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Light-cone-like spreading of correlations in a quantum many-body system

Nature volume 481, pages 484–487 (2012)Cite this article

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Abstract

In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied1. The existence of a maximal velocity, known as the Lieb–Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice2,3,4,5)—such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a ‘speed of light’ has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium6, and for engineering the efficient quantum channels necessary for fast quantum computations7.

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Figure 1: Spreading of correlations in a quenched atomic Mott insulator.
Figure 2: Time evolution of the two-point parity correlations.
Figure 3: Propagation velocity.

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Acknowledgements

We thank C. Weitenberg and J. F. Sherson for their contribution to the design and construction of the apparatus. We also thank D. Baeriswyl, T. Giamarchi, V. Gritsev and S. Huber for discussions. C.K. acknowledges previous collaboration on a related subject with A. Läuchli. We acknowledge funding by MPG, DFG, EU (NAMEQUAM, AQUTE, Marie Curie Fellowship to M.C.), JSPS (Postdoctoral Fellowship for Research Abroad to T.F.), ‘Triangle de la physique’, ANR (FAMOUS) and SNSF (under division II and MaNEP). Financial support for the computer cluster on which the calculations were performed was provided by the Fondation Ernst et Lucie Schmidheiny.

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Authors and Affiliations

  1. Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany ,

    Marc Cheneau, Manuel Endres, Peter Schauß, Takeshi Fukuhara, Christian Gross, Immanuel Bloch & Stefan Kuhr

  2. Département de physique théorique, Université de Genève, 1211 Genève, Switzerland,

    Peter Barmettler, Dario Poletti & Corinna Kollath

  3. Ludwig-Maximilians-Universität, 80799 München, Germany ,

    Immanuel Bloch

  4. Centre de physique théorique, École Polytechnique, CNRS, 91128 Palaiseau, France ,

    Corinna Kollath

  5. University of Strathclyde, SUPA, Glasgow G4 0NG, UK ,

    Stefan Kuhr

Authors
  1. Marc Cheneau
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Contributions

M.C. performed the experiment. P.B. performed the numerical simulations. P.B., D.P. and C.K. developed the analytical model. M.C. and P.B. carried out the data analysis. All authors contributed to designing the study, to interpreting the data and to writing the manuscript.

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Correspondence to Marc Cheneau.

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The authors declare no competing financial interests.

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Supplementary Information

This file contains Supplementary Text and Data including a Supplementary Discussion, Supplementary Figures 1-2 with legends, Supplementary Tables 1-2 and additional references. (PDF 319 kb)

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Cheneau, M., Barmettler, P., Poletti, D. et al. Light-cone-like spreading of correlations in a quantum many-body system. Nature 481, 484–487 (2012). https://doi.org/10.1038/nature10748

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