Resonant micro and nanostrings were found to have extraordinarily high quality factors (Qs). Since the discovery of the high Qs of silicon nitride nanostrings, the understanding of the underlying mechanisms allowing such high quality factors has been a topic of several investigations. So far it has been concluded that Q is enhanced due to the high energy stored in the string tension. In this paper, damping mechanisms in string resonators are systematically investigated by varying the geometry and the tensile stress of silicon nitride microstrings. The measured quality factors are compared to an analytical model for Q based on bending-related damping mechanisms. It is shown that internal material damping is limiting the quality factor of narrow strings with a width of 3 $\mu${}m. Q is strongly width dependent and clamping losses evidently seem to be the limiting damping mechanism for wider strings. It is further shown that Q is influenced by interference effects in the substrate and thus by the clamping of the macroscopic chip. A maximum quality factor of up to 7 million is presented for high-stress silicon nitride strings with a resonance frequency of 176 kHz.

Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can be used to experimentally explore collapse models of the wavefunction and the potential for mechanical-resonator-based quantum information and metrology applications.

Silicon nitride (SiN) micro- and nanomechanical resonators have attracted a lot of attention in various research fields due to their exceptionally high quality factors ($Q\mathrm{s}$). Despite their popularity, the origin of the limiting loss mechanisms in these structures has remained controversial. In this Letter we propose an analytical model combining acoustic radiation loss with intrinsic loss. The model accurately predicts the resulting mode-dependent $Q\mathrm{s}$ of low-stress silicon-rich and high-stress stoichiometric SiN membranes. The large acoustic mismatch of the low-stress membrane to the substrate seems to minimize radiation loss and $Q\mathrm{s}$ of higher modes ($n\wedge m\ge 3$) are limited by intrinsic losses. The study of these intrinsic losses in low-stress membranes reveals a linear dependence with the membrane thickness. This finding was confirmed by comparing the intrinsic dissipation of arbitrary (membranes, strings, and cantilevers) SiN resonators extracted from literature, suggesting surface loss as ubiquitous damping mechanism in thin SiN resonators with $Q_{\text{surf}}=\beta h$ and $\beta =6\times {10}^{10}\pm 4\times {10}^{10}{\mathrm{m}}^{-1}$. Based on the intrinsic loss the maximal achievable $Q\mathrm{s}$ and $Qf$ products for SiN membranes and strings are outlined.