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Selection rules in symmetry-broken systems by symmetries in synthetic dimensions

Author

Listed:
  • Matan Even Tzur

    (Technion-Israel Institute of Technology)

  • Ofer Neufeld

    (Technion-Israel Institute of Technology
    Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science)

  • Eliyahu Bordo

    (Technion-Israel Institute of Technology)

  • Avner Fleischer

    (Tel Aviv University)

  • Oren Cohen

    (Technion-Israel Institute of Technology)

Abstract

Selection rules are often considered a hallmark of symmetry. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions to demonstrate that symmetry-broken systems systematically exhibit a specific class of symmetries and selection rules. These selection rules constrain the scaling of a system’s observables (non-perturbatively) as it transitions from symmetric to symmetry-broken. Specifically, we drive bi-elliptical high harmonic generation (HHG), and observe that the scaling of the HHG spectrum with the pump’s ellipticities is constrained by selection rules corresponding to symmetries in synthetic dimensions. We then show the generality of this phenomenon by analyzing periodically-driven (Floquet) systems subject to two driving fields, tabulating the resulting synthetic symmetries for (2 + 1)D Floquet groups, and deriving the corresponding selection rules for high harmonic generation (HHG) and other phenomena. The presented class of symmetries and selection rules opens routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, symmetry-protected dark bands, and more.

Suggested Citation

  • Matan Even Tzur & Ofer Neufeld & Eliyahu Bordo & Avner Fleischer & Oren Cohen, 2022. "Selection rules in symmetry-broken systems by symmetries in synthetic dimensions," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-29080-3
    DOI: 10.1038/s41467-022-29080-3
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    References listed on IDEAS

    as
    1. Ofer Neufeld & Daniel Podolsky & Oren Cohen, 2019. "Floquet group theory and its application to selection rules in harmonic generation," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    2. Tran Trung Luu & Hans Jakob Wörner, 2018. "Measurement of the Berry curvature of solids using high-harmonic spectroscopy," Nature Communications, Nature, vol. 9(1), pages 1-6, December.
    3. A. Ron & E. Zoghlin & L. Balents & S. D. Wilson & D. Hsieh, 2019. "Dimensional crossover in a layered ferromagnet detected by spin correlation driven distortions," Nature Communications, Nature, vol. 10(1), pages 1-6, December.
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    Cited by:

    1. Raoul Trines & Holger Schmitz & Martin King & Paul McKenna & Robert Bingham, 2024. "Laser harmonic generation with independent control of frequency and orbital angular momentum," Nature Communications, Nature, vol. 15(1), pages 1-10, December.

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