Ultra-coherent nanomechanical resonators based on inverse design

Thermal noise-driven resonant sensors

MEMS/NEMS resonant sensors hold promise for minute mass and force sensing. However, one major challenge is that conventional externally driven sensors inevitably encounter undesired intrinsic noise, which imposes a fundamental limitation upon their signal-to-noise ratio (SNR) and, consequently, the resolution. Particularly, this restriction becomes increasingly pronounced as sensors shrink to the nanoscale. In this work, we propose a counterintuitive paradigm shift that turns intrinsic thermal noise from an impediment to a constituent of the sensor by harvesting it as the driving force, obviating the need for external actuation and realizing 'noise-driven' sensors. Those sensors employ the dynamically amplified response to thermal noise at resonances for stimulus detection. We demonstrate that lightly damped and highly compliant nano-structures with high aspect ratios are promising candidates for this class of sensors. To overcome the phase incoherence of the drive force, three noise-enabled quantitative sensing mechanisms are developed. We validated our sensor paradigm by experimental demonstrating noise-driven pressure and temperature sensors. Noise-driven sensors offer a new opportunity for delivering practical NEMS sensors that can function at room temperature and under ambient pressure, and a development that suggests a path to cheaper, simpler, and low-power-consumption sensors.

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, "regenerative coupling" in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

High-Strength Amorphous Silicon Carbide for Nanomechanics

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.

Room-temperature quantum optomechanics using an ultralow noise cavity

At room temperature, mechanical motion driven by the quantum backaction of light has been observed only in pioneering experiments in which an optical restoring force controls the oscillator stiffness1,2. For solid-state mechanical resonators in which oscillations are controlled by the material rigidity, the observation of these effects has been hindered by low mechanical quality factors, optical cavity frequency fluctuations3, thermal intermodulation noise4,5 and photothermal instabilities. Here we overcome these challenges with a phononic-engineered membrane-in-the-middle system. By using phononic-crystal-patterned cavity mirrors, we reduce the cavity frequency noise by more than 700-fold. In this ultralow noise cavity, we insert a membrane resonator with high thermal conductance and a quality factor (Q) of 180 million, engineered using recently developed soft-clamping techniques6,7. These advances enable the operation of the system within a factor of 2.5 of the Heisenberg limit for displacement sensing8, leading to the squeezing of the probe laser by 1.09(1) dB below the vacuum fluctuations. Moreover, the long thermal decoherence time of the membrane oscillator (30 vibrational periods) enables us to prepare conditional displaced thermal states of motion with an occupation of 0.97(2) phonons using a multimode Kalman filter. Our work extends the quantum control of solid-state macroscopic oscillators to room temperature.

Research on Fabrication of Phononic Crystal Soft-Supported Graphene Resonator

In aviation, aerospace, and other fields, nanomechanical resonators could offer excellent sensing performance. Among these, graphene resonators, as a new sensitive unit, are expected to offer very high mass and force sensitivity due to their extremely thin thickness. However, at present, the quality factor of graphene resonators at room temperature is generally low, which limits the performance improvement and further application of graphene resonators. Enhancing the quality factor of graphene resonators has emerged as a pressing research concern. In a previous study, we have proposed a new mechanism to reduce the energy dissipation of graphene resonators by utilizing phononic crystal soft-supported structures. We verified its feasibility through theoretical analysis and simulations. This article focuses on the fabrication of a phononic crystal soft-supported graphene resonator. In order to address the issues of easy fracture, deformation, and low success rate in the fabrication of phononic crystal soft-supported graphene resonators, we have studied key processes for graphene suspension release and focused ion beam etching. Through parameter optimization, finally, we have obtained phononic crystal soft-supported graphene resonators with varying cycles and pore sizes. Finally, we designed an optical excitation and detection platform based on Fabry-Pérot interference principle and explored the impact of laser power and spot size on phononic crystal soft-supported graphene resonators.

Mechanical overtone frequency combs

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.

Experimental Realization of Nonreciprocal Adiabatic Transfer of Phonons in a Dynamically Modulated Nanomechanical Topological Insulator

High quality nanomechanical oscillators are promising platforms for quantum entanglement and quantum technology with phonons. Realizing coherent transfer of phonons between distant oscillators is a key challenge in phononic quantum information processing. Here, we report on the realization of robust unidirectional adiabatic pumping of phonons in a parametrically coupled nanomechanical system engineered as a one-dimensional phononic topological insulator. By exploiting three nearly degenerate local modes-two edge states and an interface state between them-and the dynamic modulation of their mutual couplings, we achieve nonreciprocal adiabatic transfer of phononic excitations from one edge to the other with near unit fidelity. We further demonstrate the robustness of such adiabatic transfer of phonons in the presence of various noises in the control signals. Our experiment paves the way toward nonreciprocal phonon dynamics via adiabatic pumping and is valuable for phononic quantum information processing.

Integrated optical-readout of a high-Q mechanical out-of-plane mode

The rapid development of high-Q_M macroscopic mechanical resonators has enabled great advances in optomechanics. Further improvements could allow for quantum-limited or quantum-enhanced applications at ambient temperature. Some of the remaining challenges include the integration of high-Q_M structures on a chip, while simultaneously achieving large coupling strengths through an optical read-out. Here, we present a versatile fabrication method, which allows us to build fully integrated optomechanical structures. We place a photonic crystal cavity directly above a mechanical resonator with high-Q_M fundamental out-of-plane mode, separated by a small gap. The highly confined optical field has a large overlap with the mechanical mode, enabling strong optomechanical interaction strengths. Furthermore, we implement a novel photonic crystal design, which allows for a very large cavity photon number, a highly important feature for optomechanical experiments and sensor applications. Our versatile approach is not limited to our particular design but allows for integrating an out-of-plane optical read-out into almost any device layout. Additionally, it can be scaled to large arrays and paves the way to realizing quantum experiments and applications with mechanical resonators based on high-Q_M out-of-plane modes alike.

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. 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 room temperature quality factors as high as 7.8 × 10⁸ at 107 kHz frequency (1.1 × 10⁹ at T = 6 K). The resonators’ thermal-noise-limited force sensitivities reach 740 zN/Hz^1/2 at room temperature and 90 zN/Hz^1/2 at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. Moreover, we demonstrate hierarchically structured, ultralow dissipation membranes suitable for interferometric position measurements in Fabry-Pérot 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.

Low dissipation of fundamental mode is a determinant factor in nanomechanical resonator design. Here the authors realize soft clamping for the fundamental mode in a nanomechanical tensile structure achieving low loss, low mass, and low resonance frequency that render it a perfect force sensor.

Geometric Tuning of Stress in Predisplaced Silicon Nitride Resonators

We introduce a novel method to geometrically tune the tension in prestrained resonators by making Si₃N₄ strings with a designed predisplacement. This enables us, for example, to study their dissipation mechanisms, which are strongly dependent on the stress. After release of the resonators from the substrate, their static displacement is extracted using scanning electron microscopy. The results match finite-element simulations, which allows a quantitative determination of the resulting stress. The in- and out-of-plane eigenmodes are sensed using on-chip Mach-Zehnder interferometers, and the resonance frequencies and quality factors are extracted. The geometrically controlled stress enables tuning not only of the frequencies but also of the damping rate. We develop a model that quantitatively captures the stress dependence of the dissipation in the same SiN film. We show that the predisplacement shape provides additional flexibility, including control over the frequency ratio and the quality factor for a targeted frequency.

Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses

SignificanceCreating structures to realize function-oriented mechanical responses is desired for many applications. Yet, the use of a single material phase and heuristics-based designs may fail to attain specific target behaviors. Here, through a deterministic algorithmic procedure, multiple materials with dissimilar properties are intelligently synthesized into composite structures to achieve arbitrary prescribed responses. Created structures possess unconventional geometry and seamless integration of multiple materials. Despite geometric complexity and varied material phases, these structures are fabricated by multimaterial manufacturing, and tested to demonstrate that wide-ranging nonlinear responses are physically and accurately realized. Upon heteroassembly, resulting structures provide architectures that exhibit highly complex yet navigable responses. The proposed strategy can benefit the design of function-oriented nonlinear mechanical devices, such as actuators and energy absorbers.

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

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.