Force detection and frequency fluctuations in carbon nanotube mechanical resonators

Orateur : Joel Moser (ICN Barcelona)

Because of their low mass and of their high aspect ratio, carbon nanotube mechanical resonators offer many exciting opportunitie s in sensing applications. These traditionally include mass sensing at the single atom level and charge sensing. In addition, nanotube resonators can act as very sensitive force detectors. I will present our recent force sensing experiments in which the force noise experienced by nanotube resonators has a density measured to be as low as 10-20 N Hz-1/2 (10 zeptoNewton per square root of Hertz). This force noise has a thermal origin and is associated with the Brownian motion of the nanotube at 1 K. To detect the low amplitude vibrations of the nanotube in the Brownian motion regime at such a low temperature, we employ a sensitive method based on correlated electrical noise measurements, in combination with parametric down-conversion. We quantify the force sensitivity of our resonator by applying a known oscillating force at the mechanical resonant frequency. Fluctuations of non-thermal origin (that is, fluctuations whose density is not given by the fluctuation-dissipation theorem) pose a limitation on force sensing as they can give rise to fluctuations of the resonant frequency. Such frequency fluctuations can be caused by tension and mass fluctuations, fluctuations of the charge in the substrate, or dispersive intermode coupling. Because frequency fluctuations broaden mechanical resonances, the apparent resonance linewidth is not necessarily a measure of the energy decay rate  of the resonator. We have developed a simple technique to extract  without resorting to a ring-down measurement. Our technique relies on the combined effect of periodic driving and frequency fluctuations on the displacement spectrum of the nanotube resonator. Frequency fluctuations make forced vibrations random, leading to new spectral features that provide a direct measure of . We find that a significant fraction of the measured resonance linewid th may be ascribed to broadening induced by non-thermal frequency fluctuations. This suggests that the real quality factor of nanotube resonators, which is proportional to 1/, may be much larger than estimated so far.

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