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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.
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 o
We propose and experimentally demonstrate a technique for coupling phonons out of an optomechanical crystal cavity. By designing a perturbation that breaks a symmetry in the elastic structure, we selectively induce phonon leakage without affecting th
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 th
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of spin-mechani
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