Resolution Limits of Resonant Sensors

The resolution of resonant sensors is fundamentally limited by the presence noise. Thermomechanical noise, intrinsic to resonator, sets ultimate sensor performance when all other noise sources have been eliminated. For linear resonators, sensing can always be further improved increasing driving power. However, this trend cannot continue indefinitely, since at sufficiently high powers non-linear effects emerge and influence performance. As a consequence, resonator's characteristics play an inextricable role in determining its limits. Recently, several works studied characteristic resonators as sensors, with counter intuitive conclusion that quality factor resonator does not improve thermomechanical limit. In work we analyze limits, describe different regimes integration times below above decay time. We provide analytical model elucidate Duffing non-linearity on closed-loop validate it using numerical simulations. contrast previous works, our simulations show under certain conditions maximizing factor. With measurements nanomechanical membrane experimentally verify demonstrate frequency resolutions achieved surpass previously known