We report radio frequency (rf) electrical readout of graphene mechanical resonators. The mechanical motion is actuated and detected directly by using a vector network analyzer, employing a local gate to minimize parasitic capacitance. A resist-free doubly clamped sample with resonant frequency ~ 34 MHz, quality factor ~ 10000 at 77 K, and signal-to-background ratio of over 20 dB is demonstrated. In addition to being over two orders of magnitude faster than the electrical rf mixing method, this technique paves the way for use of graphene in rf devices such as filters and oscillators.
Contactless characterization of mechanical resonances using Fabry-Perot interferometry is a powerful tool to study the mechanical and dynamical properties of atomically thin membranes. However, amplitude calibration is often not performed, or only possible by making assumptions on the device parameters such as its mass or the temperature. In this work, we demonstrate a calibration technique that directly measures the oscillation amplitude by detecting higher harmonics that arise from nonlinearities in the optical transduction. Employing this technique, we calibrate the resonance amplitude of t…
Nanomechanical resonators with increasingly high quality factors are enabled following recent insights into energy storage and loss mechanisms in nanoelectromechanical systems (NEMS). Consequently, efficient, non-dissipative transduction schemes are required to avoid the dominating influence of coupling losses. We present an integrated NEMS transducer based on a microwave cavity dielectrically coupled to an array of doubly-clamped pre-stressed silicon nitride beam resonators. This cavity-enhanced detection scheme allows resolving the resonators' Brownian motion at room temperature while preser…
Universal sensing the motion of mechanical resonators with high precision and low back-action is of paramount importance in ultra-weak signal detection which plays a fundamental role in modern physics. Here we present a universal scheme that transfer mechanically the motion of the resonator not directly measurable to the one can be precisely measured using mechanical frequency conversion. Demonstration of the scheme at room temperature shows that both the motion imprecision and the back-action force are below the intrinsic level of the objective resonator, which agree well with our theoretical…
High electric conductivity ~100 MegaSiemens/m and Seebeck coefficient >200 mkV/K of carbon nanotubes (CNT) make them attractive for a variety of applications. Unfortunately, a high thermal conductivity ~ 3000 W/(m*K) due to the phonon transport limits their capability for transforming energy between the heat and electricity. Here we show that increasing the charge carrier concentrations not only leads to an increase of both electric conductivity and Seebeck coeffcient, but also causes a substantial suppression of the thermal conductivity due to intensifying the phonon-electron collisions. A st…
There is a recent surge of interest in amplification and detection of tiny motion in the growing field of opto and electro mechanics. Here, we demonstrate widely tunable, broad bandwidth and high gain all-mechanical motion amplifiers based on graphene/Silicon Nitride (SiNx) hybrids. In these devices, a tiny motion of a large-area SiNx membrane is transduced to a much larger motion in a graphene drum resonator coupled to SiNx. Furthermore, the thermal noise of graphene is reduced (squeezed) through parametric tension modulation. The parameters of the amplifier are measured by photothermally act…
The successes of superconducting quantum circuits at local manipulation of quantum information and photonics technology at long-distance transmission of the same have spurred interest in the development of quantum transducers for efficient, low-noise, and bidirectional frequency conversion of photons between the microwave and optical domains. We propose to realize such functionality through the coupling of electrical, piezoelectric, and optomechanical resonators. The coupling of the mechanical subsystems enables formation of a resonant mechanical supermode that provides a mechanically-mediated…
Using light to measure an object's motion is central to operating mechanical sensors that probe forces and fields. Cavity optomechanical systems embed mechanical resonators inside optical resonators. This enhances the sensitivity of optomechanical measurements, but only if the mechanical resonator does not spoil the properties of the optical cavity. For example, cavity optomechanical detection of resonators made from optically absorbing materials, or whose geometry does not possess suitable spatial symmetry, is challenging. Here we demonstrate a system that overcomes challenges in measuring hi…
We demonstrate a new optomechanical device system which allows highly efficient transduction of femtogram nanobeam resonators. Doubly clamped nanomechanical resonators with mass as small as 25 fg are embedded in a high-finesse two-dimensional photonic crystal nanocavity. Optical transduction of the fundamental flexural mode around 1 GHz was performed at room temperature and ambient conditions, with an observed displacement sensitivity of 0.94 fm/Hz^(1/2). Comparison of measurements from symmetric and asymmetric double-beam devices reveals hybridization of the mechanical modes where the structu…
Force detectors rely on resonators to transduce forces into a readable signal. Usually these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well as readout noise. Here, we demonstrate that a parametric symmetry breaking transduction leads to a novel and robust nonlinear force detection in the presence of noise. The force signal is encoded in the frequency at which the system jumps between two phase states which are inherently protected against phase noise. Consequently, the transduction effectively de…
We study the electromechanical transduction in nanoelectromechanical actuators and show that the differences in scaling for electrical and mechanical effects lead to an overall non-trivial scaling behavior. In particular, the previously neglected fringing fields considerably increase electrical forces and improve the stability of nanoscale actuators. This shows that electrostatics does not pose any limitations to downscaling of electromechanical systems, in fact in several respects, nanosystems outperform their microscale counterparts. As a specific example, we consider in-plane actuation of u…
We report here the first realization of top-down silicon nanowires (SiNW) transduced by both junction-less field effect transistor (FET) and the piezoresistive (PZR) effect. The suspended SiNWs are among the smallest top-down SiNWs reported to date, featuring widths down to ~20nm. This has been achieved thanks to a 200mm-wafer-scale, VLSI process fully amenable to monolithic CMOS co-integration. Thanks to the very small dimensions, the conductance of the silicon nanowire can be controlled by a nearby electrostatic gate. Both the junction-less FET and the previously demonstrated PZR transductio…
We report on the self-consisted semi-analytical theory of magnetoelastic excitation and electrical detection of spin waves and spin currents in hypersonic bulk acoustic waves resonator with ZnO-GGG-YIG/Pt layered structure. Electrical detection of acoustically driven spin waves occurs due to spin pumping from YIG to Pt and inverse spin Hall (ISHE) effect in Pt as well as due to electrical response of ZnO piezotransducer. The frequency-field dependences of the resonator frequencies and ISHE voltage $U_{ISHE}$ are correlated with experimental ones observed previously. Their fitting allows to det…
We have fabricated and tested mechanical resonators consisting of a single-atomic-layer of graphene deposited on suspended silicon nitride membranes. With the addition of the graphene layer we retain the desirable mechanical properties of silicon nitride but utilize the electrical and optical properties of graphene to transduce resonant motion by both optical and electrical means. By positioning the graphene-on-silicon-nitride drums in a tunable optical cavity we observe position dependent damping and resonant frequency control of the devices due to optical absorption by graphene.
Using optical diffraction, we study the mechanical vibrations of an array of micromechanical resonators. Implementing tunable electrostatic coupling between the suspended, doubly-clamped Au beams leads to the formation of a band of collective vibrational modes within these devices. The evolution of these modes with coupling strength is clearly manifested in the optical diffraction pattern of light transmitted through the array. The experimental results are analyzed using a simple model for one-dimensional phonons. These structures offer unique prospects for spectral analysis of complex mechani…
We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to it…
We present a simple micromanipulation technique to transfer suspended graphene flakes onto any substrate and to assemble them with small localized gates into mechanical resonators. The mechanical motion of the graphene is detected using an electrical, radio-frequency (RF) reflection readout scheme where the time-varying graphene capacitor reflects a RF carrier at f=5-6 GHz producing modulation sidebands at f +/- fm. A mechanical resonance frequency up to fm=178 MHz is demonstrated. We find both hardening/softening Duffing effects on different samples, and obtain a critical amplitude of ~40 pm …
We implement a cavity opto-electromechanical system integrating electrical actuation capabilities of nanoelectromechanical devices with ultrasensitive mechanical transduction achieved via intra-cavity optomechanical coupling. Electrical gradient forces as large as 0.40 microN are realized, with simultaneous mechanical transduction sensitivity of 1.5 X 10^-18 m/rtHz representing a three orders of magnitude improvement over any nanoelectromechanical system to date. Opto-electromechanical feedback cooling is demonstrated, exhibiting strong squashing of the in-loop transduction signal. Out-of-loop…
The enormous stiffness and low density of graphene make it an ideal material for nanoelectromechanical (NEMS) applications. We demonstrate fabrication and electrical readout of monolayer graphene resonators, and test their response to changes in mass and temperature. The devices show resonances in the MHz range. The strong dependence of the resonant frequency on applied gate voltage can be fit to a membrane model, which yields the mass density and built-in strain. Upon removal and addition of mass, we observe changes in both the density and the strain, indicating that adsorbates impart tension…
Aluminum nitride (AlN) has been widely used in microeletromechanical resonators for its excellent electromechanical properties. Here we demonstrate the use of AlN as an optomechanical material that simultaneously offer low optical and mechanical loss. Integrated AlN microring resonators in the shape of suspended rings exhibit high optical quality factor (Q) with loaded Q up to 125,000. Optomechanical transduction of the Brownian motion of a GHz contour mode yields a displacement sensitivity of 6.2\times10^(-18)m/Hz^(1/2) in ambient air.
We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved optomechanical cavity. Nonlinear detection mechanisms are of considerable interest as special cases allow for quantum nondemolition measurements of the mechanical resonator's energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function…
Graphene mechanical resonators are the ultimate two-dimensional nanoelectromechanical systems (NEMS) with applications in sensing and signal processing. While initial devices have shown promising results, an ideal graphene NEMS resonator should be strain engineered, clamped at the edge without trapping gas underneath, and electrically integratable. In this letter, we demonstrate fabrication and direct electrical measurement of circular SU-8 polymer-clamped chemical vapor deposition (CVD) graphene drum resonators. The clamping increases device yield and responsivity, while providing a cleaner r…
High stress stoichiometric silicon nitride resonators, whose quality factors exceed one million, have shown promise for applications in sensing and signal processing. Yet, electrical integration of the insulating silicon nitride resonators has been challenging, as depositing even a thin layer of metal degrades the quality factor significantly. In this work, we show that graphene used as a conductive coating for Si3N4 membranes reduces the quality factor by less than 30 % on average, which is minimal when compared to the effect of conventional metallization layers such as chromium or aluminum. …
We have investigated a THz detection scheme based on mixing of electrical signals in a voltage-dependent capacitance made out of suspended graphene. We have analyzed both coherent and incoherent detection regimes and compared their performance with the state of the art. Using a high-amplitude local oscillator, we anticipate potential for quantum limited detection in the coherent mode. The sensitivity stems from the extraordinary mechanical and electrical properties of atomically thin graphene or graphene-related 2D materials.
We report disk-shaped silicon optomechanical resonators with frequency up to 1.75 GHz in the ultrahigh frequency band. Optical transduction of the thermal motion of the disks' in-plane vibrational modes yields a displacement sensitivity of 4.1 \times 10^(-17) m/Hz^(1/2). Due to the reduced clamping loss, these disk resonators possess high mechanical quality factors (Q), with the highest value of 4370 for the 1.47 GHz mode measured in ambient air. Numerical simulation on the modal frequency and mechanical Q for disks of varying undercut shows modal coupling and suggests a realistic pedestal siz…
Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediat…
High quality factor ($Q$) nanomechanical resonators have received a lot of attention for sensor applications with unprecedented sensitivity. Despite the large interest, few investigations into the frequency stability of high-$Q$ resonators have been reported. Such resonators are characterized by a linewidth significantly smaller than typically employed measurement bandwidths, which is the opposite regime to what is normally considered for sensors. Here, the frequency stability of high-$Q$ silicon nitride string resonators is investigated both in open-loop and closed-loop configurations. The st…
Mechanical resonators made with monolithic piezoelectric quartz crystals are promising for studying new physical phenomena. High mechanical quality factors ($Q$) exhibited by the mm-sized quartz resonators make them ideal for studying weak couplings or long timescales in the quantum regime. However, energy losses through mechanical supports pose a serious limiting factor for obtaining high quality factors. Here we investigate how the $Q$ of quartz resonators at deep cryogenic temperatures can be limited by several types of losses related to anchoring. We first introduce means to reduce the mec…
The monolithic integration of electromechanical transduction at the nanoscale with advanced CMOS is among the most important challenges of semiconductor electronic systems to leverage the multi-domain sensing, actuation, and resonance properties of nano-mechanical systems. Here we report on the demonstration of vibrating devices enabled by atomically engineered ferroelectric Hf0.5Zr0.5O2 thin films with a variety of mechanical resonance modes with frequencies (f0) between 340kHz - 13GHz and frequency-quality (Q) factor products (f0 x Q) up to 3.97 x 10^12. Experiments based on electrical and o…
This paper discusses a logical operation of multi-memories that consist of coupled nonlinear micro-electro-mechanical systems (MEMS) resonators. A MEMS resonator shows two coexisting stable states when nonlinear responses appear. Previous studies addressed that a micro- or nano-electrical-mechanical resonator can be utilized as a mechanical 1-bit memory or mechanical logic gates. The next phase is the development of logic system with coupled multi-resonators. From the viewpoint of application of nonlinear dynamics in coupled MEMS resonators, we show the first experimental success of the contro…
Silicon nitride (SiN) mechanical resonators with high quality mechanical properties are attractive for fundamental research and applications. However, it is challenging to maintain these mechanical properties while achieving strong coupling to an electrical circuit for efficient on-chip integration. Here, we present a SiN drum resonator covered with an aluminum thin film, enabling large capacitive coupling to a suspended top-gate. Implementing the full electrical measurement scheme, we demonstrate a high quality factor ~ 1E4 (comparable to that of bare drums at room temperature) and present ou…
Graphene mechanical resonators have recently attracted considerable attention for use in precision force and mass sensing applications. To date, readout of their oscillatory motion has typically required cryogenic conditions to achieve high sensitivity, restricting their range of applications. Here we report the first demonstration of evanescent optical readout of graphene motion, using a scheme which does not require cryogenic conditions and exhibits enhanced sensitivity and bandwidth at room temperature. We utilise a high $Q$ microsphere to enable evanescent readout of a 70 $μ$m diameter gra…
The measurement of micron-sized mechanical resonators by electrical techniques is difficult, because of the combination of a high frequency and a small mechanical displacement which together suppress the electromechanical coupling. The only electromagnetic technique proven up to the range of several hundred MHz requires the usage of heavy magnetic fields and cryogenic conditions. Here we show how, without the need of either of them, to fully electrically detect the vibrations of conductive nanomechanical resonators up to the microwave regime. We use the electrically actuated vibrations to modu…
We present measurements of a hybrid system consisting of a microwave transmission-line resonator and a lateral quantum dot defined on a GaAs heterostructure. The two subsystems are separately characterized and their interaction is studied by monitoring the electrical conductance through the quantum dot. The presence of a strong microwave field in the resonator is found to reduce the resonant conductance through the quantum dot, and is attributed to electron heating and modulation of the dot potential. We use this interaction to demonstrate a measurement of the resonator transmission spectrum u…
We have developed capacitively-transduced nanomechanical resonators using sp$^2$-rich diamond-like carbon (DLC) thin films as conducting membranes. The electrically conducting DLC films were grown by physical vapor deposition at a temperature of $500{\,\,}^\circ$C. Characterizing the resonant response, we find a larger than expected frequency tuning that we attribute to the membrane being buckled upwards, away from the bottom electrode. The possibility of using buckled resonators to increase frequency tuning can be of advantage in rf applications such as tunable GHz filters and voltage-control…
Optomechanical transduction is demonstrated for nanoscale torsional resonators evanescently coupled to optical microdisk whispering gallery mode resonators. The on-chip, integrated devices are measured using a fully fiber-based system, including a tapered and dimpled optical fiber probe. With a thermomechanically calibrated optomechanical noise floor down to 7 fm/sqrt(Hz), these devices open the door for a wide range of physical measurements involving extremely small torques, as little as 4x10^-20 N*m.
In recent years, the field of microwave optomechanics has emerged as leading platform for achieving quantum control of macroscopic mechanical objects. Implementations of microwave optomechanics to date have coupled microwave photons to mechanical resonators using a moving capacitance. While simple and effective, the capacitive scheme suffers from inherent and practical limitations on the maximum achievable coupling strength. Here, we experimentally implement a fundamentally different approach: flux-mediated optomechanical coupling. In this scheme, mechanical displacements modulate the flux in …
Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow the Hooke's law and response linearly to external force, unless strong drive is used. Here we propose and experimentally realize a record-high nonlinear response in macroscopic mechanical system by exploring the anharmonicity in deforming a single chemical bond. We then demonstrate the tunabilit…
Parametric amplification is widely used in nanoelectro-mechanical systems to enhance the transduced mechanical signals. Although parametric amplification has been studied in different mechanical resonator systems, the nonlinear dynamics involved receives less attention. Taking advantage of the excellent electrical and mechanical properties of graphene, we demonstrate electrical tunable parametric amplification using a doubly clamped graphene nanomechanical resonator. By applying external microwave pumping with twice the resonant frequency, we investigate parametric amplification in the nonline…
Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute the ideal systems for applications ranging from high-precision sensing such as magnetic resonance force microscopy, to quantum transduction between disparate quantum systems. Traditionally, the improvement of the resonator's performance - often quantified by its Qf product (where Q is quality factor and f is frequency) - through nanomechanical engineering such as dissipation dilution and strain engineering, has been driven by human intuition and insight. Such an approach is inefficient and leaves aside a plet…
We present a monolithic integrated aluminum nitride (AlN) optomechanical resonator in which the mechanical motion is actuated by piezoelectric force and the displacement is transduced by a high-Q optical cavity. The AlN optomechanical resonator is excited from a radio-frequency electrode via a small air gap to eliminate resonator-to-electrode loss. We observe the electrically excited mechanical motion at 47.3 MHz, 1.04 GHz, and 3.12 GHz, corresponding to the 1st, 2nd, and 4th radial-contour mode of the wheel resonator respectively. An equivalent circuit model is developed to describe the obser…
In strained mechanical resonators, the concurrence of tensile stress and geometric nonlinearity dramatically reduces dissipation. This phenomenon, dissipation dilution, is employed in mirror suspensions of gravitational wave interferometers and at the nanoscale, where soft-clamping and strain engineering have allowed extremely high quality factors. However, these techniques have so far only been applied in amorphous materials, specifically silicon nitride. Crystalline materials exhibit significantly lower intrinsic damping at cryogenic temperatures, due to the absence of two level systems in t…
Over the past two decades, several molecules have been explored as possible building blocks of a quantum computer, a device that would provide exponential speedups for a number of problems, including the simulation of large, strongly correlated chemical systems. Achieving strong interactions and entanglement between molecular qubits remains an outstanding challenge. Here, we show that the TbPc$_2$ single-molecule magnet has the potential to overcome this obstacle due to its sensitivity to electric fields stemming from the hyperfine Stark effect. We show how this feature can be leveraged to ach…
Role of dissipation dilution in achieving high mechanical quality factors in van der Waals resonators
Technical University of Munich（慕尼黑工业大学）；Walter Schottky Institute and Physics Department, Technical University of Munich（沃尔特·施科特基研究所与物理系，慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. Hierarchical metamaterials utilize structure at multiple size scales to realize new and highly desirable properties which can be strikingly different from those of the constituent materials. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitrid…
