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

• Published in: Nature communications Vol. 13; no. 1; pp. 1312 - 10
• Main Authors: Tzur, Matan Even, Neufeld, Ofer, Bordo, Eliyahu, Fleischer, Avner, Cohen, Oren
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 14.03.2022; Nature Publishing Group; Nature Portfolio
• Subjects: 639/766/36/1121; 639/766/400/3923; Broken symmetry; Harmonic generations; Humanities and Social Sciences; multidisciplinary; Polarization (spin alignment); Rapid prototyping; Route selection; Science; Science (multidisciplinary); Spectroscopy; Spin-orbit interactions; Symmetry
• ISSN: 2041-1723; 2041-1723
• DOI: 10.1038/s41467-022-29080-3

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. The authors introduce the concept of real-synthetic symmetries and use it as a tool to derive selection rules in seemingly symmetry-broken strong-field interactions. These symmetries and their corresponding selection rules can be applied in various systems form harmonic generation to topological photonics