Nanomechanical Resonators Research Articles

3D Printed Metallic Pillar Nanomechanical Resonators Decorated with TiO2 Nanotubes for Highly Sensitive Environmental Applications

AbstractMicro and nanomechanical devices offer enhanced sensing capabilities for detecting biological and chemical small molecules. However, miniaturization necessitates advanced fabrication processes and complex measurement systems, hindering routine sensor analysis. While alternative methods like 3D printing show promise, challenges such as low device resolution persist due to intrinsic damping of polymer inks. In this study, an array of micrometric pillar resonators is fabricated in Ti6Al4 V alloy using additive manufacturing based on laser powder bed fusion technology. These metallic nanomechanical resonators exhibit a very high quality factor with minimal difference between air and vacuum measurements due to low intrinsic damping. Furthermore, titania nanotubes grown on the pillars via anodic oxidation heighten sensitivity for molecular dye degradation evaluation. Leveraging the weak coupling phenomenon among the pillars in the array, these devices facilitate large‐scale parallelized measurements, here demonstrated with real‐time analysis of dye degradation process. This approach to creating mass sensing devices via metallic additive manufacturing can usher in a new generation of highly performing resonating sensor arrays, offering a cost‐effective and efficient alternative to traditional silicon microfabrication methods.

Unconventional phonon blockade effect in array of three coupled weakly nonlinear nanomechanical resonators

Phonon antibunching, a phenomenon arising from the quantum statistics of mechanical vibrations, has attracted significant attention due to its potential applications in quantum information processing, sensing, and energy harvesting. Here, we present a comprehensive investigation of phonon antibunching in a system consisting of three weakly nonlinear coupled nanomechanical resonators. We analytically derive and study the antibunching behavior of phonons in the proposed system and bring insight into the underlying mechanisms. The optimal phonon blockade results from destructive quantum interference due to distinct two-phonon excitation pathways. Due to this quantum interference, these unconventional phonon blockade systems can achieve antibunched statistics even in weakly nonlinear regimes, in contrast to conventional phonon blockade systems that require strong nonlinearity. We show that with the inclusion of an additional resonator, there are multiple additional two-phonon excitation pathways compared to two resonator cases, which results in stronger phonon antibunching and supports single phonon for longer duration. These findings are interesting for practical phononics using coupled-resonator systems.

Frequency stabilization of self-sustained oscillations in a sideband-driven electromechanical resonator

We present a method to stabilize the frequency of self-sustained vibrations in micromechanical and nanomechanical resonators. The method refers to a two-mode system with the vibrations at significantly different frequencies. The signal from one mode is used to control the other mode. In the experiment, self-sustained oscillations of micromechanical modes are excited by pumping at the blue-detuned sideband of the higher-frequency mode. Phase fluctuations of the two modes show near-perfect anticorrelation. They can be compensated in either of the modes by a stepwise change of the pump phase. The phase change of the controlled mode is proportional to the pump phase change, with the proportionality constant independent of the pump amplitude and frequency. This finding allows us to stabilize the phase of one mode against phase diffusion using the measured phase of the other mode. We demonstrate that phase fluctuations of either the high-frequency mode or the low-frequency mode can be significantly reduced. The results open new opportunities in generating stable vibrations in a broad frequency range via parametric down-conversion in nonlinear resonators. Published by the American Physical Society 2024

Unveiling the tradeoff between device scale and surface nonidealities for an optimized quality factor at room temperature in 2D MoS2 nanomechanical resonators

A high quality (Q) factor is essential for enhancing the performance of resonant nanoelectromechanical systems (NEMS). NEMS resonators based on two-dimensional (2D) materials such as molybdenum disulfide (MoS2) have high frequency tunability, large dynamic range, and high sensitivity, yet room-temperature Q factors are typically less than 1000. Here, we systematically investigate the effects of device size and surface nonidealities on Q factor by measuring 52 dry-transferred fully clamped circular MoS2 NEMS resonators with diameters ranging from 1 μm to 8 μm, and optimize the Q factor by combining these effects with the strain-modulated dissipation model. We find that Q factor first increases and then decreases with diameter, with an optimized room-temperature Q factor up to 3315 ± 115 for a 2-μm-diameter device. Through extensive characterization and analysis using Raman spectroscopy, atomic force microscopy, and scanning electron microscopy, we demonstrate that surface nonidealities such as wrinkles, residues, and bubbles are especially significant for decreasing Q factor, especially for larger suspended membranes, while resonators with flat and smooth surfaces typically have larger Q factors. To further optimize Q factors, we measure and model Q factor dependence on the gate voltage, showing that smaller DC and radio-frequency (RF) driving voltages always lead to a higher Q factor, consistent with the strain-modulated dissipation model. This optimization of the Q factor delineates a straightforward and promising pathway for designing high-Q 2D NEMS resonators for ultrasensitive transducers, efficient RF communications, and low-power memory and computing.

Nanomechanical Crystalline AlN Resonators with High Quality Factors for Quantum Optoelectromechanics.

High-quality factor (Qm) mechanical resonators are crucial for applications where low noise and long coherence time are required, as mirror suspensions, quantum cavity optomechanical devices, or nanomechanical sensors. Tensile strain in the material enables the use of dissipation dilution and strain engineering techniques, which increase the mechanical quality factor. These techniques have been employed for high-Qm mechanical resonators made from amorphous materials and, recently, from crystalline materials such as InGaP, SiC, and Si. A strained crystalline film exhibiting substantial piezoelectricity expands the capability of high-Qm nanomechanical resonators to directly utilize electronic degrees of freedom. In this work, nanomechanical resonators with Qm up to 2.9 × 107 made from tensile-strained 290 nm-thick AlN are realized. AlN is an epitaxially-grown crystalline material offering strong piezoelectricity. Nanomechanical resonators that exploit dissipation dilution and strain engineering to reach a Qm × fm-product approaching 1013 Hz at room temperature are demonstrated. A novel resonator geometry is realized, triangline, whose shape follows the Al-N bonds and offers a central pad patterned with a photonic crystal. This allows to reach an optical reflectivity above 80% for efficient coupling to out-of-plane light. The presented results pave the way for quantum optoelectromechanical devices at room temperature based on tensile-strainedAlN.

Modeling and Vibration Analysis of Carbon Nanotubes as Nanomechanical Resonators for Force Sensing.

Carbon nanotubes (CNTs) have attracted considerable attention as nanomechanical resonators because of their exceptional mechanical properties and nanoscale dimensions. In this study, a novel CNT-based probe is proposed as an efficient nanoforce sensing nanomaterial that detects external pressure. The CNT probe was designed to be fixed by clamping tunable outer CNTs. By using the mobile-supported outer CNT, the position of the partially clamped outer CNT can be controllably shifted, effectively tuning its resonant frequency. This study comprehensively investigates the modeling and vibration analysis of gigahertz frequencies with loaded CNTs used in sensing applications. The vibration frequency of a partially clamped CNT probe under axial loading was modeled using continuum mechanics, considering various parameters such as the clamping location, length, and boundary conditions. In addition, the interaction between external forces and CNT resonators was investigated to evaluate their sensitivity for force sensing. Our results provide valuable insights into the design and optimization of CNT-based nanomechanical resonators for high-performance force sensing applications.

Evaluation of highly sensitive vibration states of nanomechanical resonators in liquid using a convolutional neural network

Nanomechanical resonators can detect various small physical quantities with high sensitivity using changes in resonant properties. However, viscous damping in liquids significantly reduces the measurement sensitivity. This study proposes convolutional neural network (CNN) vibration spectrum analysis to evaluate the highly sensitive vibration states of nanomechanical resonators, which are useful for in-liquid measurements. This research was carried out through the measurement of acetone concentration. First, we compared the concentration classification ability between the proposed and conventional methods and determined that the proposed method of analyzing vibration spectral changes using the CNN model can provide higher measurement sensitivity than the conventional measurement method of observing resonance properties changes and comparing the values for each measurement condition. This result shows that CNN-based spectral analysis is effective for the vibration spectra of in-liquid measurements. Next, gradient-weighted class activation mapping (Grad-CAM) was applied to verify which frequency bands are important for concentration classification in CNN model decision-making. The vibration states in these frequency bands were analyzed in terms of oscillation modes. This analysis revealed significant oscillation modes of the nanomechanical resonator in the liquid environment. Notably, in addition to the resonance states utilized in the conventional method, several other oscillation modes were found to be significant for measurements. This finding suggests that these oscillation modes may be highly sensitive for measurements in liquid environments. Among these oscillation modes, the mode with very small amplitude is highly promising for achieving unprecedented levels of sensitivity in sensing technologies.

Strong Cavity-Optomechanical Transduction of Nanopillar Motion.

Nanomechanical resonators can serve as ultrasensitive, miniaturized force probes. While vertical structures such as nanopillars are ideal for this purpose, transducing their motion is challenging. Pillar-based photonic crystals (PhCs) offer a potential solution by integrating optical transduction within the pillars. However, achieving high-quality PhCs is hindered by inefficient vertical light confinement. Here, we present a full-silicon photonic crystal cavity based on nanopillars as a platform for applications in force sensing and biosensing areas. Its unit cell consists of a silicon pillar with a larger diameter at its top portion than at the bottom, which allows vertical light confinement and an energy band gap in the near-infrared range for transverse-magnetic polarization. We experimentally demonstrate optical cavities with Q factors exceeding 103, constructed by inserting a defect within a periodic arrangement of this type of pillars. Each nanopillar naturally behaves as a nanomechanical cantilever, making the fabricated geometries excellent optomechanical (OM) photonic crystal cavities in which the mechanical motion of each nanopillar composing the cavity can be optically transduced. These geometries display enhanced mechanical properties, cost-effectiveness, integration possibilities, and scalability. They also present an alternative in front of the widely used suspended Si beam OM cavities made on silicon-on-insulator substrates.

Tunable Stochastic State Switching in 2D MoS2 Nanomechanical Resonators with Nonlinear Mode Coupling and Internal Resonance.

Coupled nanomechanical resonators have unveiled fascinating physical phenomena, including phonon-cavity coupling, coupled energy decay pathway, avoided crossing, and internal resonance. Despite these discoveries, the mechanisms and control techniques of nonlinear mode coupling phenomena with internal resonances require further exploration. Here, we report on the observation of stochastic switching between the two resonance states with coupled 1:1 internal resonance, for resonant two-dimensional (2D) molybdenum disulfide (MoS2) nanoelectromechanical systems (NEMS), which is directly driven to the critical coupling regime without parametric pumping. We further demonstrate that the probability of state switching is linearly tunable from ∼0% to ∼100% by varying the driving voltage. Furthermore, we gradually increase the white noise amplitude and show that the probability of obtaining the higher-energy state decreases, and the stochastic switching phenomenon eventually disappears. The results provide insights into the dynamics of coupled NEMS resonators and open up new possibilities for sensing and stochastic computing.

Mode-dependent scaling of nonlinearity and linear dynamic range in a NEMS resonator

Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of nanoelectromechanical systems' (NEMSs) resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. Here, we characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. We find that the modal Duffing constant increases as n4, while the critical amplitude for the onset of nonlinearity decreases as 1/n. The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further.

Mass and Stiffness Deconvolution in Nanomechanical Resonators for Precise Mass Measurement and In Vivo Biosensing.

Nanomechanical sensors, due to their small size and high sensitivity to the environment, hold significant promise for various sensing applications. These sensors enable rapid, highly sensitive, and selective detection of biological and biochemical entities as well as mass spectrometry by utilizing the frequency shift of nanomechanical resonators. Nanomechanical systems have been employed to measure the mass of cells and biomolecules and study the fundamentals of surface science such as phase transitions and diffusion. Here, we develop a methodology using both experimental measurements and numerical simulations to explore the characteristics of nanomechanical resonators when the detection entities are absorbed on the cantilever surface and quantify the mass, density, and Young's modulus of adsorbed entities. Moreover, based on this proposed concept, we present an experimental method for measuring the mass of molecules and living biological entities in their physiological environment. This approach could find applications in predicting the behavior of bionanoelectromechanical resonators functionalized with biological capture molecules, as well as in label-free, nonfunctionalized micro/nanoscale biosensing and mass spectrometry of living bioentities.

Enhanced Pressure Response of Edge-Deposited Graphene Nanomechanical Resonators.

Nanomechanical resonators made of suspended graphene exhibit high sensitivity to pressure changes. Nevertheless, the graphene resonator pressure performance is affected owing to the gas permeation problem between the graphene film and the substrate. Therefore, we prepared edge-deposited graphene resonators by focused ion beam (FIB) deposition of SiO2, and their gas leakage velocities and pressure-sensing ability were demonstrated. In this paper, we characterize the pressure-sensing response and gas leakage velocities of graphene membranes using an all-optical actuation system. The gas leakage velocities of graphene resonators with diameters of 10, 20, and 40 μm are reduced by 5.0 × 106, 2.0 × 107, and 8.1 × 107 atoms/s, respectively, which demonstrates that the edge deposition structure can reduce the gas leakage of the resonator. Furthermore, the pressure-sensing performance of three graphene resonators with different diameters was evaluated, and their average pressure sensitivities were calculated to be 3.4, 2.4, and 1.9 kHz/kPa, with the largest full-range hysteresis errors of 0.6, 0.7, and 1.0%, respectively. The temperature stabilities of the three sizes of resonators in the temperature range of 300-400 K are 0.016, 0.015, and 0.016%/K, and the maximum resonance frequency drift over 1 h is 0.0058, 0.0048, and 0.0112%, respectively. This work has great significance for the improvement of gas leakage velocity characterization of graphene membrane and graphene resonant pressure sensor performance optimization.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport.

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9)Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Centimeter-scale nanomechanical resonators with low dissipation

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.

Multiple optomechanically induced transparency generated slow light in an array of optomechanical system

We present an array of optomechanical systems which consist of an optical cavity and three nanomechanical resonators. Introducing Jaynes-Cumming (J-C) coupling in the nearest neighbor resonator allows for the formation of optomechanical systems with arrays of N nanomechanical resonators. Using a strong pump field and a weak probe field to drive the optical cavity simultaneously, we investigated the coherent optical response and the probe transmission spectrum manifested as multiple optomechanically induced transparency. We illustrate the impact of probe-cavity detuning, J-C coupling strength, and the number of nanomechanical resonators on the transparent window. In particular, we analyze nanomechanical resonators and find that increasing their number results in multiple transparent windows and slow light at different frequencies. We also find that the slow light effect can be enhanced by increasing the number of nanomechanical resonators with odd numbers at resonance. These findings imply that the arrays of optomechanical system can be used for multichannel optical communications and multichannel quantum information processing.

QUEST-DMC: Background Modelling and Resulting Heat Deposit for a Superfluid Helium-3 Bolometer

We report the results of radioactivity assays and heat leak calculations for a range of common cryogenic materials, considered for use in the QUEST-DMC superfluid 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3$$\\end{document}He dark matter detector. The bolometer, instrumented with nanomechanical resonators, will be sensitive to energy deposits from dark matter interactions. Events from radioactive decays and cosmic rays constitute a significant background and must be precisely modelled, using a combination of material screening and Monte Carlo simulations. However, the results presented here are of wider interest for experiments and quantum devices sensitive to minute heat leaks and spurious events, thus we present heat leak per unit mass or surface area for every material studied. This can inform material choices for other experiments, especially if underground operation is considered – where the radiogenic backgrounds will dominate even at shallow depths.

Deformation state of a graphene sheet within the framework of the continuum moment-membrane theory of elasticity

The paper proposes an approach to finding the stress-strain state (SSS) of structures containing graphene, a novel nanomaterial that has currently found а wide range of practical applications in nanoelectromechanical systems. Graphene is a 2D basic building block for other carbon structures such as membranes, sheets, nanotubes, etc. To describe the SSS of a graphene sheet, the phenomenological continuum moment-membrane theory of plates is used, from which, due to the fact that graphene is an ultrathin material, the concept of thickness is excluded. The physical elasticity relationships of a graphene sheet are expressed through its rigidity characteristics, determined using the harmonic potential of interatomic interactions in carbon. A differential formulation and the corresponding variational formulation are given for the problem of static deformation and determination of the natural frequencies and modes of vibration of a graphene sheet. The variational formulation is based on the Lagrange principle and is implemented numerically using the finite element method. Finite element relations are constructed taking into account moment effects of the behavior of a graphene sheet. For approximation, a 4-node rectangular finite element is used. Numerical solutions to several problems of static deformation of a graphene sheet under conditions of a plane stress state and transverse bending are presented, and the analysis of its natural vibrations is also performed. Good convergence of numerical simulation results in all considered problems is demonstrated. The obtained numerical solutions are essential in designing and calculating resonators in which ultrathin nanostructures are used. The establishment of the fact that a graphene sheet has a high intrinsic frequency falling in the GHz region (for example, quartz resonators are characterized by megahertz frequencies) opens up new prospects for using graphene itself as an ultrasensitive nanomechanical resonator for detecting small masses and ultrasmall displacements.

Graphene–fullerene heterostructures as robust and flexible nanomechanical bits

Electrical computers have revolutionized society over the past several decades, but questions have remained about their ability to perform in extreme environments, such as their stability at high-temperature conditions. This has motivated the recent surge of interest in developing mechanical computing platforms at all length scales, including the nanoscale, in which traditional electrical computers are augmented with mechanical ones. However, the most proposed nanomechanical bits are volatile memory bits based on the dynamic response of nanomechanical resonators, and as such, there is a need to develop robust and reprogrammable entirely non-volatile nanomechanical bits. Here, we exploit the multiple quasi-stable configurations of the graphene/fullerene/graphene (GFG) van der Waals heterostructure to work as a novel nonvolatile nanomechanical bit. The GFG heterostructure is unique and robust in that it can return to its initial state without further mechanical input, it can be used for logic functions at relevant operating temperatures through simple application of uniaxial strain, it can exhibit reprogrammability between five basic logic gates (NOT, AND, NAND, OR, NOR) by varying the magnitude or direction of applied strain, and it can be used to represent combinatorial logic through full and half adders. These findings provide a new opportunity to develop mechanical computers based on the large class of nanomaterials.

Photon–phonon entanglement and spin squeezing via dynamically strain-mediated Kerr nonlinearity in dressed nitrogen–vacancy centers

We propose a scheme to generate photon–phonon entanglement and spin squeezing in a hybrid system which is composed of the nitrogen–vacancy (NV) centers, nanomechanical resonator (NMR), and optical cavity. The triplet ground states of the NV centers which have been embedded in the middle of the clamped–clamped NMR are dressed by two strong microwave fields. Kerr nonlinearity is established by an applied microwave field and the vibrational modes of NMR coupling to the dressed-state transitions. The quantum correlations of the applied microwave field, vibrational mode, and NV centers are realized based on the parametric down-conversion-like and beam-splitter-like interactions in the hybrid system, which generate the photon–phonon entanglement and spin squeezing. In this nonlinear processes, the dynamically mediated strain of NMR, as a nonlinear switch, plays the central role in the establishment of such quantum correlations. Our scheme can be applied to quantum nondemolition measurement, quantum sensing, and quantum metrology.

Analysis of Interference Effect in Double Optomechanically Induced Transparency System

We propose a scheme to investigate the interference properties of a double optomechanically induced transparency system, which involves two charged nanomechanical resonators, coupled via Coulomb interaction. The results show that the opening of transparency windows is caused by a destructive interference effect only in the weak optical coupling region. For strong optical coupling, normal mode splitting dominates the transparency phenomenon. In the intermediate region, both destructive interference and normal mode splitting contribute to the transparency windows. When the Coulomb coupling is much weaker than the optical coupling, the Coulomb interaction strength linearly determines the distance between the two transparency windows, and has nearly no influence on the destructive interference effect. Otherwise, the system will work in a nonlinear region.