Quantum Friction of Micromechanical Resonators at Low Temperatures

Dissipation of micro- and nano-scale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequencies–usually, for smaller, micron-scale structures–a novel mechanism of phonon pumping of two-level defects gives rise to weakly temperature-dependent internal friction, $Q^{-1}$, concomitant to the effects observed in recent experiments. Due to their size, comparable to or shorter than the emitted phonon wavelength, these structures suffer from superradiance-enhanced dissipation by the collective relaxation of a large number of two-level defects contained within the wavelength.