High Stability Mechanical Frequency Sensing beyond the Linear Regime

Abstract: Sensing via a mechanical frequency shift is a powerful measurement tool, and, therefore, understanding and mitigating frequency noise affecting mechanical resonators is imperative. Thermomechanical noise fundamentally limits mechanical frequency stability, and its impact can be reduced with increased coherent amplitude of mechanical motion. However, large enough actuation places the resonator in the nonlinear (Duffing) regime, where conversion of amplitude noise (AM) into frequency noise (FM) can worsen sensor performance. Here, we present an experimentally straightforward method to evade this amplitude tradeoff in micromechanical sensors. Combining knowledge of the Duffing coefficients with readily available amplitude measurements, we avoid AM-FM conversion. Our approach uses dual-mechanical-mode operation on a tensioned thin-film resonator to set a baseline thermomechanically-limited stability by eliminating correlated single-mode frequency drifts. Thus, we cleanly observe AM-FM conversion at high drive, and reduce it using our method. The resulting high-stability operation beyond the linear regime contrasts long-standing perspectives in the field.