We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si ₃N ₄ string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano) mechanical resonators with optimized performance for a wide variety of applications. (Figure presented.)

The computational analysis of nanophotonic devices is usually carried out via the standard finite element method (FEM). However, FEM requires meshes that are fitted to the devices’ boundaries, so making changes to the geometry (and thus the mesh) results in an inefficient process at best. Such an approach is therefore at odds when conducting design, which requires the analysis of multiple device geometries until reaching a satisfactory solution. Computational design tools such as topology optimization are often used, but the use of density-based representations of geometry inevitably leads to other issues—e.g., pixelized fuzzy boundaries with “gray material” (that does not correspond to dielectric nor vacuum) have an adverse effect on the devices’ interaction with electromagnetic waves. In this paper we propose an interface-enriched generalized finite element method (IGFEM) for the analysis of two-dimensional electromagnetic scattering and eigenvalue problems. IGFEM enables the use of finite element meshes that are completely decoupled from the problem's geometry. The analysis procedure is further coupled to a level set description of topology, resulting in a versatile enriched approach to topology optimization; this level set-based interface-enriched topology optimization procedure is devoid of the issues mentioned above regarding density-based methods, and yields crisp “black-and-white” designs that are devoid of jagged fuzzy edges. We first demonstrate that the analysis procedure achieves the same convergence rate as that of standard FEM using geometry-fitted meshes. We then compare the convergence properties of IGFEM with Nitsche's method on a problem containing an embedded straight interface. Finally, we conduct topology optimization for designing both a 2-D metalens and a 2-D reflector, maximizing their ability to focus light onto a target point.

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies – comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si₃N₄ nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

We demonstrate scanning nitrogen-vacancy center magnetometry using a tapered diamond nanobeam optically coupled to a tapered optical fiber as the scanning probe, facilitating implementation of NV magnetometry in low-temperature setups and other challenging environments.

Mechanical frequency combs are poised to bring the applications and utility of optical frequency combs into the mechanical domain. So far, their main challenge has been strict requirements on drive frequencies and power, which complicate operation. We demonstrate a straightforward mechanism to create a frequency comb consisting of mechanical overtones (integer multiples) of a single eigenfrequency, by monolithically integrating a suspended dielectric membrane with a counter-propagating optical trap. The periodic optical field modulates the dielectrophoretic force on the membrane at the overtones of a membrane’s motion. These overtones share a fixed frequency and phase relation, and constitute a mechanical frequency comb. The periodic optical field also creates an optothermal parametric drive that requires no additional power or external frequency reference. This combination of effects results in an easy-to-use mechanical frequency comb platform that requires no precise alignment, no additional feedback or control electronics, and only uses a single, mW continuous wave laser beam. This highlights the overtone frequency comb as the straightforward future for applications in sensing, metrology and quantum acoustics.

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 10⁸ at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Resonant sensors hold great promise in measuring small masses, to enable future mass spectrometers, and small forces in applications like atomic and magnetic force microscopy. During the last decades, scaling down the size of resonators has led to huge enhancements in sensing resolution, but has also raised the question of what the ultimate limit is. Current knowledge suggests that this limit is reached when a resonator oscillates at the maximum amplitude for which its response is predominantly linear. We present experimental evidence that it is possible to obtain better resolutions by oscillation amplitudes beyond the onset of nonlinearities. An analytical model is developed that explains the observations and unravels the relation between ultimate sensing resolution and speed. In the high-speed limit, we find that the ultimate resolution of a resonator is improved when decreasing its damping. This conclusion contrasts with previous works, which proposed that lowering the damping does not affect or even harms the ultimate sensing resolution.

Magnetic imaging with nitrogen-vacancy (NV) spins in diamond is becoming an established tool for studying nanoscale physics in condensed matter systems. However, the optical access required for NV spin readout remains an important hurdle for operation in challenging environments such as millikelvin cryostats or biological systems. Here, we demonstrate a scanning-NV sensor consisting of a diamond nanobeam that is optically coupled to a tapered optical fiber. This nanobeam sensor combines a natural scanning-probe geometry with high-efficiency through-fiber optical excitation and readout of the NV spins. We demonstrate through-fiber optically interrogated electron spin resonance and proof-of-principle magnetometry operation by imaging spin waves in an yttrium-iron-garnet thin film. Our scanning-nanobeam sensor can be combined with nanophotonic structuring to control the light-matter interaction strength and has potential for applications that benefit from all-fiber sensor access, such as millikelvin systems.

Efficient coupling of light from an optical fiber to silicon waveguides is a challenging task in integrated photonics. Couplers based on adiabatic mode evolution have the advantages of high bandwidth and low loss but are often accompanied by longer device lengths. In this paper, we introduce the concept of adiabaticity map and optimize the coupling between an optical fiber and Si waveguides by selecting routes on the map that minimize unwanted mode coupling. The map clearly indicates areas in mode evolution where supermode coupling is large and identifies optimal routes for efficient mode evolution. Optimized interaction length and widths are obtained from the adiabaticity map. We obtain highly efficient coupling (96%) with large bandwidth (1-dB bandwidth 280 nm) and misalignment tolerance (⪆90 nm lateral misalignment range for 1-dB excess losses) for the TE polarization.

In recent years, the Q-factor of Si 3 N 4 nanomechanical resonators has significantly been increased by soft-clamping techniques using large and complex support structures. To date, however, obtaining similar performance with smaller supports has remained a challenge. Here, we make use of torsion beam supports to tune the Q-factor of Si 3 N 4 string resonators. By design optimization of the supports, we obtain a 50% Q-factor enhancement compared to the standard clamped-clamped string resonators. By performing experimental and numerical studies, we show that further improvement of the Q-factor is limited by a trade-off between maximizing stress and minimizing torsional support stiffness. Thus, our study also provides insight into dissipation limits of high-stress string resonators and outlines how advanced designs can be realized for reaching ultimate f 0 × Q product while maintaining a small footprint.

Studying the interplay between multiple coupled mechanical resonators is a promising new direction in the field of optomechanics. Understanding the dynamics of the interaction can lead to rich new effects, such as enhanced coupling and multi-body physics. In particular, multi-resonator optomechanical systems allow for distinct dynamical effects due to the optical cavity coherently coupling mechanical resonators. Here, we study the mechanical response of two SiN membranes and a single optical mode, and find that the cavity induces a time delay between the local and cavity-transduced thermal noises experienced by the resonators. This results in an optomechanical phase lag that causes destructive interference, cancelling the mechanical thermal noise by up to 20 dB in a controllable fashion and matching our theoretical expectation. Based on the effective coupling between membranes, we further propose, derive, and measure a collective effect, cooperativity competition on mechanical dissipation, whereby the linewidth of one resonator depends on the coupling efficiency (cooperativity) of the other resonator.

For the weak equivalence principle (WEP) to hold, we should not be able to gain any information about mass from its interaction with gravitational fields. This motivates the use of information theoretic techniques to investigate WEP violation. Using this approach, we demonstrate that the WEP holds for a quantum particle in a uniform gravitational field, but is violated in non-uniform and time-dependent gravitational fields, such as in gravitational waves. This provides a precise characterization ofWEP violation by quantum systems in gravitational fields, that should be useful in formalizing other works that have argued for such violations heuristically. In particular, we discuss the possibility of detecting the gravitational Casimir effect with superconductors from an information theoretic perspective.

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.