Frequency stabilization via backbone curve feedback

Abstract

High-performance mechanical resonators are essential for precision sensing and time-keeping, yet their performance is fundamentally limited by nonlinear mechanical effects at high oscillation amplitudes. Existing strategies—such as zero-dispersion engineering or mode coupling—are restricted to specific operating points or require complex structural redesigns, and hence only partially mitigate nonlinear frequency shifts. In this work, we propose and experimentally validate a general nonlinear control strategy that restores linear resonator characteristics at amplitudes significantly exceeding the conventional linear regime. Our scheme cancels parasitic nonlinearities by utilizing the feedback loop phase as the primary control input, making it widely applicable across resonator designs. Our results demonstrate a robust path toward enhancing the dynamic range and signal-to-noise ratio of resonator devices.