Nanoscale Mechanical Resonators Research Articles

Acoustic Resonance Tuning by High-Order Lorentzian Mixing.

Nanoscale mechanical resonators have attracted a great deal of attention for signal processing, sensors, and quantum applications. Recent progress in ultrahigh-Q acoustic cavities in nanostructures allows strong interactions with various physical systems and advanced functional devices. Those acoustic cavities are highly sensitive to external perturbations, and it is hard to control those resonance properties since those responses are determined by the geometry and material. In this paper, we demonstrate a novel acoustic resonance tuning method by mixing high-order Lorentzian responses in an optomechanical system. Using weakly coupled phononic-crystal acoustic cavities, we achieve coherent mixing of second- and third-order Lorentzian responses, which is capable of the fine-tunability of the bandwidth and peak frequency of the resonance with a tuning range comparable to the acoustic dissipation rate of the device. This novel resonance tuning method can be widely applied to Lorentzian-response systems and optomechanics, especially active compensation for environmental fluctuation and fabrication errors.

Analysis of the vibrational characteristics of diamane nanosheet based on the Kirchhoff plate model and atomistic simulations

Single layer diamond—diamane, has been reported with excellent mechanical properties. In this work, molecular dynamics (MD) simulation and Kirchhoff plate model are utilized to investigate the vibrational characteristics of diamane sheets. The mechanical parameters of diamane sheets, including bending stiffness, Young’s modulus, Poisson’s ratio and coefficient of thermal expansion, are calibrated by using MD simulations. The natural frequencies and corresponding modal shapes of the diamane sheets predicted by the Kirchhoff plate model agree well with that obtained from the MD simulations. It is found that the edges exert marginal effect on the modal shapes when free boundary conditions are applied. Additionally, the Kirchhoff plate model considering the thermal expansion provides reasonable prediction for the natural frequencies of the diamane sheets with all boundary clamped under varying temperatures. This study offers valuable insights into the vibrational properties of diamane sheets, from both a simulation and theoretical standpoint. The findings would be beneficial for the design of nanoscale mechanical resonators utilizing these novel carbon materials.

Size effect on transverse free vibrations of ultrafine nanothreads

Due to their unique properties and appealing applications, low dimensional sp3 carbon nanostructures have attracted increasing attention recently. Based on the beam theory and atomistic studies, this work carries out a comprehensive investigation on the vibrational properties of the ultrathin carbon nanothreads (NTH). Size effect is observed in transverse free vibrations of NTHs. To quantify such effects, the modified couple stress theory (MCST) is utilized to modify the Timoshenko beam theory. According to the first four order frequencies of NTHs from atomistic simulations, the critical length scale parameter of MCST is calibrated as 0.1 nm. It is shown that MCST has minor effect on the first four order modal shapes, except for the clamped boundary. MCST makes the modal shapes at the clamped boundary closer to those observed in atomistic simulations. This study suggests that to some extent the MCST-based Timoshenko beam theory can well describe the transverse vibration characteristics of the ultrafine NTHs, which are helpful for designing and fabricating the NTH-based nanoscale mechanical resonators.

Resonant modal interactions in micro/nano-mechanical structures

This paper considers nonlinear interactions between vibration modes with a focus on recent studies relevant to micro- and nanoscale mechanical resonators. Due to their inherently small damping and high susceptibility to nonlinearity, these devices have brought to light new phenomena and offer the potential for novel applications. Nonlinear interactions between vibration modes are well known to have the potential for generating a “zoo” of complicated bifurcation patterns and a wide variety of dynamic behaviors, including chaos. Here, we focus on more regular, robust, and predictable aspects of their dynamics, since these are most relevant to applications. The investigation is based on relatively simple two-mode models that are able to capture and predict a wide range of transient and sustained dynamical behaviors. The paper emphasizes modeling and analysis that has been done in support of recent experimental investigations and describes in full detail the analysis and attendant insights obtained from the models that are briefly described in the experimental papers. Standard analytical tools are employed, but the questions posed and the conclusions drawn are novel, as motivated by observations from experiments. The paper considers transient dynamics, response to harmonic forcing, and self-excited systems and describes phenomena such as extended coherence time during transient decay, zero dispersion response, and nonlinear frequency veering. The paper closes with some suggested directions for future studies in this area.

A quantum memory at telecom wavelengths

Nanofabricated mechanical resonators are gaining significant momentum among potential quantum technologies due to their unique design freedom and independence from naturally occurring resonances. With their functionality being widely detached from material choice, they constitute ideal tools to be used as transducers, i.e. intermediaries between different quantum systems, and as memory elements in conjunction with quantum communication and computing devices. Their capability to host ultra-long lived phonon modes is particularity attractive for non-classical information storage, both for future quantum technologies as well as for fundamental tests of physics. Here we demonstrate such a mechanical quantum memory with an energy decay time of $T_1\approx2$ ms, which is controlled through an optical interface engineered to natively operate at telecom wavelengths. We further investigate the coherence of the memory, equivalent to the dephasing $T_2^*$ for qubits, which exhibits a power dependent value between 15 and 112 $\mu$s. This demonstration is enabled by a novel optical scheme to create a superposition state of $\rvert{0}\rangle+\rvert{1}\rangle$ mechanical excitations, with an arbitrary ratio between the vacuum and single phonon components.

Detecting a phonon flux in superfluid He4 by a nanomechanical resonator

Nanoscale mechanical resonators are widely utilized to provide high sensitivity force detectors. Here we demonstrate that such high quality factor resonators immersed in superfluid \(^4\mathrm{He}\) can be excited by a modulated flux of phonons. A nanosized heater immersed in superfluid \(^4\mathrm{He}\) acts as a source of ballistic phonons in the liquid -- "phonon wind". When the modulation frequency of the phonon flux matches the resonance frequency of the mechanical resonator, the motion of the latter can be excited. This ballistic thermomechanical effect can potentially open up new types of experiments in quantum fluids.

Probing superfluid He4 with high-frequency nanomechanical resonators down to millikelvin temperatures

Superfluids, such as superfluid $^3\mathrm{He}$ and $^4\mathrm{He}$, exhibit a broad range of quantum phenomena and excitations which are unique to these systems. Nanoscale mechanical resonators are sensitive and versatile force detectors with the ability to operate over many orders of magnitude in damping. Using nanomechanical-doubly clamped beams of extremely high quality factors ($Q>10^6$), we probe superfluid $^4\mathrm{He}$ from the superfluid transition temperature down to $\mathrm{mK}$ temperatures at frequencies up to $11.6 \, \mathrm{MHz}$. Our studies show that nanobeam damping is dominated by hydrodynamic viscosity of the normal component of $^4\mathrm{He}$ above $1\,\mathrm{K}$. In the temperature range $0.3-0.8\,\mathrm{K}$, the ballistic quasiparticles (phonons and rotons) determine the beams' behavior. At lower temperatures, damping saturates and is determined either by magnetomotive losses or acoustic emission into helium. It is remarkable that all these distinct regimes can be extracted with just a single device, despite damping changing over six orders of magnitude.

Hydrogel Microelectromechanical System (MEMS) Resonators: Beyond Cost‐Effective Sensing Platform

AbstractMechanical resonators have been used for various applications including timing references, filters, accelerometers, and inertial sensors. Mostly, silicon‐based materials have been thought to be ideal considering robustness and stability and thus used to fabricate micro and nanoscale mechanical resonators. When enhanced sensitivity becomes more important than long‐term stability, materials repertoires other than silicon might be better suited. Herein, a novel manufacturing approach is proposed, which rapidly fabricates microelectromechanical system resonators with hydrogel by single UV exposure via dynamic mask and dry‐state “plugging out” sacrificial process where hydrogel structures are defined by spatially modulated UV light. For practical demonstrations, rectangular cantilevers and closed circular membranes are employed for humidity and pressure sensing applications, respectively. The cost‐effective fabrication route suggested herein not only enables rapid prototyping of suspended hydrogel structures outside a cleanroom, but also offers spatially tunable elastic modulus. Most remarkably, sensitivity enhancement resulting from high swelling rate and/or low elastic modulus exceeds stability deterioration, one of the major concerns for polymeric materials. Such exclusive beneficial features, yet demonstrated with any microfabrication materials and methods or their combinations, open a new avenue for photocurable polymeric materials to be used for specific applications as well as fundamental investigations.

Phonon quantum nondemolition measurements in nonlinearly coupled optomechanical cavities

In the field of cavity optomechanics, proposals for quantum nondemolition (QND) measurements of phonon number provide a promising avenue by which one can study the quantum nature of nanoscale mechanical resonators. Here, we investigate these QND measurements for an optomechanical system whereby quadratic coupling arises due to shared symmetries between a single optical resonance and a mechanical mode. We establish a relaxed limit on the amount of linear coupling that can exist in this type of system while still allowing for a QND measurement of Fock states. This new condition enables optomechanical QND measurements, which can be used to probe the decoherence of mesoscopic mechanical Fock states, providing an experimental testbed for quantum collapse theories.

Coupling a Superconducting Quantum Circuit to a Phononic Crystal Defect Cavity

Connecting nanoscale mechanical resonators to microwave quantum circuits opens new avenues for storing, processing, and transmitting quantum information. In this work, we couple a phononic crystal cavity to a tunable superconducting quantum circuit. By fabricating a one-dimensional periodic pattern in a thin film of lithium niobate and introducing a defect in this artificial lattice, we localize a 6 gigahertz acoustic resonance to a wavelength-scale volume of less than one cubic micron. The strong piezoelectricity of lithium niobate efficiently couples the localized vibrations to the electric field of a widely tunable high-impedance Josephson junction array resonator. We measure a direct phonon-photon coupling rate $g/2\pi \approx 1.6 \, \mathrm{MHz}$ and a mechanical quality factor $Q_\mathrm{m} \approx 3 \times 10^4$ leading to a cooperativity $C\sim 4$ when the two modes are tuned into resonance. Our work has direct application to engineering hybrid quantum systems for microwave-to-optical conversion as well as emerging architectures for quantum information processing.

Reconsidering resonator sensing

Nanotechnology Changes in the frequency of a nanoscale mechanical resonator can be used for many sensing applications, provided that there is an adequate signal-to-noise ratio. Normally, this ratio is improved by creating resonators with higher quality factors that “ring” for longer times.

Size-dependent damping of a nanobeam using nonlocal thermoelasticity: extension of Zener, Lifshitz, and Roukes’ damping model

Thermoelastic damping is an important issue for micro-/nanoscale mechanical resonators. In this work, an Euler–Bernoulli beam with different types of mechanical boundary conditions at the two ends is adopted. Once it bends, the half compressed (stretched) will be heated (cooled), then a transverse heat conduction appears, and energy dissipation occurs. First, size-dependent thermoelasticity based on generalized thermodynamics is introduced by combining the nonlocal elasticity and hydrodynamic heat-conductive model heat conduction, and the governing equations of the nonlocal thermal Euler–Bernoulli beam are sequently formulated. Second, an analytical solution to the inverse quality factor is obtained by using the complex-frequency approach, and it is observed that the solution is related to the nonlocal parameter of both elastic and thermal fields, as well as material constants. Meanwhile, another numerical method to get the inverse quality factor is proposed. Third, the effects of nonlocal parameters of both thermal and elastic fields, the height of the beam, and the material constants on the quality factor are evaluated. Finally, conclusive remarks are summarized. The predicted results are expected to be beneficial to micro-/nanomechanical resonators design.

Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators

Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P0 is α times that of a scaled-up microscale resonator at a reduced pressure α P0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.

Robust continuous-variable entanglement of microwave photons with cavity electromechanics

We investigate the controllable generation of robust photon entanglement with a circuit cavity electromechanical system, consisting of two superconducting coplanar waveguide cavities (CPWC's) capacitively coupled by a nanoscale mechanical resonator (MR). We show that, with this electromechanical system, two-mode continuous-variable entanglement of cavity photons can be engineered deterministically either via coherent control on the dynamics of the system, or through a dissipative quantum dynamical process. The first scheme, operating in the strong coupling regime, explores the excitation of the cavity Bogoliubov modes, and is insensitive to the initial thermal noise. The second one is based on the reservoir-engineering approach, which exploits the mechanical dissipation as a useful resource to perform ground state cooling of two delocalized cavity Bogoliubov modes. The achieved amount of entanglement in both schemes is determined by the relative ratio of the effective electromechanical coupling strengths, which thus can be tuned and made much lager than that in previous studies.

Model-independent quantitative measurement of nanomechanical oscillator vibrations using electron-microscope linescans

Nanoscale mechanical resonators are highly sensitive devices and, therefore, for application as highly sensitive mass balances, they are potentially superior to micromachined cantilevers. The absolute measurement of nanoscale displacements of such resonators remains a challenge, however, since the optical signal reflected from a cantilever whose dimensions are sub-wavelength is at best very weak. We describe a technique for quantitative analysis and fitting of scanning-electron microscope (SEM) linescans across a cantilever resonator, involving deconvolution from the vibrating resonator profile using the stationary resonator profile. This enables determination of the absolute amplitude of nanomechanical cantilever oscillations even when the oscillation amplitude is much smaller than the cantilever width. This technique is independent of any model of secondary-electron emission from the resonator and is, therefore, applicable to resonators with arbitrary geometry and material inhomogeneity. We demonstrate the technique using focussed-ion-beam-deposited tungsten cantilevers of radius ~60-170 nm inside a field-emission SEM, with excitation of the cantilever by a piezoelectric actuator allowing measurement of the full frequency response. Oscillation amplitudes approaching the size of the primary electron-beam can be resolved. We further show that the optimum electron-beam scan speed is determined by a compromise between deflection of the cantilever at low scan speeds and limited spatial resolution at high scan speeds. Our technique will be an important tool for use in precise characterization of nanomechanical resonator devices.

Energy transfer performance of mechanical nanoresonators coupled with electromagnetic fields

We study the energy transfer performance in electrically and magnetically coupled mechanical nanoresonators. Using the resonant scattering theory, we show that magnetically coupled resonators can achieve the same energy transfer performance as for their electrically coupled counterparts or even outperform them within the scale of interest. Magnetic and electric coupling are compared in the nanotube radio, a realistic example of a nano-scale mechanical resonator. The energy transfer performance is also discussed for a newly proposed bio-nanoresonator composed of magnetosomes coated with a net of protein fibers.

All-Electrical Control of the Photon-Charge-Qubit Interfaces for Quantum Networks

Out of the consideration of scalability and convenience, all-electrical control of quantum dynamics in quantum information processing is highly desirable. Here we describe a scheme of all-electrical control of the quantum interface between optical qubits and charge qubits mediated by a nanoscale mechanical resonator. This quantum interface can accomplish many key tasks of a quantum network, such as transferring, swapping, and entangling qubits between distant nodes of a quantum network. Numerical simulations show that high fidelity operations on this quantum interface under realistic experimental conditions are reachable.

Nanomechanical resonators

We review the current state of research into the development of nanomechanical resonators and their application as components of nanoelectromechanical and optomechanical systems for the highly sensitive detection and visualization of material structure. Methods for the manufacture and characterization of nanoscale mechanical resonators are described. We discuss quantum properties of nanomechanical resonators and dynamical cooling schemes for suppressing fluctuations in order to increase the threshold sensitivity of optomechanical and electromechanical systems.

Phonon-tunnelling dissipation in mechanical resonators

Microscale and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example, in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavours. Their performance is in many cases limited by the deleterious effects of mechanical damping. In this study, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the 'phonon-tunnelling' approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform a rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with the theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunnelling solver represents a major step towards accurate prediction of the mechanical quality factor.

The versatility of nanoscale mechanical resonators

The vibrations of tiny “diving boards” enable scientists to view the world one atom at a time and may allow the observation of quantum effects in mechanical systems.