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Sideband attraction via internal resonance in a multimode membrane as a mechanism for frequency combs

Mengqi Fu1,*, Orjan Ameye1,*, Fan Yang1, Jan Košata2, Javier del Pino1, Oded Zilberberg1,†, and Elke Scheer1,‡

  • *These authors contributed equally to this work.
  • †Contact author: oded.zilberberg@uni-konstanz.de
  • ‡Contact author: elke.scheer@uni-konstanz.de
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Phys. Rev. Research 7, 033127 – Published 6 August, 2025

DOI: https://doi.org/10.1103/3mtc-j9r9

Abstract

We explore self-induced parametric coupling between a driven (low frequency) and an undriven (high frequency) mode, also called internal resonances, in a membrane micromechanical system. Specifically, we focus on the formation of a limit cycle (LC) manifesting as a phononic frequency comb. As the LC formation involves a Hopf bifurcation, we developed a dedicated pump-noisy-probe technique to investigate which mechanical sidebands merge at the bifurcation. We reveal that the sideband of the driven lower mode is up-converted via a cross-Duffing nonlinearity to hybridize with the undriven high mode. When the up-conversion is initially red detuned relative to the high mode, significant squeezing and bimodality in the high mode occurs. Crucially, only when the up-converted sideband is initially blue detuned relative to the high mode, the sideband is attracted to the high mode and merges to form the Hopf bifurcation. This process delineates the microscopic origin of frequency comb formation. Our study reveals a key instability mechanism in driven nonlinear systems with implications for advanced sensing technologies and phononic metamaterials.

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Phys. Rev. Research 7, 033127– Published 6 August, 2025
  • Received 21 September 2024
  • Accepted 16 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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