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.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Haldane, F. D. M. Model for a Quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988).
Hu, Y., Zoller, P. & Budich, J. C. Dynamical buildup of a quantized Hall response from nontopological states. Phys. Rev. Lett. 117, 126803 (2016).
Ünal, F. N., Mueller, E. J. & Oktel, Ö. Noneqilibrium fraction Hall response after a topological quench. Phys. Rev. A 94, 053604 (2016).
Caio, D. M., Cooper, N. R. & Bhaseen, M. J. Quantum quenches in Chern insulators. Phys. Rev. Lett. 115, 236403 (2015).
D’Alessio, L. & Rigol, M. Dynamical preparation of Floquet Chern insulators. Nat. Commun 6, 8336 (2015).
Fläschner, N. et al. Experimental reconstruction of the Berry curvature in a Floquet Bloch band. Science 352, 1091–1094 (2016).
Brandner, K., Maisi, V. F., Pekola, J. P., Garrahan, J. P. & Flindt, C. Experimental observation of dynamical Lee-Yang zeros. Phys. Rev. Lett. 118, 180601 (2017).
Heyl, M., Polkovnikov, A. & Kehrein, S. Dynamical quantum phase transitions in the transverse-field Ising model. Phys. Rev. Lett. 110, 135704 (2013).
Vajna, S. & Dora, B. Topological classification of dynamical phase transitions. Phys. Rev. B 91, 155127 (2015).
Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold fermions. Nature 515, 237–240 (2014).
Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys 11, 162–166 (2015).
Kennedy, C. J., Burton, W. C., Chung, W. C. & Ketterle, W. Observation of Bose–Einstein condensation in a strong synthetic magnetic field. Nat. Phys 11, 859–864 (2015).
Eckardt, A. Colloquium: atomic quantum gases in periodically driven optical lattices. Rev. Mod. Phys. 89, 011004 (2017).
Fausti, D. et al. Light-induced superconductivity in a stripe-ordered cuprate. Science 331, 189–191 (2011).
Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Colloquium: nonequilibrium dynamics of closed interacting quantum system. Rev. Mod. Phys. 83, 863–883 (2011).
Soltan-Panahi, P. et al. Multi-component quantum gases in spin-dependent hexagonal lattices. Nat. Phys 7, 434–440 (2011).
Parker, C. V., Ha, L.-C. & Chin, C. Direct observation of effective ferromagnetic domains of cold atoms in shaken optical lattices. Nat. Phys 9, 769–774 (2013).
Zheng, W. & Zhai, H. Floquet topological states in shaking optical lattices. Phys. Rev. A 89, 061603 (2014). (R).
Hauke, P., Lewenstein, M. & Eckardt, A. Tomography of band insulators from quench dynamics. Phys. Rev. Lett. 113, 045303 (2014).
Yu, J. Phase vortices of the quenched Haldane model. Phys. Rev. A 96, 023601 (2017).
Heyl, M. Scaling and universality at dynamical quantum phase transitions. Phys. Rev. Lett. 115, 140602 (2015).
Canovi, E., Werner, P. & Eckstein, M. First-order dynamical phase transitions. Phys. Rev. Lett. 113, 265702 (2014).
Schmitt, M. & Kehrein, S. Dynamical quantum phase transitions in the Kitaev honeycomb model. Phys. Rev. B 92, 075114 (2015).
Budich, J. C. & Heyl, M. Dynamical topological order parameters far from equilibrium. Phys. Rev. B 93, 085416 (2016).
Huang, Z. & Balatsky, A. V. Dynamical quantum phase transitions: role of topological nodes in wave function overlaps. Phys. Rev. Lett. 117, 086802 (2016).
Jurcevic, P. et al. Direct observation of dynamical quantum phase transitions in an interacting many-body system. Phys. Rev. Lett. 119, 080501 (2017).
Billy, J. et al. Anderson localization of a non-interacting Bose–Einstein condensate. Nature 453, 891–894 (2008).
Roati, G. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 895–898 (2008).
Schreiber, M. et al. Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349, 842–845 (2015).
Wang, C., Zhang, P., Chen, X., Yu, J. & Zhai, H. Measuring topological number of a Chern-insulator from quench dynamics. Phys. Rev. Lett. 118, 185701 (2017).
Tarnowski, M. et al. Characterizing topology by dynamics: chern number from linking number. Preprint at http://arXiv.org/abs/1709.01046 (2017).
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.
Author information
Authors and Affiliations
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.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Supplementary Information
Supplementary Note 1, Supplementary Fig. 1
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-017-0013-8
This article is cited by
-
Indication of critical scaling in time during the relaxation of an open quantum system
Nature Communications (2024)
-
Anomalous correlation-induced dynamical phase transitions
Scientific Reports (2023)
-
Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
npj Quantum Information (2022)
-
Topological holographic quench dynamics in a synthetic frequency dimension
Light: Science & Applications (2021)
-
Electronic Floquet gyro-liquid crystal
Nature Communications (2021)