Abstract
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.
Highlights
Selection rules are often considered a hallmark of symmetry
In the three examples presented in the left panel, the DS forbids even harmonic generation polarized along the ^x axis due to a dynamical reflection symmetry denoted by Z^i 1⁄4 ^τ2 Á σ^^i, where ^τ2 is a halfcycle time translation and σ^i is a spatial reflection relative to ^i axis[10]
To summarize, we have demonstrated that systems that are traditionally regarded as symmetry-broken, systematically exhibit a specific class of symmetries and selection rules through synthetic dimensions
Summary
Selection rules are often considered a hallmark of symmetry. Here, we employ symmetrybreaking degrees of freedom as synthetic dimensions to demonstrate that symmetry-broken systems systematically exhibit a specific class of symmetries and selection rules. We observe selection rules that manifest as restricted scaling laws of the harmonic orders and polarization states as the system transitions from the symmetric to the symmetry broken state. To obtain the corresponding harmonic generation selection rules, we employ the invariance of the emitted field fs laser pulse
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