Measuring frequency fluctuations in nonlinear nanomechanical resonators

TL;DR

This paper introduces a simple method to measure frequency noise in nonlinear nanomechanical resonators using bistability, revealing damping fluctuations and mode-dependent noise levels, advancing understanding of noise sources in these devices.

Contribution

The authors present a novel, straightforward technique to measure frequency noise in nonlinear nanomechanical devices based on bistability, applicable to various structures.

Findings

Frequency noise follows a T/f dependence consistent with literature.

Damping fluctuations are amplified near bifurcation points.

Relative frequency noise decreases with mode number.

Abstract

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS$_2$ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive up to date. In this Letter we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly-clamped beams, in a cryogenic environment. We report on the same $T/f$ dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected {\it damping fluctuations}, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing, and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure $\delta f/f_0$ lies in the range $0.5 - 0.01~$ppm (consistent with literature for cryogenic MHz devices), and decreases with mode number in the range studied. The technique can be applied to {\it any types} of nano-mechanical structures, enabling progresses towards the understanding of intrinsic sources of noise in these devices.