1/f frequency-noise reduction in nanomechanical resonators by dissipation dilution
Abstract
The frequency noise of a resonant nanomechanical sensor is well understood down to its thermomechanical limit, but the longest useful averaging time is set by a flicker, or 1/f, frequency-noise floor whose origin has remained unknown. We show that this floor is the thermal noise of the tension. By the fluctuation-dissipation theorem, the tension of a resonator with fixed ends fluctuates by an amount set by the loss angle of its material; for structural damping, these fluctuations produce 1/f frequency noise with a flicker coefficient h−1=E kB T/(2πVσ02 Qel), with Qel the intrinsic loss under elongation, that contains no free parameter and is diluted by the tensile stress σ0 in the same way as damping is in dissipation dilution. Silicon nitride strings and membranes from 30 to 340~nm thickness follow the predicted volume scaling, the predicted σ0−2 dilution across resonators and within stress-engineered strings, and the predicted thickness dependence, which places noise-active two-level systems in the volume and at the surfaces of the resonators, all at the absolute level set by the independently measured intrinsic loss. The same relation accounts for published data between 78 and 296~K; below 78~K, the loss measured at the resonance no longer represents the loss probed by the noise, marking the limit of the structural-damping assumption. Dissipation dilution therefore lowers the 1/f floor, and the longest useful integration time of a resonant sensor is set by its prestress, volume, temperature, and intrinsic loss angle.
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BibTeX
@misc{kanellopulos2026frequencynoise,
title = {{1/f frequency-noise reduction in nanomechanical resonators by dissipation dilution}},
author = {Kostas Kanellopulos and Silvan Schmid},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16711},
eprint = {2610.16711},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16711},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - 1/f frequency-noise reduction in nanomechanical resonators by dissipation dilution
AU - Kostas Kanellopulos
AU - Silvan Schmid
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.16711
UR - https://arxiv.org/abs/2610.16711
AB - The frequency noise of a resonant nanomechanical sensor is well understood down to its thermomechanical limit, but the longest useful averaging time is set by a flicker, or 1/f, frequency-noise floor whose origin has remained unknown. We show that this floor is the thermal noise of the tension. By the fluctuation-dissipation theorem, the tension of a resonator with fixed ends fluctuates by an amount set by the loss angle of its material; for structural damping, these fluctuations produce 1/f frequency noise with a flicker coefficient h_−1=E k_B T/(2πVσ_0^2 Q_el), with Q_el the intrinsic loss under elongation, that contains no free parameter and is diluted by the tensile stress σ_0 in the same way as damping is in dissipation dilution. Silicon nitride strings and membranes from 30 to 340~nm thickness follow the predicted volume scaling, the predicted σ_0^−2 dilution across resonators and within stress-engineered strings, and the predicted thickness dependence, which places noise-active two-level systems in the volume and at the surfaces of the resonators, all at the absolute level set by the independently measured intrinsic loss. The same relation accounts for published data between 78 and 296~K; below 78~K, the loss measured at the resonance no longer represents the loss probed by the noise, marking the limit of the structural-damping assumption. Dissipation dilution therefore lowers the 1/f floor, and the longest useful integration time of a resonant sensor is set by its prestress, volume, temperature, and intrinsic loss angle.
ER -