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Floquet group theory and its application to selection rules in harmonic generation

Author

Listed:
  • Ofer Neufeld

    (Technion—Israel Institute of Technology
    Technion—Israel Institute of Technology)

  • Daniel Podolsky

    (Technion—Israel Institute of Technology)

  • Oren Cohen

    (Technion—Israel Institute of Technology
    Technion—Israel Institute of Technology)

Abstract

Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.

Suggested Citation

  • 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.
    • Handle: RePEc:nat:natcom:v:10:y:2019:i:1:d:10.1038_s41467-018-07935-y
    DOI: 10.1038/s41467-018-07935-y
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    Cited by:

    1. 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.
    2. Steven Gassner & Clara S. Weber & Martin Claassen, 2024. "Light-induced switching between singlet and triplet superconducting states," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    3. Jared S. Ginsberg & M. Mehdi Jadidi & Jin Zhang & Cecilia Y. Chen & Nicolas Tancogne-Dejean & Sang Hoon Chae & Gauri N. Patwardhan & Lede Xian & Kenji Watanabe & Takashi Taniguchi & James Hone & Angel, 2023. "Phonon-enhanced nonlinearities in hexagonal boron nitride," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    4. Sha Li & Yaguo Tang & Lisa Ortmann & Bradford K. Talbert & Cosmin I. Blaga & Yu Hang Lai & Zhou Wang & Yang Cheng & Fengyuan Yang & Alexandra S. Landsman & Pierre Agostini & Louis F. DiMauro, 2023. "High-order harmonic generation from a thin film crystal perturbed by a quasi-static terahertz field," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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