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  • Open Access

Topological Phases of Sound and Light

V. Peano1, C. Brendel1, M. Schmidt1, and F. Marquardt1,2

  • 1Institute for Theoretical Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
  • 2Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1, 91058 Erlangen, Germany

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Phys. Rev. X 5, 031011 – Published 28 July, 2015

DOI: https://doi.org/10.1103/PhysRevX.5.031011

Abstract

Topological states of matter are particularly robust, since they exploit global features of a material’s band structure. Topological states have already been observed for electrons, atoms, and photons. It is an outstanding challenge to create a Chern insulator of sound waves in the solid state. In this work, we propose an implementation based on cavity optomechanics in a photonic crystal. The topological properties of the sound waves can be wholly tuned in situ by adjusting the amplitude and frequency of a driving laser that controls the optomechanical interaction between light and sound. The resulting chiral, topologically protected phonon transport can be probed completely optically. Moreover, we identify a regime of strong mixing between photon and phonon excitations, which gives rise to a large set of different topological phases and offers an example of a Chern insulator produced from the interaction between two physically distinct particle species, photons and phonons.

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Popular Summary

Recently, a new topology-based paradigm in the classification of the phases of matter has emerged. Topological states of matter have already been observed for electrons, atoms, and photons. It is an outstanding challenge to engineer a solid-state device on the nanoscale, supporting topologically protected sound waves. We show that such waves could emerge in a surprisingly simple setting: a suitably patterned slab of dielectric illuminated by a laser with an appropriately chosen phase pattern.

Our proposal takes advantage of the enhanced radiation pressure interaction in so-called optomechanical crystals. These crystals are the optomechanical analog of photonic crystals and support defects with co-localized optical and vibrational modes. In our analysis, we predict that creating an optomechanical array formed by a periodic arrangement of such defects will yield a Chern insulator when driven by a suitable laser field. The setup is easily tunable in situ by varying the laser drive amplitude and frequency. We show that the resulting chiral, topologically protected phonon transport along the edges can be probed completely optically. In addition to the phonon Chern insulator, we predict a second regime in which photons and phonons form hybrid topological bands, giving rise to a multitude of topological phases of sound and light. This regime represents a novel example of a Chern insulator produced from the interaction of two physically distinct particle species.

We expect that our results will motivate experimentalists and theoreticians to begin exploiting the possibilities offered by engineering phonon-photon band structures using light. Experimental verification of our theory would be the first demonstration of topologically protected sound propagation on the nanoscale.

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Phys. Rev. X 5, 031011– Published 28 July, 2015
  • Received 6 February 2015
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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