Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning

Abstract

temperature conditions where thermomechanical noise can dominate. The degree of mechanical isolation is characterized by a resonator's mechanical quality factor, Q m . Typically, Q m is defined as the ratio of energy stored in a resonator over the energy dissipated over one cycle of oscillation. Inversely, mechanical quality factors can indicate the dissipation of mechanical noise into a resonator from ambient environments. For mechanical sensors, a resonator's isolation from ambient thermal noise can greatly enhance their ability to detect ultrasmall forces, pressures, positions, masses, velocities, and accelerations. For quantum technologies, mechanical quality factor dictates the average number of coherent oscillations a nanomechanical resonator (in the quantum regime) can undergo before one phonon of thermal noise enters the resonator and causes decoherence of its quantum properties. [1] From microchip sensing to quantum networks, cryogenics are conventionally required to counteract thermal noise but enabling these burgeoning technologies to operate in ambient temperatures would have a significant impact on their widespread use.In room-temperature environments, on-chip mechanical resonators with state-of-the-art quality factors have mostly consisted of high-aspect-ratio suspended nanostructures From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

Hierarchical tensile structures with ultralow mechanical dissipation

“…Furthermore, phononic bandgap engineering is impractical at low frequencies due to the large device sizes required (tens of millimeters for the 100 kHz range). Contemporaneous work such as perimeter modes 21 and “spider-web” resonators 22 have demonstrated low dissipation at low frequencies, but not for the fundamental mode of the structure.…”

Photonic and Optomechanical Thermometry

“…To optimize this trade-off, we fabricated resonators with different devices and geometries which led to a wide range of quality factors up to 10 9 at room temperature [24]. Hence, we acquired the spectrum of each resonator and found that, above Q m = 10 7 , our read-out protocol cannot detect the change of the mechanical displacement x 2 as function of temperature, due to the low linewidth Γ m .…”

Mechanical mode engineering with orthotropic metamaterial membranes

“…Along with micro-and nano-structuration, the miniaturization of whole mechanical resonators has been pushed to the micrometric scale; among the others, a wide investigation has interested nanometer-thick, micrometer-wide membranes [6][7][8] . Thanks to their large quality factors 6,9,10 and extreme aspect ratio, these kinds of device have been used as a standard platform for classical and quantum effects in optomechanics 9,11 and for light 12 , pressure 13 , mass 14 and other sensing applications 7,15 . The mechanical membranes are an ideal platform for hosting photonic metasurfaces, which can be introduced by periodically patterning a portion of the device.…”

“…where σ and ε are the stress and strain tensor, respectively. σ ex is an extra contribution possibly given by initial strain, as in the case of strongly pre-stressed materials such as Si 3 N 4 10,32,33 . The constituent materials of the membrane, namely Si 3 N 4 and Au, are fully isotropic and can be described by the Young's modulus E and Poisson's ratio ν, which are embedded inside the compliance tensor S. The material density ρ completes the set of parameters needed for the simulation.…”