Clamp-tapering increases the quality factor of stressed nanobeams

Stressed nanomechanical resonators are known to have exceptionally high quality factors ($Q$) due to the dilution of intrinsic dissipation by stress. Typically, the amount of dissipation dilution and thus the resonator $Q$ is limited by the high mode curvature region near the clamps. Here we study the effect of clamp geometry on the $Q$ of nanobeams made of high-stress $\mathrm{Si_3N_4}$. We find that tapering the beam near the clamp - and locally increasing the stress - leads to increased $Q$ of MHz-frequency low order modes due to enhanced dissipation dilution. Contrary to recent studies of tethered-membrane resonators, we find that widening the clamps leads to decreased $Q$ despite increased stress in the beam bulk. The tapered-clamping approach has practical advantages compared to the recently developed "soft-clamping" technique. Tapered-clamping enhances the $Q$ of the fundamental mode and can be implemented without increasing the device size

Hierarchical tensile structures with ultralow mechanical dissipation

Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. Hierarchical metamaterials utilize structure at multiple size scales to realize new and highly desirable properties which can be strikingly different from those of the constituent materials. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitride nanomechanical resonators and realize binary tree-shaped resonators with quality factors as high as $10^9$ at 107 kHz frequency, reaching the parameter regime of levitated particles. The resonators' thermal-noise-limited force sensitivities reach $740\ \mathrm{zN/\sqrt{Hz}}$ at room temperature and $\mathrm{90\ zN/\sqrt{Hz}}$ at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. We also find that the self-similar structure of binary tree resonators results in fractional spectral dimensions, which is characteristic of fractal geometries. Moreover, we show that the hierarchical design principles can be extended to 2D trampoline membranes, and we fabricate ultralow dissipation membranes suitable for interferometric position measurements in Fabry-P\'erot cavities. Hierarchical nanomechanical resonators open new avenues in force sensing, signal transduction and quantum optomechanics, where low dissipation is paramount and operation with the fundamental mode is often advantageous.Comment: 19 pages, 11 figures. Fixed link to Zenodo repositor

Generalized dissipation dilution in strained mechanical resonators

Mechanical resonators with high quality factors are of relevance in precision experiments, ranging from gravitational wave detection and force sensing to quantum optomechanics. Beams and membranes are well known to exhibit flexural modes with enhanced quality factors when subjected to tensile stress. The mechanism for this enhancement has been a subject of debate, but is typically attributed to elastic energy being "diluted" by a lossless potential. Here we clarify the origin of the lossless potential to be the combination of tension and geometric nonlinearity of strain. We present a general theory of dissipation dilution that is applicable to arbitrary resonator geometries and discuss why this effect is particularly strong for flexural modes of nanomechanical structures with high aspect ratios. Applying the theory to a non-uniform doubly clamped beam, we show analytically how dissipation dilution can be enhanced by modifying the beam shape to implement "soft clamping", thin clamping and geometric strain engineering, and derive the ultimate limit for dissipation dilution

Elastic strain engineering for ultralow mechanical dissipation

Extreme stresses can be produced in nanoscale structures, a feature which has been used to realize enhanced materials properties, such as the high mobility of silicon in modern transistors. Here we show how nanoscale stress can be used to realize exceptionally low mechanical dissipation, when combined with "soft-clamping" - a form of phononic engineering. Specifically, using a non-uniform phononic crystal pattern, we colocalize the strain and flexural motion of a freestanding Si3N4 nanobeam. Ringdown measurements at room temperature reveal string-like modes with quality (Q) factors as high as 800 million and Q x frequency exceeding 10(15) Hz

Ultralow Dissipation Mechanical Resonators for Quantum Optomechanics

We demonstrate dissipation dilution engineering techniques for ultralow dissipation mechanical resonators. The Si3N4 nanobeams show quality factors (Q) as high as 800 million and Q x f exceeding 10(15) Hz-both records at room temperature. (C) 2019 The Author(s