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High-frequency stability is a defining metric for the performance of nanomechanical resonators in advanced sensing and timekeeping applications. While 2D materials like graphene offer extreme miniaturization, high mechanical compliance, and high responsivity, these properties make them highly susceptible to nonlinearities that degrade frequency stability. Here, we demonstrate that graphene parametric oscillators unlock an alternative nonlinear operating regime, in which short-term frequency stability is enhanced by strong nonlinear damping.
To trace the nonlinear dynamics of graphene nanomechanical resonators, we operate them in a closed loop via a phase-locked loop (PLL). We experimentally demonstrate that parametric oscillations in the post-bifurcation regime yield a lower Allan deviation at fast integration times compared to standard Duffing oscillations at equivalent drive amplitudes. We attribute the physical origin of this improvement to strong nonlinear damping inherent to parametric oscillators, a mechanism that effectively suppresses amplitude-to-frequency noise conversion even at large operational amplitudes.
To validate our experimental findings, we present a minimalistic theoretical model that captures the observed phase diffusion dynamics. The model confirms nonlinear damping as the dominant mechanism governing phase noise reduction. Ultimately, while traditional sensing views nonlinearities as detrimental, these results provide a new framework for operating highly compliant nano-, electro-, and optomechanical systems, highlighting how nonlinear damping can be harnessed to push precision sensing beyond the conventional limits of graphene oscillators.
This work has recently been published in Nano Letters:
Kartal, E., Shoshani, O., Botnaru, E., Martín-Pérez, A., Manzaneque, T., & Alijani, F. Frequency Stability of Graphene Nonlinear Parametric Oscillator. Nano Letters. https://doi.org/10.1021/acs.nanolett.6c00581