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

• URL: http://arxiv.org/abs/2106.04301v1
• Date: Tue, 8 Jun 2021 12:57:26 GMT
• Title: Selection rules in symmetry-broken systems by symmetries in synthetic dimensions
• Authors: Matan Even Tzur, Ofer Neufeld, Avner Fleischer, Oren Cohen
• Abstract summary: We show that symmetry-broken systems systematically exhibit a new class of symmetries and selection rules. The new class of symmetries & selection rules extends the scope of existing symmetry breaking spectroscopy techniques.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Selection rules are often considered a hallmark of symmetry. When a symmetry is broken, e.g., by an external perturbation, the system exhibits selection rule deviations which are often analyzed by perturbation theory. Here, we employ symmetry-breaking degrees of freedom as synthetic dimensions, to demonstrate that symmetry-broken systems systematically exhibit a new class of symmetries and selection rules. These selection rules determine the scaling of a system's observables (to all orders in the strength of the symmetry-breaking perturbation) as it transitions from symmetric to symmetry-broken. We specifically analyze periodically driven (Floquet) systems subject to two driving fields, where the first field imposes a spatio-temporal symmetry, and the second field breaks it, imposing a symmetry in synthetic dimensions. We tabulate the resulting synthetic symmetries for (2+1)D Floquet group symmetries and derive the corresponding selection rules for high harmonic generation (HHG) and above-threshold ionization (ATI). Finally, we observe experimentally HHG selection rules imposed by symmetries in synthetic dimensions. The new class of symmetries & selection rules extends the scope of existing symmetry breaking spectroscopy techniques, opening new routes for ultrafast spectroscopy of phonon-polarization, spin-orbit coupling, and more.

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