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Simulating hyperbolic space on a circuit board

Author

Listed:
  • Patrick M. Lenggenhager

    (Paul Scherrer Institute
    University of Zurich
    Institute for Theoretical Physics, ETH Zurich)

  • Alexander Stegmaier

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Lavi K. Upreti

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Tobias Hofmann

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Tobias Helbig

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Achim Vollhardt

    (University of Zurich)

  • Martin Greiter

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Ching Hua Lee

    (National University of Singapore)

  • Stefan Imhof

    (Physikalisches Institut, Universität Würzburg)

  • Hauke Brand

    (Physikalisches Institut, Universität Würzburg)

  • Tobias Kießling

    (Physikalisches Institut, Universität Würzburg)

  • Igor Boettcher

    (University of Alberta
    Theoretical Physics Institute, University of Alberta)

  • Titus Neupert

    (University of Zurich)

  • Ronny Thomale

    (Institut für Theoretische Physik und Astrophysik, Universität Würzburg)

  • Tomáš Bzdušek

    (Paul Scherrer Institute
    University of Zurich)

Abstract

The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space. Here we discuss and experimentally demonstrate that the spectral ordering of Laplacian eigenstates for hyperbolic (negatively curved) and flat two-dimensional spaces has a universally different structure. We use a lattice regularization of hyperbolic space in an electric-circuit network to measure the eigenstates of a ‘hyperbolic drum’, and in a time-resolved experiment we verify signal propagation along the curved geodesics. Our experiments showcase both a versatile platform to emulate hyperbolic lattices in tabletop experiments, and a set of methods to verify the effective hyperbolic metric in this and other platforms. The presented techniques can be utilized to explore novel aspects of both classical and quantum dynamics in negatively curved spaces, and to realise the emerging models of topological hyperbolic matter.

Suggested Citation

  • Patrick M. Lenggenhager & Alexander Stegmaier & Lavi K. Upreti & Tobias Hofmann & Tobias Helbig & Achim Vollhardt & Martin Greiter & Ching Hua Lee & Stefan Imhof & Hauke Brand & Tobias Kießling & Igor, 2022. "Simulating hyperbolic space on a circuit board," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-32042-4
    DOI: 10.1038/s41467-022-32042-4
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    References listed on IDEAS

    as
    1. Alicia J. Kollár & Mattias Fitzpatrick & Andrew A. Houck, 2019. "Hyperbolic lattices in circuit quantum electrodynamics," Nature, Nature, vol. 571(7763), pages 45-50, July.
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    Cited by:

    1. Qiaolu Chen & Zhe Zhang & Haoye Qin & Aleksi Bossart & Yihao Yang & Hongsheng Chen & Romain Fleury, 2024. "Anomalous and Chern topological waves in hyperbolic networks," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    2. Anffany Chen & Hauke Brand & Tobias Helbig & Tobias Hofmann & Stefan Imhof & Alexander Fritzsche & Tobias Kießling & Alexander Stegmaier & Lavi K. Upreti & Titus Neupert & Tomáš Bzdušek & Martin Greit, 2023. "Hyperbolic matter in electrical circuits with tunable complex phases," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Lei Huang & Lu He & Weixuan Zhang & Huizhen Zhang & Dongning Liu & Xue Feng & Fang Liu & Kaiyu Cui & Yidong Huang & Wei Zhang & Xiangdong Zhang, 2024. "Hyperbolic photonic topological insulators," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    4. Weixuan Zhang & Fengxiao Di & Xingen Zheng & Houjun Sun & Xiangdong Zhang, 2023. "Hyperbolic band topology with non-trivial second Chern numbers," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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