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 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 to date. In this article 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 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 δ f/ f lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.

A macroscopic object passively cooled into its quantum ground state of motion beyond single-mode cooling

“…The behaviour of σ ph is completely different from frequency and damping noises measured at the same time. They both display true 1/f 2 spectra (with no low-frequency cutoff observed), and shall thus be characterised for a given time span (so-called Allan deviation) 50 . Their temperature dependence is similar and reversed from the one of phonon population, see inset of Fig.…”

On-chip Thermometry for Microwave Optomechanics Implemented in a Nuclear Demagnetization Cryostat

“…It does not alter the area A measurement, but does corrupt both frequency and linewidth estimates. This noise comes in with a 1/ftype component [52,53], plus telegraph-like jumps [56]. It leads to the finite error bars in Fig.…”

“…The low temperature properties of NEMS are described within the tunneling model of Two-Level-Systems (TLSs): for damping, frequency shifts, and phase fluctuations [30,50,52]. It is thus natural to consider strongly coupled individual TLSs as the most probable source of our problems.…”

Nonlinear Nanomechanical Mass Spectrometry at the Single-Nanoparticle Level

“…, we present mass spectra for 500 gold nanoparticles with a nominal diameter of 20 nm (12% dispersion in size) obtained by projecting the individual mass distributions onto the mass and diameter planes. For the mass measurements, the peak with maximum probability density is found at 57 25. MDa which corresponds to a diameter of 20.84 nm.…”

“…Many of the work in the past used the openloop response of nonlinear resonators, [21][22][23][24] including a recent technique for accurate characterization of frequency fluctuations in the nonlinear regime. 25 However, continuously sweeping the frequency in the open-loop cannot be applied effectively to the sensing of abrupt changes induced by single analytes for two reasons. First, open-loop technique requires judicious re-setting of the sweep parameters every time after a particle adsorption.…”