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Register a new userDissipation due to tunneling two-level systems in gold nanomechanical resonators
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We present measurements of the dissipation and frequency shift in nanomechanical gold resonators at temperatures down to 10 mK. The resonators were fabricated as doubly-clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 MHz and 3.87 MHz revealed that from 30 mK to 500 mK the dissipation increases with temperature as $T^{0.5}$, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous solids suggest that the dissipation in our resonators is dominated by two-level systems.
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State of the art nanomechanical resonators present quality factors Q ~ 10^3 - 10^5, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the dissipation mechanism that arises in nanomechanical beam-structures due to the tunneling of mesoscopic phonons between the beam and its supports (known as clamping losses). We derive the environmental force spectral density that determines the quantum Brownian motion of a given resonance. Our treatment is valid for low frequencies and provides the leading contribution in the aspect ratio. This yields fundamental limits for the Q-values which are described by simple scaling laws and are relevant for state of the art experimental structures. In this context, for resonant frequencies in the 0.1-1GHz range, while this dissipation mechanism can limit flexural resonators it is found to be negligible for torsional ones. In the case of structureless 3D supports the corresponding environmental spectral densities are Ohmic for flexural resonators and super-Ohmic for torsional ones, while for 2D slab supports they yield 1/f noise. Furthermore analogous results are established for the case of suspended semiconducting single-walled carbon nanotubes. Finally, we provide a general expression for the spectral density that allows to extend our treatment to other geometries and illustrate its use by applying it to a microtoroid. Our analysis is relevant for applications in high precision measurements and for the prospects of probing quantum effects in a macroscopic mechanical degree of freedom.
In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, dissipation dilution, is employed in mirror suspensions of gravitational wave interferometers and at the nanoscale, where soft-clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far only been applied in amorphous materials, specifically silicon nitride. Crystalline materials exhibit significantly lower intrinsic damping at cryogenic temperatures, due to the absence of two level systems in the bulk, as exploited in Weber bars and silicon optomechanical cavities. Applying dissipation dilution engineering to strained crystalline materials could therefore enable extremely low loss nanomechanical resonators, due to the combination of reduced internal friction, high intrinsic strain, and high yield strength. Pioneering work has not yet fully exploited this potential. Here, we demonstrate that single crystal strained silicon, a material developed for high mobility transistors, can be used to realize mechanical resonators with ultralow dissipation. We observe that high aspect ratio ($>10^5$) strained silicon nanostrings support MHz mechanical modes with quality factors exceeding $10^{10}$ at 7 K, a tenfold improvement over values reported in silicon nitride. At 7 K, the thermal noise-limited force sensitivity is approximately $45 mathrm{{zN}/{sqrt{Hz}}}$ - approaching that of carbon nanotubes - and the heating rate is only 60 quanta-per-second. Our nanomechanical resonators exhibit lower dissipation than the most pristine macroscopic oscillators and their low mass makes them particularly promising for quantum sensing and transduction.
The energy dissipation 1/Q (where Q is the quality factor) and resonance frequency characteristics of single-crystal 3C-SiC ultrahigh frequency (UHF) nanomechanical resonators are measured, for a family of UHF resonators with resonance frequencies of 295MHz, 395MHz, 411MHz, 420MHz, 428MHz, and 482MHz. A temperature dependence of dissipation, 1/Q ~ T^(0.3) has been identified in these 3C-SiC devices. Possible mechanisms that contribute to dissipation in typical doubly-clamped beam UHF resonators are analyzed. Device size and dimensional effects on the dissipation are also examined. Clamping losses are found to be particularly important in these UHF resonators. The resonance frequency decreases as the temperature is increased, and the average frequency temperature coefficient is about -45ppm/K.
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes the system develops spontaneous oscillations of amplitude modulation that also show period doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model.
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.
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