High-Stability Mechanical Frequency Sensing beyond the Linear Regime

Sensing a mechanical frequency shift is a powerful measurement tool. Therefore, understanding and mitigating frequency noise affecting mechanical resonators is imperative. The impact of noise on frequency sensing 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 into frequency noise can worsen the sensor performance. Here, we present an experimentally straightforward method to evade this amplitude trade-off in nano- or micromechanical sensors. Combining knowledge of the Duffing coefficients with readily available amplitude measurements, we avoid amplitude-to-frequency noise conversion. We use 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 observe amplitude-to-frequency noise 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.