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

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.

The conditions for the analog of QED photons in semi-classical periodically driven systems

“…In this domain, the Hamiltonian H Q approximately commutes with any symmetry operation X of the Floquet Hamiltonian H f . This revelation resolves a long-standing tension in strong-field physics where the conservation of discrete photon spin and parity emerge from classical analyses, even without quantizing the electromagnetic field [8,10,24,25]. Photonic conservation laws emerge as selection rules of Floquet groups due to the equivalence of Floquet and QED photons.…”

Symmetries and correlations in solids probed by ultrafast high-harmonic spectroscopy

“…6.4.1. This route has been further explored by Tzur et al [46]. In solids, the combined symmetries of the solid and the irradiated field result in a selection criterion, which prohibits the generation of certain harmonic orders.…”

“…By generalizing the bi-circular fields to bi-elliptically polarized driving pulses, a framework for probing a large variety of symmetry broken states is presented in Ref. [46]. In the context of ultrafast material research, this approach is particularly promising for the study of dynamical symmetry breaking such as phonon or magnon excitations [46], topological insulators [47], CDW materials [49], and superconductivity [48].…”

“…[46]. In the context of ultrafast material research, this approach is particularly promising for the study of dynamical symmetry breaking such as phonon or magnon excitations [46], topological insulators [47], CDW materials [49], and superconductivity [48].…”

“…In contrast to classical spectroscopy, the HHG process spans the whole Brillouin zone and encodes full band structure information in the emitted light. At the same time, orientational information such as symmetry groups are easy to obtain and can be used to probe symmetry breaking effects which relate to ultrafast phase transitions [42,43,44,45,46,47,48,49]. The various accessible observables of both techniques are summarized in Fig.…”