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

Matan Even Tzur; Ofer Neufeld; Eliyahu Bordo; Avner Fleischer; Oren Cohen

doi:10.1038/s41467-022-29080-3

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

Matan Even Tzur^*, Ofer Neufeld, Eliyahu Bordo, Avner Fleischer, Oren Cohen

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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.

Original language	English
Article number	1312
Journal	Nature Communications
Volume	13
Issue number	1
DOIs	https://doi.org/10.1038/s41467-022-29080-3
State	Published - Dec 2022
Externally published	Yes

Access to Document

10.1038/s41467-022-29080-3

Cite this

@article{d3bfe619c09d41d1b747c93d24b2fa4d,

title = "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{\textquoteright}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{\textquoteright}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.",

author = "Tzur, {Matan Even} and Ofer Neufeld and Eliyahu Bordo and Avner Fleischer and Oren Cohen",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",

year = "2022",

month = dec,

doi = "10.1038/s41467-022-29080-3",

language = "英语",

volume = "13",

journal = "Nature Communications",

issn = "2041-1723",

publisher = "Nature Publishing Group",

number = "1",

}

TY - JOUR

T1 - Selection rules in symmetry-broken systems by symmetries in synthetic dimensions

AU - Tzur, Matan Even

AU - Neufeld, Ofer

AU - Bordo, Eliyahu

AU - Fleischer, Avner

AU - Cohen, Oren

PY - 2022/12

Y1 - 2022/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85126249521&partnerID=8YFLogxK

U2 - 10.1038/s41467-022-29080-3

DO - 10.1038/s41467-022-29080-3

M3 - 文章

C2 - 35288566

AN - SCOPUS:85126249521

SN - 2041-1723

VL - 13

JO - Nature Communications

JF - Nature Communications

IS - 1

M1 - 1312

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this