Selection rules for breaking selection rules

Matan Even Tzur, Ofer Neufeld, Avner Fleischer, Oren Cohen

Research output: Contribution to journalArticlepeer-review


Floquet systems often exhibit dynamical symmetries (DS) that govern the time-dependent dynamics and result in selection rules. When a DS is broken, selection rule deviations are expected. Typically, information about the symmetry-breaking perturbation/phase and the time-dependent dynamics can be extracted from these deviations, hence they are regarded as a background free gauge of symmetry breaking. However, to date, DS breaking & selection rule deviations are not described by a general approach, thus there is no universal insight about the interplay between selection rule deviations, the symmetry breaking perturbation, and the broken DS. Here we consider DS breaking in Floquet systems from a general standpoint, formulating a general theory that analytically connects the symmetry-broken and fully symmetric systems. Using an external laser (of arbitrary frequency and polarization), as a model DS breaking perturbation, we discover that the broken symmetry systematically imposes selection rules on the symmetry-broken system, which physically manifest as scaling laws of selection rule deviations. We term these rules 'selection rules for breaking selection rules'-a new concept in physics. We numerically validate the analytical theory in the context of high harmonic generation. Our discovery is a general feature of nonlinear wave-mixing phenomena, and we expect it to apply to any Floquet system (classical & quantum) and to any DS breaking mechanism (either by intrinsic or extrinsic elements of the system).

Original languageEnglish
Article number103039
JournalNew Journal of Physics
Issue number10
StatePublished - Oct 2021


  • Dynamical symmetry
  • Floquet group theory
  • Floquet perturbation theory
  • High harmonic generation
  • Selection rules
  • Symmetry breaking
  • dynamical symmetry
  • high harmonic generation
  • selection rules
  • symmetry breaking

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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