Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators

TL;DR

This paper introduces a new ultrasensitive force detection method using nonlinear resonators that exhibit a double jump hysteresis, enabling detection of extremely weak forces in the atto-newton range.

Contribution

The authors demonstrate a novel hysteresis-based detection scheme leveraging nonlinear dynamics for ultrasensitive weak force measurement.

Findings

Double jump hysteresis depends on external force presence.

Frequency of the jump varies linearly with force amplitude.

Potential to detect forces in the atto-newton range.

Abstract

We propose a novel method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay between the parametric drive, external force and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the atto-newton range.