Measuring frequency fluctuations in nonlinear nanomechanical resonators

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.

arXiv commentPublished 7 may 2018

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• Temperature Dependent Non-linear Damping in Palladium Nano-mechanical Resonators
• Suppressing Frequency Fluctuations of Self-Sustained Vibrations in Underdamped Nonlinear Resonators
• Nanomechanical damping via electron-assisted relaxation of two-level systems
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• Mesoscopic Quantum Thermo-mechanics: a new frontier of experimental physics
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• Optomechanically Induced Transparency/Absorption in a 3D Microwave Cavity Architecture at Ambient Temperature
• High Stability Mechanical Frequency Sensing beyond the Linear Regime