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

Matan Even Tzur*, Ofer Neufeld, Eliyahu Bordo, Avner Fleischer, Oren Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish
Article number1312
JournalNature Communications
Issue number1
StatePublished - Dec 2022
Externally publishedYes


Dive into the research topics of 'Selection rules in symmetry-broken systems by symmetries in synthetic dimensions'. Together they form a unique fingerprint.

Cite this