TY - JOUR

T1 - Selection rules for breaking selection rules

AU - Tzur, Matan Even

AU - Neufeld, Ofer

AU - Fleischer, Avner

AU - Cohen, Oren

N1 - Publisher Copyright:
© 2021 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft

PY - 2021/10

Y1 - 2021/10

N2 - 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).

AB - 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).

KW - Dynamical symmetry

KW - Floquet group theory

KW - Floquet perturbation theory

KW - High harmonic generation

KW - Selection rules

KW - Symmetry breaking

UR - http://www.scopus.com/inward/record.url?scp=85118956393&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/ac27e2

DO - 10.1088/1367-2630/ac27e2

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AN - SCOPUS:85118956393

SN - 1367-2630

VL - 23

JO - New Journal of Physics

JF - New Journal of Physics

IS - 10

M1 - 103039

ER -