Ultrasensitive force detection with a nanotube mechanical resonator

Two-color electromagnetically induced transparency generated slow light in double-mechanical-mode coupling carbon nanotube resonators

We theoretically propose a multiple-mode-coupling hybrid quantum system comprising two-mode-coupling nanomechanical carbon nanotube (CNT) resonators realized by a phase-dependent phonon-exchange interaction interacting with the same nitrogen-vacancy (NV) center in diamond. We investigate the coherent optical responses of the NV center under the condition of resonance and detuning. In particular, two-color electromagnetically induced transparency (EIT) can be achieved by controlling the system parameters and coupling regimes. Combining the spin-phonon interactions and phonon-phonon coupling with the modulation phase, the switching of one and two EIT windows has been demonstrated, which generates a light delay or advance. The slow-to-fast and fast-to-slow light transitions have been studied in different coupling regimes, and the switch between slow and fast light can be controlled periodically by tuning the modulation phase. The study can be applied to phonon-mediated optical information storage or information processing with spin qubits based on multiple-mode hybrid quantum systems.

Achieving Ultrawide Tunability in Monolithically Fabricated Si Nanoresonator Devices

Nanoresonators are powerful and versatile tools promising to revolutionize a wide range of technological areas by delivering unparalleled performance in physical, chemical, biological sensing, signal and information processing, quantum computation, etc., via their high-frequency resonant vibration and rich dynamic behavior. Having the ability to tune the resonance frequency and dynamic behavior at the application stage promises further improvement in their effectiveness and enables novel applications. However, achieving significant room-temperature tunability in conventional (monolithically fabricated) nanoresonators is considered challenging. Here we demonstrate ultrawide electrostatic tuning (∼70%) of (initial) resonance-frequency (∼7% V-1) at room temperature in a monolithically fabricated ultrathin Si nanoresonator (width ∼ 40 nm, length ∼ 200 μm) device. Extreme electrostatic tuning of nonlinear behavior is also demonstrated by canceling the cubic-nonlinear coefficient and subsequently flipping its sign. Thus, these results are expected to provide remarkable operational flexibility and new capabilities to microfabricated resonators, which will benefit many technological areas.

Ultrahigh-quality graphene resonators by liquid-based strain-engineering

Two-dimensional (2D) material-based nanoelectromechanical (NEM) resonators are expected to be enabling components in hybrid qubits that couple mechanical and electromagnetic degrees of freedom. However, challenges in their sensitivity and coherence time have to be overcome to realize such mechanohybrid quantum systems. We here demonstrate the potential of strain engineering to realize 2D material-based resonators with unprecedented performance. A liquid-based tension process was shown to enhance the resonance frequency and quality factor of graphene resonators six-fold. Spectroscopic and microscopic characterization reveals a surface-energy enhanced wall interaction as the origin of this effect. The response of our tensioned resonators is not limited by external loss factors and exhibits near-ideal internal losses, yielding superior resonance frequencies and quality factors to all previously reported 2D material devices. Our approach represents a powerful method of enhancing 2D NEM resonators for future quantum systems.

Constitutive Modeling of Mechanical Behaviors of Carbon-Based CNTs and GSs, and Their Sensing Applications as Nanomechanical Resonators: A Review

Carbon-based nanomaterials, including carbon nanotubes (CNTs) and graphene sheets (GSs), have garnered considerable research attention owing to their unique mechanical, physical, and chemical properties compared with traditional materials. Nanosensors are sensing devices with sensing elements made of nanomaterials or nanostructures. CNT- and GS-based nanomaterials have been proved to be very sensitive nanosensing elements, being used to detect tiny mass and force. In this study, we review the developments in the analytical modeling of mechanical behavior of CNTs and GSs, and their potential applications as next-generation nanosensing elements. Subsequently, we discuss the contributions of various simulation studies on theoretical models, calculation methods, and mechanical performance analyses. In particular, this review intends to provide a theoretical framework for a comprehensive understanding of the mechanical properties and potential applications of CNTs/GSs nanomaterials as demonstrated by modeling and simulation methods. According to analytical modeling, nonlocal continuum mechanics pose small-scale structural effects in nanomaterials. Thus, we overviewed a few representative studies on the mechanical behavior of nanomaterials to inspire the future development of nanomaterial-based sensors or devices. In summary, nanomaterials, such as CNTs and GSs, can be effectively utilized for ultrahigh-sensitivity measurements at a nanolevel resolution compared to traditional materials.

Optomechanical force sensor operating over wide detection range

A detector with both broad operation range and high sensitivity is desirable in the measurement of weak periodic forces. Based on a nonlinear dynamical mechanism of locking the mechanical oscillation amplitude in optomechanical systems, we propose a force sensor that realizes the detection through the cavity field sidebands modified by an unknown external periodic force. Under the mechanical amplitude locking condition, the unknown external force happens to modify the locked oscillation amplitude linearly to its magnitude, thus achieving a linear scaling between the sideband changes read by the sensor and the magnitude of the force to be measured. This linear scaling range is found to be comparable to the applied pump drive amplitude, so the sensor can measure a wide range of force magnitude. Because the locked mechanical oscillation is rather robust against thermal perturbation, the sensor works well at room temperature. In addition to weak periodic forces, the same setup can as well detect static forces, though the detection ranges are much narrower.

Artificial-intelligence-assisted mass fabrication of nanocantilevers from randomly positioned single carbon nanotubes

Nanoscale cantilevers (nanocantilevers) made from carbon nanotubes (CNTs) provide tremendous benefits in sensing and electromagnetic applications. This nanoscale structure is generally fabricated using chemical vapor deposition and/or dielectrophoresis, which contain manual, time-consuming processes such as the placing of additional electrodes and careful observation of single-grown CNTs. Here, we demonstrate a simple and Artificial Intelligence (AI)-assisted method for the efficient fabrication of a massive CNT-based nanocantilever. We used randomly positioned single CNTs on the substrate. The trained deep neural network recognizes the CNTs, measures their positions, and determines the edge of the CNT on which an electrode should be clamped to form a nanocantilever. Our experiments demonstrate that the recognition and measurement processes are automatically completed in 2 s, whereas comparable manual processing requires 12 h. Notwithstanding the small measurement error by the trained network (within 200 nm for 90% of the recognized CNTs), more than 34 nanocantilevers were successfully fabricated in one process. Such high accuracy contributes to the development of a massive field emitter using the CNT-based nanocantilever, in which the output current is obtained with a low applied voltage. We further showed the benefit of fabricating massive CNT-nanocantilever-based field emitters for neuromorphic computing. The activation function, which is a key function in a neural network, was physically realized using an individual CNT-based field emitter. The introduced neural network with the CNT-based field emitters recognized handwritten images successfully. We believe that our method can accelerate the research and development of CNT-based nanocantilevers for realizing promising future applications.

Beating thermal noise in a dynamic signal measurement by a nanofabricated cavity optomechanical sensor

Thermal fluctuations often impose both fundamental and practical measurement limits on high-performance sensors, motivating the development of techniques that bypass the limitations imposed by thermal noise outside cryogenic environments. Here, we theoretically propose and experimentally demonstrate a measurement method that reduces the effective transducer temperature and improves the measurement precision of a dynamic impulse response signal. Thermal noise-limited, integrated cavity optomechanical atomic force microscopy probes are used in a photothermal-induced resonance measurement to demonstrate an effective temperature reduction by a factor of ≈25, i.e., from room temperature down as low as ≈12 K, without cryogens. The method improves the experimental measurement precision and throughput by >2×, approaching the theoretical limit of ≈3.5× improvement for our experimental conditions. The general applicability of this method to dynamic measurements leveraging thermal noise-limited harmonic transducers will have a broad impact across a variety of measurement platforms and scientific fields.

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems

We study the enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric, with the two involved cavities being dissipatively coupled via the waveguide. The anti-PT symmetry may break down when a weak waveguide-mediated coherent coupling is introduced. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity measured by an enhancement factor is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the enhancement factor shows resistance to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength and has potential applications in high-precision measurements with systems involving Kerr-type nonlinearity.

Enhancing the force sensitivity of a squeezed light optomechanical interferometer

Application of frequency-dependent squeezed vacuum improves the force sensitivity of an optomechanical interferometer beyond the standard quantum limit by a factor of e^-r, where r is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum back-action nullifying meter in an optomechanical cavity with mechanical mirror in middle configuration can enhance the sensitivity beyond the standard quantum limit by a factor of e^-reff, where r_eff = r + ln(4Δ/ζ)/2, for 0 < ζ/Δ < 1, with ζ as the optomechanical cavity decay rate and Δ as the detuning between cavity eigenfrequency and driving field. The technique described in this work is restricted to frequencies much smaller than the resonance frequency of the mechanical mirror. We further studied the sensitivity as a function of temperature, mechanical mirror reflectivity, and input laser power.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

Mode coupling bi-stability and spectral broadening in buckled carbon nanotube mechanical resonators

Bi-stable mechanical resonators play a significant role in various applications, such as sensors, memory elements, quantum computing and mechanical parametric amplification. While carbon nanotube based resonators have been widely investigated as promising NEMS devices, a bi-stable carbon nanotube resonator has never been demonstrated. Here, we report a class of carbon nanotube resonators in which the nanotube is buckled upward. We show that a small upward buckling yields record electrical frequency tunability, whereas larger buckling can achieve Euler-Bernoulli bi-stability, the smallest mechanical resonator with two stable configurations to date. We believe that these recently-discovered carbon nanotube devices will open new avenues for realizing nano-sensors, mechanical memory elements and mechanical parametric amplifiers. Furthermore, we present a three-dimensional theoretical analysis revealing significant nonlinear coupling between the in-plane and out-of-plane static and dynamic modes of motion, and a unique three-dimensional Euler-Bernoulli snap-through transition. We utilize this coupling to provide a conclusive explanation for the low quality factor in carbon nanotube resonators at room temperature, key in understanding dissipation mechanisms at the nano scale.

Computing, memories, and digital electronics are based on the operation principle of bi-stable systems. Here, Yaish et al. report the unusual non-linear behaviour of buckled up carbon nanotubes mechanical resonators, which allows high electrical frequency tunability and snap-through bi-stability.

Soft-Clamped Silicon Nitride String Resonators at Millikelvin Temperatures

We demonstrate that soft-clamped silicon nitride strings with a large aspect ratio can be operated at mK temperatures. The quality factors (Q) of two measured devices show consistent dependency on the cryostat temperature, with soft-clamped mechanical modes reaching Q>10^{9} at roughly 46 mK. For low optical readout power, Q is found to saturate, indicating good thermalization between the sample and the stage it is mounted on. Our best device exhibits a calculated force sensitivity of 9.6  zN/sqrt[Hz] and a thermal decoherence time of 0.38 s, which bode well for future applications such as nanomechanical force sensing.

Superconducting Cavity Electromechanics: The Realization of an Acoustic Frequency Comb at Microwave Frequencies

We present a nonlinear multimode superconducting electroacoustic system, where the interplay between superconducting kinetic inductance and piezoelectric strong coupling establishes an effective Kerr nonlinearity among multiple acoustic modes at 10 GHz that could hardly be achieved via intrinsic mechanical nonlinearity. By exciting this multimode Kerr system with a single microwave tone, we further demonstrate a coherent electroacoustic frequency comb and provide theoretical understanding of multimode nonlinear interaction in the superstrong coupling limit. This nonlinear superconducting electroacoustic system sheds light on the active control of multimode resonator systems and offers an enabling platform for the dynamic study of microcombs at microwave frequencies.

Optimal metrology with programmable quantum sensors

Quantum sensors are an established technology that has created new opportunities for precision sensing across the breadth of science. Using entanglement for quantum enhancement will allow us to construct the next generation of sensors that can approach the fundamental limits of precision allowed by quantum physics. However, determining how state-of-the-art sensing platforms may be used to converge to these ultimate limits is an outstanding challenge. Here we merge concepts from the field of quantum information processing with metrology, and successfully implement experimentally a programmable quantum sensor operating close to the fundamental limits imposed by the laws of quantum mechanics. We achieve this by using low-depth, parametrized quantum circuits implementing optimal input states and measurement operators for a sensing task on a trapped-ion experiment. With 26 ions, we approach the fundamental sensing limit up to a factor of 1.45 ± 0.01, outperforming conventional spin-squeezing with a factor of 1.87 ± 0.03. Our approach reduces the number of averages to reach a given Allan deviation by a factor of 1.59 ± 0.06 compared with traditional methods not using entanglement-enabled protocols. We further perform on-device quantum-classical feedback optimization to 'self-calibrate' the programmable quantum sensor with comparable performance. This ability illustrates that this next generation of quantum sensor can be used without previous knowledge of the device or its noise environment.

Real-Time Sensing with Multiplexed Optomechanical Resonators

Nanoelectromechanical resonators have been successfully used for a variety of sensing applications. Their extreme resolution comes from their small size, which strongly limits their capture area. This leads to a long analysis time and the requirement for large sample quantity. Moreover, the efficiency of the electrical transductions commonly used for silicon resonators degrades with increasing frequency, limiting the achievable mechanical bandwidth and throughput. Multiplexing a large number of high-frequency resonators appears to be a solution, but this is complex with electrical transductions. We propose here a route to solve these issues, with a multiplexing scheme for very high-frequency optomechanical resonators. We demonstrate the simultaneous frequency measurement of three silicon microdisks fabricated with a 200 mm wafer large-scale process. The readout architecture is simple and does not degrade the sensing resolutions. This paves the way toward the realization of sensors for multiparametric analysis with an extremely low limit of detection and response time.

Phonon-Induced Pairing in Quantum Dot Quantum Simulator

Quantum simulations can provide new insights into the physics of strongly correlated electronic systems. A well-studied system, but still open in many regards, is the Hubbard-Holstein Hamiltonian, where electronic repulsion is in competition with attraction generated by the electron-phonon coupling. In this context, we study the behavior of four quantum dots in a suspended carbon nanotube and coupled to its flexural degrees of freedom. The system is described by a Hamiltonian of the Hubbard-Holstein class, where electrons on different sites interact with the same phonon. We find that the system presents a transition from the Mott insulating state to a polaronic state, with the appearance of pairing correlations and the breaking of the translational symmetry. These findings will motivate further theoretical and experimental efforts to employ nanoelectromechanical systems to simulate strongly correlated systems with electron-phonon interactions.

Reaching silicon-based NEMS performances with 3D printed nanomechanical resonators

The extreme miniaturization in NEMS resonators offers the possibility to reach an unprecedented resolution in high-performance mass sensing. These very low limits of detection are related to the combination of two factors: a small resonator mass and a high quality factor. The main drawback of NEMS is represented by the highly complex, multi-steps, and expensive fabrication processes. Several alternatives fabrication processes have been exploited, but they are still limited to MEMS range and very low-quality factor. Here we report the fabrication of rigid NEMS resonators with high-quality factors by a 3D printing approach. After a thermal step, we reach complex geometry printed devices composed of ceramic structures with high Young’s modulus and low damping showing performances in line with silicon-based NEMS resonators ones. We demonstrate the possibility of rapid fabrication of NEMS devices that present an effective alternative to semiconducting resonators as highly sensitive mass and force sensors.

NEMS devices, nano-electro-mechanical systems, by virtue of their minute size, offer ultra-high sensitivity, though at the expense of manufacturing complexity. Here, Stassi et al succeed in manufacturing high quality factor NEMS devices using high resolution 3D printing.

Ultrasensitive nano-optomechanical force sensor operated at dilution temperatures

Cooling down nanomechanical force probes is a generic strategy to enhance their sensitivities through the concomitant reduction of their thermal noise and mechanical damping rates. However, heat conduction becomes less efficient at low temperatures, which renders difficult to ensure and verify their proper thermalization. Here we implement optomechanical readout techniques operating in the photon counting regime to probe the dynamics of suspended silicon carbide nanowires in a dilution refrigerator. Readout of their vibrations is realized with sub-picowatt optical powers, in a situation where less than one photon is collected per oscillation period. We demonstrate their thermalization down to 32 ± 2 mK, reaching very large sensitivities for scanning probe force sensors, 40 zN Hz^−1/2, with a sensitivity to lateral force field gradients in the fN m⁻¹ range. This opens the road toward explorations of the mechanical and thermal conduction properties of nanoresonators at minimal excitation level, and to nanomechanical vectorial imaging of faint forces at dilution temperatures.

Optical readout techniques for nanomechanical force probes usually generate more heat than what can be dissipated through the nanoresonators. Here, the authors use an interferometric readout scheme, achieving large force sensitivity using suspended silicon carbide nanowires at dilution temperatures.

The Recent Progress of MEMS/NEMS Resonators

MEMS/NEMS resonators are widely studied in biological detection, physical sensing, and quantum coupling. This paper reviews the latest research progress of MEMS/NEMS resonators with different structures. The resonance performance, new test method, and manufacturing process of single or double-clamped resonators, and their applications in mass sensing, micromechanical thermal analysis, quantum detection, and oscillators are introduced in detail. The material properties, resonance mode, and application in different fields such as gyroscope of the hemispherical structure, microdisk structure, drum resonator are reviewed. Furthermore, the working principles and sensing methods of the surface acoustic wave and bulk acoustic wave resonators and their new applications such as humidity sensing and fast spin control are discussed. The structure and resonance performance of tuning forks are summarized. This article aims to classify resonators according to different structures and summarize the working principles, resonance performance, and applications.

Interrelation of Elasticity and Thermal Bath in Nanotube Cantilevers

We report the first study on the thermal behavior of the stiffness of individual carbon nanotubes, which is achieved by measuring the resonance frequency of their fundamental mechanical bending modes. We observe a reduction of the Young's modulus over a large temperature range with a slope -(173±65)  ppm/K in its relative shift. These findings are reproduced by two different theoretical models based on the thermal dynamics of the lattice. These results reveal how the measured fundamental bending modes depend on the phonons in the nanotube via the Young's modulus. An alternative description based on the coupling between the measured mechanical modes and the phonon thermal bath in the Akhiezer limit is discussed.

Revolution of a trapped particle in counter-propagating dual-beam optical tweezers under low pressure

We presented faster and more accurate simulations and experiments describing the revolution of a suspended particle in optical tweezers under a low pressure. Instead of the state-of-the-art offline method of pinhole alignment, we proposed an in situ method of revolution suppression by adjusting the laser beam while observing the power spectral density and time-domain plot of the particle centroid displacement. The experimental results under different air pressures show that our method is more effective at low pressures. We observed that "revolution occurs when radial alignment error is below the threshold" and uncovered the mechanism behind this phenomenon. The rapidly growing Q value of the revolution indicates a high-precision resonance measurement method under lower air pressure compared with random translation measurements.

On-chip torsion balances with femtonewton force resolution at room temperature enabled by carbon nanotube and graphene

The torsion balance, consisting of a rigid balance beam suspended by a fine thread, is an ancient scientific instrument, yet it is still a very sensitive force sensor to date. As the force sensitivity is proportional to the lengths of the beam and thread, but inversely proportional to the fourth power of the diameter of the thread, nanomaterials should be ideal building blocks for torsion balances. Here, we report a torsional balance array on a chip with the highest sensitivity level enabled by using a carbon nanotube as the thread and a monolayer graphene coated with Al nanofilms as the beam and mirror. It is demonstrated that the femtonewton force exerted by a weak laser can be easily measured. The balances on the chip should serve as an ideal platform for investigating fundamental interactions up to zeptonewton in accuracy in the near future.

Color-detuning-dynamics-based quantum sensing with dressed states driving

Exploring quantum technology to precisely measure physical quantities is a meaningful task for practical scientific researches. Here, we propose a novel quantum sensing model based on color detuning dynamics with dressed states driving (DSD) in stimulated Raman adiabatic passage. The model is valid for sensing different physical quantities, such as magnetic field, mass, rotation and so on. For different sensors, the used systems can range from macroscopic scale, e.g. optomechanical systems, to microscopic nanoscale, e.g. solid spin systems. The dynamics of color detuning of DSD passage indicates the sensitivity of sensors can be enhanced by tuning system with more adiabatic or accelerated processes in different color detuning regimes. To show application examples, we apply our approach to build optomechanical mass sensor and solid spin magnetometer with practical parameters.

Multimode Nonlinear Coupling Induced by Internal Resonance in a Microcantilever Resonator

Coupled resonators represent a generic model for many physical systems. In this context, a microcantilever is a multimode resonator clamped at one end, and it finds extensive application in high-precision metrology and is expected to be of great potential use in emerging quantum technologies. Here, we explore the microcantilever as a flexible platform for realizing multimode nonlinear interactions. Multimode nonlinear coupling is achieved by (1:2) internal resonance (IR) and parametric excitation with efficient coherent energy transfer. Specifically, we demonstrate abundant tunable parametric behaviors via frequency and voltage sweeps; these behaviors include mode veering, degenerate four-wave mixing (D4WM) with satellite resonances, partial amplitude suppression, acoustic frequency comb (AFC) generation, mechanically induced transparency (MIT), and normal-mode splitting. The experiments depict a new scheme for manipulating multimode microresonators with IR and parametric excitation.

Observation of coupled mechanical resonance modes within suspended 3D nanowire arrays

Complex yet compact nanoscale mechanisms have largely been absent due to the rather limited availability of components and integration techniques. Especially missing have been efficient interconnects with adjustable characteristics. To address this issue, we report here, for the first time, the transduction of collective modes in vertically stacked arrays of silicon nanowires suspended between couplers. In addition to the ambitious miniaturization, this composite resonator enables the control of coupling strength through the lithographic definition of coupler stiffness. A direct link is thus established between coupling strength and spectral response for two array architectures with nominally identical resonators but different couplers. A series of unique observations emerged in this platform, such as the splitting of a single mode into two closely spaced modes which raises the possibility of tunable bandpass filters with enhanced spectrum characteristics. Finally, intermodal coupling strengths were measured providing strong evidence about the collective nature of these modes.

Approaching the Strain-Free Limit in Ultrathin Nanomechanical Resonators

Ultrathin mechanical structures are ideal building platforms to pursue the ultimate limit of nanomechanical resonators for applications in sensing, signal processing, and quantum physics. Unfortunately, as the thickness of the vibrating structures is reduced, the built-in strain of the structural materials plays an increased role in determining the mechanical performance of the devices. As a consequence, it is very challenging to fabricate resonators working in the modulus-dominant regime, where their dynamic behavior is exclusively determined by the device geometry. In this Letter, we report ultrathin doubly clamped nanomechanical resonators with aspect ratios as large as L/t ∼5000 and working in the modulus-dominant regime. We observed room temperature thermomechanically induced motion of multiple vibration modes with resonant frequencies closely matching the predicted values of Euler-Bernoulli beam theory under an axial strain of 6.3 × 10^-8. The low strain of the devices enables a record frequency tuning ratio of more than 50 times. These results illustrate a new strategy for the quantitative design of nanomechanical resonators with unprecedented performance.

Ultralow Dissipation Patterned Silicon Nanowire Arrays for Scanning Probe Microscopy

In recent years, self-assembled semiconductor nanowires have been successfully used as ultrasensitive cantilevers in a number of unique scanning probe microscopy (SPM) settings. We describe the fabrication of ultralow dissipation patterned silicon nanowire (SiNW) arrays optimized for scanning probe applications. Our fabrication process produces ultrahigh aspect ratio vertical SiNWs that exhibit exceptional force sensitivity. The highest sensitivity SiNWs have thermomechanical noise-limited force sensitivity of [Formula: see text] at room temperature and [Formula: see text] at 4 K. To facilitate their use in SPM, the SiNWs are patterned within 7 μm from the edge of the substrate, allowing convenient optical access for displacement detection.

Magnetic Resonance Force Microscopy with a One-Dimensional Resolution of 0.9 Nanometers

Magnetic resonance force microscopy (MRFM) is a scanning probe technique capable of detecting MRI signals from nanoscale sample volumes, providing a paradigm-changing potential for structural biology and medical research. Thus far, however, experiments have not reached sufficient spatial resolution for retrieving meaningful structural information from samples. In this work, we report MRFM imaging scans demonstrating a resolution of 0.9 nm and a localization precision of 0.6 nm in one dimension. Our progress is enabled by an improved spin excitation protocol furnishing us with sharp spatial control on the MRFM imaging slice, combined with overall advances in instrument stability. From a modeling of the slice function, we expect that our arrangement supports spatial resolutions down to 0.3 nm given sufficient signal-to-noise ratio. Our experiment demonstrates the feasibility of subnanometer MRI and realizes an important milestone toward the three-dimensional imaging of macromolecular structures.

Hybrid Shape Memory Alloy-Based Nanomechanical Resonators for Ultrathin Film Elastic Properties Determination and Heavy Mass Spectrometry

Micro-/nanomechanical resonators are often used in material science to measure the elastic properties of ultrathin films or mass spectrometry to estimate the mass of various chemical and biological molecules. Measurements with these sensors utilize changes in the resonant frequency of the resonator exposed to an investigated quantity. Their sensitivities are, therefore, determined by the resonant frequency. The higher resonant frequency and, correspondingly, higher quality factor (Q-factor) yield higher sensitivity. In solution, the resonant frequency (Q-factor) decreases causing a significant lowering of the achievable sensitivity. Hence, the nanomechanical resonator-based sensors mainly operate in a vacuum. Identification by nanomechanical resonator also requires an additional reference measurement on the identical unloaded resonator making experiments, due to limiting achievable accuracies in current nanofabrication processes, yet challenging. In addition, the mass spectrometry by nanomechanical resonator can be routinely performed for light analytes (i.e., analyte is modelled as a point particle). For heavy analytes such as bacteria clumps neglecting their stiffness result in a significant underestimation of determined mass values. In this work, we demonstrate the extraordinary capability of hybrid shape memory alloy (SMA)-based nanomechanical resonators to i) notably tune the resonant frequencies and improve Q-factor of the resonator immersed in fluid, ii) determine the Young’s (shear) modulus of prepared ultrathin film only from frequency response of the resonator with sputtered film, and iii) perform heavy analyte mass spectrometry by monitoring shift in frequency of just a single vibrational mode. The procedures required to estimate the Young’s (shear) modulus of ultrathin film and the heavy analyte mass from observed changes in the resonant frequency caused by a phase transformation in SMA are developed and, afterward, validated using numerical simulations. The present results demonstrate the outstanding potential and capability of high frequency operating hybrid SMA-based nanomechanical resonators in sensing applications that can be rarely achieved by current nanomechanical resonator-based sensors.

Dynamic modulation of modal coupling in microelectromechanical gyroscopic ring resonators

Understanding and controlling modal coupling in micro/nanomechanical devices is integral to the design of high-accuracy timing references and inertial sensors. However, insight into specific physical mechanisms underlying modal coupling, and the ability to tune such interactions is limited. Here, we demonstrate that tuneable mode coupling can be achieved in capacitive microelectromechanical devices with dynamic electrostatic fields enabling strong coupling between otherwise uncoupled modes. A vacuum-sealed microelectromechanical silicon ring resonator is employed in this work, with relevance to the gyroscopic lateral modes of vibration. It is shown that a parametric pumping scheme can be implemented through capacitive electrodes surrounding the device that allows for the mode coupling strength to be dynamically tuned, as well as allowing greater flexibility in the control of the coupling stiffness. Electrostatic pump based sideband coupling is demonstrated, and compared to conventional strain-mediated sideband operations. Electrostatic coupling is shown to be very efficient, enabling strong, tunable dynamical coupling.

Dependence of enhancement factor on electrode size for field emission current from carbon nanotube on silicon wafer

This work studies the enhancement factor associated with a current emitted from a multi-wall carbon nanotube to an extremely small counter electrode. The experimental data show that the field enhancement factor increases by 1.15 times when the width of the counter electrode increases from 50 to 200 nm. To better understand this enhancement effect, field intensities at the emitter surface are numerically simulated. The experimental work and simulations demonstrate that the observed field enhancement results from increases in the capacitance between the emitter and counter electrode. In addition, corrugated counter electrodes are found to greatly affect both the capacitance and enhancement factor. This is because the corrugation of the anode surface raises the capacitance and thus provides a higher current. We experimentally show that an effective surface area enlargement of 1.67 times due to the corrugation provides a 1.06-fold increase of the enhancement factor. These results should assist in the future development of field emission devices based on semiconductor fabrication processes.

Mass Sensing for the Advanced Fabrication of Nanomechanical Resonators

We report on a nanomechanical engineering method to monitor matter growth in real time via e-beam electromechanical coupling. This method relies on the exceptional mass sensing capabilities of nanomechanical resonators. Focused electron beam-induced deposition (FEBID) is employed to selectively grow platinum particles at the free end of singly clamped nanotube cantilevers. The electron beam has two functions: it allows both to grow material on the nanotube and to track in real time the deposited mass by probing the noise-driven mechanical resonance of the nanotube. On the one hand, this detection method is highly effective as it can resolve mass deposition with a resolution in the zeptogram range; on the other hand, this method is simple to use and readily available to a wide range of potential users because it can be operated in existing commercial FEBID systems without making any modification. The presented method allows one to engineer hybrid nanomechanical resonators with precisely tailored functionalities. It also appears as a new tool for studying the growth dynamics of ultrathin nanostructures, opening new opportunities for investigating so far out-of-reach physics of FEBID and related methods.

Accurate Mass Measurement of a Levitated Nanomechanical Resonator for Precision Force-Sensing

Nanomechanical resonators are widely operated as force and mass sensors with sensitivities in the zepto-Newton (10^-21) and yocto-gram (10^-24) regime, respectively. Their accuracy, however, is usually undermined by high uncertainties in the effective mass of the system, whose estimation is a nontrivial task. This critical issue can be addressed in levitodynamics, where the nanoresonator typically consists of a single silica nanoparticle of well-defined mass. Yet, current methods assess the mass of the levitated nanoparticles with uncertainties up to a few tens of percent, therefore preventing to achieve unprecedented sensing performances. Here, we present a novel measurement protocol that uses the electric field from a surrounding plate capacitor to directly drive a charged optically levitated particle in moderate vacuum. The developed technique estimates the mass within a statistical error below 1% and a systematic error of ∼2%, and paves the way toward more reliable sensing and metrology applications of levitodynamics systems.

Force sensing with nanowire cantilevers

Nanometer-scale structures with high aspect ratios such as nanowires and nanotubes combine low mechanical dissipation with high resonance frequencies, making them ideal force transducers and scanning probes in applications requiring the highest sensitivity. Such structures promise record force sensitivities combined with ease of use in scanning probe microscopes. A wide variety of possible material compositions and functionalizations is available, allowing for the sensing of various kinds of forces. In addition, nanowires possess quasi-degenerate mechanical mode doublets, which allow for sensitive vectorial force and mass detection. These developments have driven researchers to use nanowire cantilevers in various force sensing applications, which include imaging of sample surface topography, detection of optomechanical, electrical, and magnetic forces, and magnetic resonance force microscopy. In this review, we discuss the motivation behind using nanowires as force transducers, explain the methods of force sensing with nanowire cantilevers, and give an overview of the experimental progress so far and future prospects of the field.

Resonantly Induced Friction and Frequency Combs in Driven Nanomechanical Systems

We propose a new mechanism of friction in resonantly driven vibrational systems. The form of the friction force follows from the time- and spatial-symmetry arguments. We consider a microscopic mechanism of this resonant force in nanomechanical systems. The friction can be negative, leading to the onset of self-sustained oscillations of the amplitude and phase of forced vibrations, which result in a frequency comb in the power spectrum.

Nonlinear Mode Coupling and One-to-One Internal Resonances in a Monolayer WS2 Nanoresonator

Nanomechanical resonators make exquisite force sensors due to their small footprint, low dissipation, and high frequencies. Because the lowest resolvable force is limited by ambient thermal noise, resonators are either operated at cryogenic temperatures or coupled to a high-finesse optical or microwave cavity to reach sub aN Hz^-1/2 sensitivity. Here, we show that operating a monolayer WS₂ nanoresonator in the strongly nonlinear regime can lead to comparable force sensitivities at room temperature. Cavity interferometry was used to transduce the nonlinear response of the nanoresonator, which was characterized by multiple pairs of 1:1 internal resonance. Some of the modes exhibited exotic line shapes due to the appearance of Hopf bifurcations, where the bifurcation frequency varied linearly with the driving force and forms the basis of the advanced sensing modality. The modality is less sensitive to the measurement bandwidth, limited only by the intrinsic frequency fluctuations, and therefore, advantageous in the detection of weak incoherent forces.

Carbon nanotube bridges fabricated by laser comb

Suspended bridge-shaped carbon nanotube (CNT) has great potential in nano-electromechanical systems, highly-sensitive sensors, various nanodevices and so on. However, complex processing largely restricts its practical applications. This work presents a novel laser comb (Laco) effect, stimulating a simple and effective fabrication strategy to achieve aligned suspended CNTs, which are bridge-shaped, direction-controlled, easily-patterned and all-carbon based. The Laco phenomenon is ascribed to different heat accumulations in two vertical directions under pulse laser-raster scanning (PLrS).

Optomechanical Measurement of Thermal Transport in Two-Dimensional MoSe2 Lattices

Nanomechanical resonators have emerged as sensors with exceptional sensitivities. These sensing capabilities open new possibilities in the studies of the thermodynamic properties in condensed matter. Here, we use mechanical sensing as a novel approach to measure the thermal properties of low-dimensional materials. We measure the temperature dependence of both the thermal conductivity and the specific heat capacity of a transition metal dichalcogenide monolayer down to cryogenic temperature, something that has not been achieved thus far with a single nanoscale object. These measurements show how heat is transported by phonons in two-dimensional systems. Both the thermal conductivity and the specific heat capacity measurements are consistent with predictions based on first-principles.

The effect of strain on effective Duffing nonlinearity in the CVD-MoS2 resonator

We demonstrate all electrical measurements on NEMS devices fabricated using CVD grown monolayer MoS2. The as-grown monolayer film of MoS2 on top of the SiO2/Si wafer is processed to fabricate arrays and individual NEMS devices without the complex pick and transfer techniques associated with graphene. The electromechanical properties of the devices are on par with those fabricated using the exfoliation method. The frequency response of these devices is then used as a probe to estimate the linear thermal expansion coefficient of the material and evaluate the effect of strain on the effective Duffing nonlinearity in the devices.

Giant, Voltage Tuned, Quality Factors of Single Wall Carbon Nanotubes and Graphene at Room Temperature

Mastering dissipation in graphene-based nanostructures is still the major challenge in most fundamental and technological exploitations of these ultimate mechanical nanoresonators. Although high quality factors have been measured for carbon nanotubes (>10⁶) and graphene (>10⁵) at cryogenic temperatures, room-temperature values are orders of magnitude lower (≃10²). We present here a controlled quality factor increase of up to ×10³ for these basic carbon nanostructures when externally stressed like a guitar string. Quantitative agreement is found with theory attributing this decrease in dissipation to the decrease in viscoelastic losses inside the material, an effect enhanced by tunable "soft clamping". Quality factors exceeding 25 000 for SWCNTs and 5000 for graphene were obtained on several samples, reaching the limits of the graphene material itself. The combination of ultralow size and mass with high quality factors opens new perspectives for atomically localized force sensing and quantum computing as the coherence time exceeds state-of-the-art cryogenic devices.

Properties of the Geometric Phase in Electromechanical Oscillations of Carbon-Nanotube-Based Nanowire Resonators

The geometric phase is an extra phase evolution in the wave function of vibrations that is potentially applicable in a broad range of science and technology. The characteristics of the geometric phase in the squeezed state for a carbon-nanotube-based nanowire resonator have been investigated by means of the invariant operator method. The introduction of a linear invariant operator, which is useful for treating a complicated time-dependent Hamiltonian system, enabled us to derive the analytical formula of the geometric phase. By making use of this, we have analyzed the time behavior of the geometric phase based on relevant illustrations. The influence of squeezing parameters on the evolution of the geometric phase has been investigated. The geometric phase, in large, oscillates, and the envelope of such oscillation increases over time. The rate of the increase of the geometric phase is large when the parameters, such as the classical amplitude of the oscillation, the damping factor, and the amplitude of the driving force, are large. We have confirmed a very sharp increase of the geometric phase over time in the case that the angular frequency of the system reaches near the resonance angular frequency. Our development regarding the characteristics of the geometric phase is crucial for understanding the topological features in nanowire oscillations.

Nanomechanical pump-probe measurements of insulating electronic states in a carbon nanotube

Transport measurements have been an indispensable tool in studying conducting states of matter. However, there exists a large set of interesting states that are insulating, often due to electronic interactions or topology, and are difficult to probe via transport. Here, through an experiment on carbon nanotubes, we present a new approach capable of measuring insulating electronic states through their back action on nanomechanical motion. We use a mechanical pump-probe scheme, allowing the detection of shifts in both frequency and dissipation rate of mechanical vibrational modes, in an overall insulating system. As an example, we use this method to probe the non-conducting configurations of a double quantum dot, allowing us to observe the theoretically predicted signature of nanomechanical back action resulting from a coherently tunnelling electron. The technique opens a new way for measuring the internal electronic structure of a growing variety of insulating states in one- and two-dimensional systems.

Phonon-Number-Sensitive Electromechanics

We use the strong intrinsic nonlinearity of a microwave superconducting qubit with a 4 GHz transition frequency to directly detect and control the energy of a micromechanical oscillator vibrating at 25 MHz. The qubit and the oscillator are coupled electrostatically at a rate of approximately 2π×22  MHz. In this far off-resonant regime, the qubit frequency is shifted by 0.52 MHz per oscillator phonon, or about 14% of the 3.7 MHz qubit linewidth. The qubit behaves as a vibrational energy detector and from its line shape we extract the phonon number distribution of the oscillator. We manipulate this distribution by driving number state sensitive sideband transitions and creating profoundly nonthermal states. Finally, by driving the lower frequency sideband transition, we cool the oscillator and increase its ground state population up to 0.48±0.13, close to a factor of 8 above its value at thermal equilibrium. These results demonstrate a new class of electromechanics experiments that are a promising strategy for quantum nondemolition measurements and nonclassical state preparation.

Sensing Static Forces with Free-Falling Nanoparticles

Miniaturized mechanical sensors rely on resonant operation schemes, unsuited to detect static forces. We demonstrate a nanomechanical sensor for static forces based on an optically trapped nanoparticle in vacuum. Our technique relies on an off-resonant interaction of the particle with a weak static force, and a resonant readout of the displacement caused by this interaction. We demonstrate a sensitivity of 10 aN to static gravitational and electric forces. Our work provides a tool for the closer investigation of short-range forces, and marks an important step towards the realization of matter-wave interferometry with macroscopic objects.

Ultrasensitive Displacement Noise Measurement of Carbon Nanotube Mechanical Resonators

Mechanical resonators based on a single carbon nanotube are exceptional sensors of mass and force. The force sensitivity in these ultralight resonators is often limited by the noise in the detection of the vibrations. Here, we report on an ultrasensitive scheme based on a RLC resonator and a low-temperature amplifier to detect nanotube vibrations. We also show a new fabrication process of electromechanical nanotube resonators to reduce the separation between the suspended nanotube and the gate electrode down to ∼150 nm. These advances in detection and fabrication allow us to reach [Formula: see text] displacement sensitivity. Thermal vibrations cooled cryogenically at 300 mK are detected with a signal-to-noise ratio as high as 17 dB. We demonstrate [Formula: see text] force sensitivity, which is the best force sensitivity achieved thus far with a mechanical resonator. Our work is an important step toward imaging individual nuclear spins and studying the coupling between mechanical vibrations and electrons in different quantum electron transport regimes.

Detecting Ultrasound Vibrations with Graphene Resonators

Ultrasound detection is one of the most-important nondestructive subsurface characterization tools for materials, the goal of which is to laterally resolve the subsurface structure with nanometer or even atomic resolution. In recent years, graphene resonators have attracted attention for their use in loudspeakers and ultrasound radios, showing their potential for realizing communication systems with air-carried ultrasound. Here, we show a graphene resonator that detects ultrasound vibrations propagating through the substrate on which it was fabricated. We ultimately achieve a resolution of ∼7 pm/[Formula: see text] in ultrasound amplitude at frequencies up to 100 MHz. Thanks to an extremely high nonlinearity in the mechanical restoring force, the resonance frequency itself can also be used for ultrasound detection. We observe a shift of 120 kHz at a resonance frequency of 65 MHz for an induced vibration amplitude of 100 pm with a resolution of 25 pm. Remarkably, the nonlinearity also explains the generally observed asymmetry in the resonance frequency tuning of the resonator when it is pulled upon with an electrostatic gate. This work puts forward a sensor design that fits onto an atomic force microscope cantilever and therefore promises direct ultrasound detection at the nanoscale for nondestructive subsurface characterization.

Driven nonlinear nanomechanical resonators as digital signal detectors

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities.

Measuring Frequency Fluctuations in Nonlinear Nanomechanical Resonators

Advances in nanomechanics within recent years have demonstrated an always expanding range of devices, from top-down structures to appealing bottom-up MoS₂ and graphene membranes, used for both sensing and component-oriented applications. One of the main concerns in all of these devices is frequency noise, which ultimately limits their applicability. This issue has attracted a lot of attention recently, and the origin of this noise remains elusive to date. In this article we present a very simple technique to measure frequency noise in nonlinear mechanical devices, based on the presence of bistability. It is illustrated on silicon-nitride high-stress doubly clamped beams, in a cryogenic environment. We report on the same T/ f dependence of the frequency noise power spectra as reported in the literature. But we also find unexpected damping fluctuations, amplified in the vicinity of the bifurcation points; this effect is clearly distinct from already reported nonlinear dephasing and poses a fundamental limit on the measurement of bifurcation frequencies. The technique is further applied to the measurement of frequency noise as a function of mode number, within the same device. The relative frequency noise for the fundamental flexure δ f/ f₀ lies in the range 0.5-0.01 ppm (consistent with the literature for cryogenic MHz devices) and decreases with mode number in the range studied. The technique can be applied to any type of nanomechanical structure, enabling progress toward the understanding of intrinsic sources of noise in these devices.