Fluctuation instabilities via internal resonance in a multimode membrane as a mechanism for frequency combs

TL;DR

This paper investigates how internal resonance in a multimode membrane can lead to the formation of phononic frequency combs through nonlinear parametric interactions, revealing new mechanisms for frequency generation.

Contribution

It introduces a novel mechanism for frequency comb formation via internal resonance in a membrane system, extending understanding beyond standard linear coupling.

Findings

Frequency combs arise from Hopf bifurcations in parametric mode coupling.

Significant squeezing and bimodality occur during energy hybridization.

A variety of internal resonance effects extend beyond linear phenomena.

Abstract

We explore self-induced parametric coupling, also called internal resonances (IRs), in a membrane nanoelectromechanical system. Specifically, we focus on the formation of a limit cycle manifesting as a phononic frequency comb. Utilizing a pump-noisy-probe technique and theoretical modeling, we reveal the behavior of mechanical excitations revealing themselves as sidebands of the stationary IR response. We find that when the energy-absorbing excitation of a lower mode is parametrically-upconverted to hybridize with a higher mode, significant squeezing and bimodality in the upper mode occurs. Instead, when the upconverted absorbing excitation hybridizes with an emitting sideband of the higher mode, a Hopf bifurcation occurs and a limit cycle forms, manifesting as a frequency comb. We thus reveal a unique mechanism to obtain frequency combs in parametrically-coupled modes. We furthermore demonstrate a rich variety of IR effects, the origin of which significantly extends beyond standard linear parametric coupling phenomena. Our findings enhance the understanding of energy transfer mechanisms with implications for advanced sensing technologies and novel phononic metamaterials.