Journal
NATURE COMMUNICATIONS
Volume 10, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/s41467-018-07935-y
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Funding
- Israel Science Foundation [1802/12, 1781/18]
- Israeli Center of Research Excellence Circle of Light - I-CORE Program of the Planning and Budgeting Committee
- joint UGC-ISF Research Grant Program [1903/14]
- Wolfson foundation
- National Science Foundation through Harvard-Smithsonian Center for Astrophysics
- Adams Fellowship Program of the Israel Academy of Sciences and Humanities
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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.
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