,6. Here, we experimentally study the dynamical evolution of the wavefunction using time- and momentum-resolved full state tomography for spin-polarized fermionic atoms in driven optical lattices7. We observe the appearance, movement and annihilation of dynamical vortices in momentum space after sudden quenches close to the topological phase transition. These dynamical vortices can be interpreted as dynamical Fisher zeros of the Loschmidt amplitude8, which signal a so-called dynamical phase transition9,10. Our results pave the way to a deeper understanding of the connection between topological phases and non-equilibrium dynamics.

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Fig. 1: Quenches in the topological Haldane model.
Fig. 2: Experimental sequence for time-resolved state tomography.
Fig. 3: Observation of dynamical vortices in momentum space.
Fig. 4: Relation between the occurrence of dynamical vortices and the equilibrium phase diagram.

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Acknowledgements

We acknowledge financial support by the excellence cluster ‘The Hamburg Centre for Ultrafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale’ and the GrK 1355 of the Deutsche Forschungsgemeinschaft. B.S.R. acknowledges financial support from the European Commission (Marie Curie Fellowship), M.H. from the Deutsche Akademie der Naturforscher Leopoldina (grant no. LPDR 2015-01), and J.C.B. from the ERC synergy grant UQUAM.

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Author notes

  1. N. Fläschner, D. Vogel and M. Tarnowski contributed equally to this work.

Authors and Affiliations

  1. ILP - Institut für Laserphysik, Universität Hamburg, Hamburg, Germany

    N. Fläschner, D. Vogel, M. Tarnowski, B. S. Rem, D.-S. Lühmann, L. Mathey, K. Sengstock & C. Weitenberg

  2. The Hamburg Centre for Ultrafast Imaging, Hamburg, Germany

    N. Fläschner, M. Tarnowski, B. S. Rem, L. Mathey, K. Sengstock & C. Weitenberg

  3. Physik Department, Technische Universität München, Garching, Germany

    M. Heyl

  4. Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria

    J. C. Budich

  5. Institute for Theoretical Physics, University of Innsbruck, Innsbruck, Austria

    J. C. Budich

  6. ZOQ - Zentrum für Optische Quantentechnologien, Universität Hamburg, Hamburg, Germany

    L. Mathey & K. Sengstock

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  1. N. Fläschner
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Contributions

N.F., D.V. and M.T. took and analysed the data and performed numerical simulations. C.W., B.S.R. and K.S. conceived the experiment. All authors contributed to the interpretation of the data and to the writing of the manuscript.

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Correspondence to K. Sengstock.

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Supplementary Note 1, Supplementary Fig. 1

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Fläschner, N., Vogel, D., Tarnowski, M. et al. Observation of dynamical vortices after quenches in a system with topology. Nature Phys 14, 265–268 (2018). https://doi.org/10.1038/s41567-017-0013-8

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