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

TL;DR

This paper introduces a novel approach using synthetic dimensions to analyze symmetry-breaking systems, revealing new symmetries and selection rules that influence observable phenomena like high harmonic generation.

Contribution

It demonstrates that synthetic dimensions can systematically reveal new symmetries and selection rules in symmetry-broken systems, extending the understanding of symmetry breaking beyond perturbation theory.

Findings

Derived selection rules for high harmonic generation and above-threshold ionization.

Tabulated synthetic symmetries for (2+1)D Floquet systems.

Experimentally observed HHG selection rules from synthetic dimension symmetries.

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.