Nanomechanical Measurement of the Brownian Force Noise in a Viscous Liquid

TL;DR

This study measures the spectral properties of Brownian force noise on nanomechanical resonators in viscous liquids, revealing a colored spectrum consistent with viscous dissipation, using combined spectral and response measurements.

Contribution

It introduces a method to determine the force noise PSD in viscous liquids using combined spectral and response measurements of nanomechanical resonators, validated by a single-mode viscous dissipation model.

Findings

Force noise PSD exhibits a colored spectrum.

Force noise PSD aligns with viscous dissipation model.

Method applicable across broad frequency range.

Abstract

We study the spectral properties of the thermal force giving rise to the Brownian motion of a continuous mechanical system -- namely, a nanomechanical beam resonator -- in a viscous liquid. To this end, we perform two separate sets of experiments. First, we measure the power spectral density (PSD) of the position fluctuations of the resonator around its fundamental mode at its center. Then, we measure the frequency-dependent linear response of the resonator, again at its center, by driving it with a harmonic force that couples well to the fundamental mode. These two measurements allow us to determine the PSD of the Brownian force noise acting on the structure in its fundamental mode. The PSD of the force noise extracted from multiple resonators spanning a broad frequency range displays a "colored spectrum". Using a single-mode theory, we show that, around the fundamental resonances of the resonators, the PSD of the force noise follows the dissipation of a blade oscillating in a viscous liquid -- by virtue of the fluctuation-dissipation theorem.