Diffusion-induced dephasing in nanomechanical resonators

TL;DR

This paper investigates how diffusion of molecules or particles along nanomechanical resonators causes spectral broadening and shape changes, providing a detailed analysis of the spectral effects under different diffusion conditions.

Contribution

It extends the method of interfering partial spectra to continuous diffusion along nanobeams, establishing conditions for fluctuation-dissipation relations and spectral convolution descriptions.

Findings

Spectral broadening depends on diffusion confinement

Conditions for fluctuation-dissipation relations are identified

Spectral shape changes are characterized for different diffusion regimes

Abstract

We study resonant response of an underdamped nanomechanical resonator with fluctuating frequency. The fluctuations are due to diffusion of molecules or microparticles along the resonator. They lead to broadening and change of shape of the oscillator spectrum. The spectrum is found for the diffusion confined to a small part of the resonator and where it occurs along the whole nanobeam. The analysis is based on extending to the continuous limit, and appropriately modifying, the method of interfering partial spectra. We establish the conditions of applicability of the fluctuation-dissipation relations between the susceptibility and the power spectrum. We also find where the effect of frequency fluctuations can be described by a convolution of the spectra without these fluctuations and with them as the only source of the spectral broadening.