The equivalence between different physical systems permits us to transfer knowledge between them and to characterize the universal nature of their dynamics. We demonstrate that a nanopillar driven by a spin-transfer torque is equivalent to a rotating magnetic plate, which permits us to consider the nanopillar as a macroscopic system under a time-modulated injection of energy, that is, a simple parametric resonator. This equivalence allows us to characterize the phases diagram and to predict magnetic states and dynamical behaviors, such as solitons, stationary textures, and oscillatory localized states, among others. Numerical simulations confirm these predictions.
Self-sustained oscillators are ubiquitous and essential for metrology, communications, time reference, and geolocation. In its most basic form an oscillator consists of a resonator driven on-resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic, regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special point…
The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)] involving a parametrically-excited micromechanical resonator array. Future experiments are suggested that could provide quantitative tests of the the…
This work investigates the behavior of an AlGaAs/GaAs piezoelectric nonlinear MEMS oscillator exhibiting a 1:3 internal resonance. The device is explored in an open-loop configuration, i.e. as a driven resonator, where depending on the drive conditions we observe energy transfer between the first and third modes, and the emergence of supercritical Hopf limit cycles. We examine the dependence of these bifurcations on the oscillator's frequency and amplitude, and reproduce the observed behavior using a system of nonlinearly coupled equations which show interesting scaling behavior.
The low quality factor (Q) of Single-walled carbon nanotube (SWNT) resonators has limited their sensitivity in sensing application. To this end, we employ the technique of parametric amplification by modulating the spring constant of SWNT resonators at twice the resonant frequency, and achieve 10 times Q enhancement. The highest Q obtained at room temperature is around ~700, which is 3-4 times better than previous Q record reported for doubly-clamped SWNT resonators. Furthermore, efficient parametric amplification is found to only occur in the catenary vibration regime. Our results open up the…
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent os…
We present superconducting microwave-frequency resonators based on NbTiN nanowires. The small cross section of the nanowires minimizes vortex generation, making the resonators resilient to magnetic fields. Measured intrinsic quality factors exceed $2\times 10^5$ in a $6$ T in-plane magnetic field, and $3\times 10^4$ in a $350$ mT perpendicular magnetic field. Due to their high characteristic impedance, these resonators are expected to develop zero-point voltage fluctuations one order of magnitude larger than in standard coplanar waveguide resonators. These properties make the nanowire resonato…
Magnetically coupling a nano-mechanical resonator to a double quantum dot confining two electrons can enable the manipulation of a single electron spin and the readout of the resonator's natural frequency. When the Larmor frequency matches the resonator frequency, the electron spin in one of the dots can be selectively flipped by the magnetised resonator. By simultaneously measuring the charge state of the two-electron double quantum dots, this transition can be detected thus enabling the natural frequency of the mechanical resonator to be determined.
We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states scales exponentially with the diffusion coefficient. It also displays a characteristic scaling dependence on the distance to bifurcation points.
The current noise spectrum of a single-electron transistor (SET) coupled to a nano-mechanical resonator is calculated in the classical regime. Correlations between the charge on the SET island and the position of the resonator give rise to a distinctive noise spectrum which can be very different from that of the uncoupled SET. The current noise spectrum of the coupled system contains peaks at both the frequency of the resonator and double the resonator frequency, as well as a strong enhancement of the zero-frequency noise. The heights of the peaks are controlled by the strength of the coupling…
We provide a detailed description of a general procedure by which a nano/micro-mechanical resonator can be calibrated using its thermal motion. A brief introduction to the equations of motion for such a resonator is presented, followed by a detailed derivation of the corresponding power spectral density (PSD) function. The effective masses for a number of different resonator geometries are determined using both finite element method (FEM) modeling and analytical calculations.
A suspended, doubly clamped single wall carbon nanotube is characterized as driven nano-electromechanical resonator at cryogenic temperatures. Electronically, the carbon nanotube displays small bandgap behaviour with Coulomb blockade oscillations in electron conduction and transparent contacts in hole conduction. We observe the driven mechanical resonance in dc-transport, including multiple higher harmonic responses. The data shows a distinct negative frequency tuning at finite applied gate voltage, enabling us to electrostatically decrease the resonance frequency to 75% of its maximum value. …
Coupling, synchronization, and non-linear dynamics of resonator modes are omnipresent in nature and highly relevant for a multitude of applications ranging from lasers to Josephson arrays and spin torque oscillators. Nanomechanical resonators are ideal candidates to study these effects on a fundamental level and to realize all-mechanical platforms for information processing and storage. For larger resonator networks, however, this requires the ability to tune the mode frequencies selectively and to operate the resonators in the strong coupling regime. Here, we present a proof-of-principle real…
A resonator can be effectively used as a cooler for another linear oscillator with a much smaller frequency. A huge cooling effect, which could be used to cool a mechanical oscillator below the energy of quantum fluctuations, has been predicted by several authors. However, here we show that there is a lower limit T* on the achievable temperature that was not considered in previous works and can be higher than the quantum limit in realistic experimental realizations. We also point out that the decay rate of the resonator, which previous studies stress should be small, must be larger than the de…
We report on the design of loop-gap resonators (LGR) operating in the frequency range 34-36 GHz with the goal to achieve single electron spin resonance (ESR) in quantum dot nanostructures. We present a comprehensive study of the magnetic field strength and the spatial distribution of the electric and magnetic fields in the resonator by means of experiments and numerical simulations.
We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks const…
We analyze the dynamics of a nano-mechanical resonator coupled to a single-electron transistor (SET) in the regime where the resonator behaves classically. A master equation is derived describing the dynamics of the coupled system which is then used to obtain equations of motion for the average charge state of the SET and the average position of the resonator. We show that the action of the SET on the resonator is very similar to that of a thermal bath, as it leads to a steady-state probability-distribution for the resonator which can be described by mean values of the resonator position, a re…
We solve Schrödinger equation describing a tunneling macrospin coupled to a torsional oscillator. Energy spectrum is studied for various quantum regimes. Magnetic susceptibility and noise spectrum are computed. We show that entanglement of the spin with mechanical modes of a subnanometer oscillator results in the decoherence of spin tunneling. For larger oscillators the presence of a tunneling spin can be detected through splitting of the mechanical mode at the resonance. Our results apply to experiments with magnetic molecules coupled to nanoresonators.
A suspended, doubly clamped single wall carbon nanotube is characterized at cryogenic temperatures. We observe specific switching effects in dc-current spectroscopy of the embedded quantum dot. These have been identified previously as nano-electromechanical self-excitation of the system, where positive feedback from single electron tunneling drives mechanical motion. A magnetic field suppresses this effect, by providing an additional damping mechanism. This is modeled by eddy current damping, and confirmed by measuring the resonance quality factor of the rf-driven nano-electromechanical resona…
We study electron mechanical coupling in a suspended carbon nanotube (CNT) quantum dot device. Electron spin couples to the flexural vibration mode due to spin-orbit coupling in the electron tunneling processes. In the weak coupling limit, i.e. electron-vibration coupling is much smaller than the electron energy scale, the damping and resonant frequency shift of the CNT resonator can be obtained by calculating the dynamical spin susceptibility. We find that strong spin-flip scattering processes in Kondo regime significantly affect the mechanical motion of the carbon nanotube: Kondo effect indu…
We show how to engineer an extensive range of non-linear Hamiltonians for a nano-mechanical resonator. The technique requires only a time dependent drive applied to a Cooper-pair box or second oscillator to which the nano-resonator is coupled. This method allows one to generate a large number of non-classical states, as well as Hamiltonians whose classical counterparts are chaotic.
Magnetic torque is used to actuate nano-torsional resonators, which are fabricated by focused-ion-beam milling of permalloy coated silicon nitride membranes. Optical interferometry is used to measure the mechanical response of two torsion modes at resonance, which is proportional to the magnetization vector of the nanomagnetic volume. By varying the bias magnetic field, the magnetic behavior can be measured with excellent sensitivity ($\approx 10^8 μ_B$) for single magnetic elements.
We show that a continuous quantum non-demolition measurement of the energy of a nanomechanical resonator can be achieved by monitoring the resonator with a quantum point contact via a Cooper-pair box. This technique can further be used to prepare highly non-classical states of two resonators, such as canonical phase-reference states, and so-called "noon" states.
Networks of coupled resonators are an ubiquitous concept in physics, forming the basis of synchronization phenomena, metamaterial formation, nonreciprocal behavior and topological effects. Such systems are typically explored using optical or microwave resonators. In recent years, mechanical resonators have entered the stage as universal building block for resonator networks, both for their well-controlled mechanical properties and for their eigenfrequencies conveniently located in the radio-frequency regime. Vertically oriented nanomechanical pillar resonators are ideally suited for the dense …
Owing to their extraordinary sensitivity to external forces, nanomechanical systems have become important tools for studying a variety of mesoscopic physical systems and realizing hybrid quantum systems. While nanomechanics has been widely applied in solid-state systems, its use in liquid is scantily studied. There it finds unique applications such as biosensing, rheological sensing, and studying fluid dynamics in unexplored regimes. Its use in quantum fluids offers new opportunities in studying fluids at low excitation levels all the way down to the quantum limit and in nano-metric scales rea…
Different damping mechanisms in graphene nanoresonators are studied: charges in the substrate, ohmic losses in the substrate and the graphene sheet, breaking and healing of surface bonds (Velcro effect), two level systems, attachment losses, and thermoelastic losses. We find that, for realistic structures and contrary to semiconductor resonators, dissipation is dominated by ohmic losses in the graphene layer and metallic gate. An extension of this study to carbon nanotube-based resonators is presented.
We have demonstrated a new photonic structure to achieve strong optical coupling between nanoparticle and photonic molecule by utilizing a notched micro ring resonators. By creating a notch in the ring resonator and putting a nanoparticle inside the notch, large spectral shifts and splittings at nm scale can be achieved, compared to only pm scale observed by fiber tip evanescently coupled to the surface of microsphere, thereby significantly lowered the quality factor requirement for single nanoparticle detection. The ability for sorting the type of nanoparticles due to very different mode shif…
A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the lineshape of the resonance (without pumping), supporting the recently reported scenar…
Bi-stable mechanical resonators play a significant role in various applications, such as sensors, memory elements, and quantum computing. While carbon nanotube (CNT) based resonators have been widely investigated as promising nano electro-mechanical devices, a bi-stable CNT resonator has never been demonstrated. Here, we report a new class of CNT 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 (EB) bi-stability, the smallest mechanical resonator with two s…
Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, such as the dynamics of individual electron spins, persistent currents in normal metal rings, and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN Hz^(-1/2) at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultra-sensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to dete…
We experimentally study stochastic resonance in a nonlinear bistable nanomechanical resonator. The device consists of a PdAu doubly clamped beam serving as a nanomechanical resonator excited capacitively by an adjacent gate electrode and its vibrations are detected optically. The resonator is tuned to its bistability region by an intense pump near a point of equal transition rates between its two metastable states. The pump is amplitude modulated, inducing modulation of the activation barrier between the states. When noise is added to the excitation, the resonator's displacement exhibits noise…
Low-cost spintronic devices functioning in zero applied magnetic field are required for bringing the idea of spin-based electronics into the real-world industrial applications. Here we present first microwave measurements performed on nanomagnet devices fabricated by electrodeposition inside porous membranes. In the paper, we discuss in details a microwave resonator consisting of three nanomagnets, which functions in zero external magnetic field. By applying a microwave signal at a particular frequency, the magnetization of the middle nanomagnet experiences the ferromagnetic resonance (FMR), a…
We show that a nano-resonator can be prepared in mesoscopic-superposition states merely by monitoring a qubit coupled to the square of the resonators position. This works for thermal initial states, and does not require a third-order nonlinearity. The required coupling can be generated using a simple open-loop control protocol, obtained with optimal control theory. We simulate the complete preparation process, including environmental noise. Our results indicate the power of open-loop control for state-engineering and measurement in quantum nano-systems.
We give a quantum master equation description of the measurement scheme based on a coplanar microwave cavity capacitively coupled to nano mechanical resonator. The system exhibits a rich bifurcation structure that is analogous to sub/second harmonic generation in nonlinear optics. We show how it may be configured as a bifurcation amplifier transducer for weak force detection.
We report actuation and detection of gigahertz-range resonance frequencies in nano-crystalline diamond mechanical resonators. High order transverse vibration modes are measured in coupled-beam resonators exhibiting frequencies up to 1.441 GHz. The cantilever-array design of the resonators translates the gigahertz-range resonant motion of micron-long cantilever elements to the displacement of the central supporting structure. Use of nano-crystalline diamond further increases the frequency compared to single crystal silicon by a factor of three. High clamping losses usually associated with micro…
We seek the first indications that a nanoelectromechanical system (NEMS) is entering the quantum domain as its mass and temperature are decreased. We find them by studying the transition from classical to quantum behavior of a driven nonlinear Duffing resonator. Numerical solutions of the equations of motion, operating in the bistable regime of the resonator, demonstrate that the quantum Wigner function gradually deviates from the corresponding classical phase-space probability density. These clear differences that develop due to nonlinearity can serve as experimental evidence, in the near fut…
We describe a cavity QED analogue for the coupling system of a spin and a nanomechanical resonator with a magnetic tip. For the quantized nanomechanical resonator, a spin-boson model for this coupling system can refer to a Jaynes-Cummings(JC) or an anti-JC model. These observations predict some quantum optical phenomena, such as squeezing and "collapse-revival" in the single oscillation mode of the nanomechanical resonator when it is initially prepared in the quasi-classical state. By modulating the phase of RF magnetic field one can switch the system between the JC and anti-JC model, which pr…
We present a ground state cooling scheme for a nanomechanical resonator linearly coupled with a LC oscillator. The linear coupling, when periodically modulated at red detuning, up-converts the low-frequency nanomechanical mode to the high-frequency LC oscillator mode and generates backaction force that can cool the resonator to its ground state in the resolved-sideband regime. We also study the effect of the quantum backaction noise on the cooling due to the counter rotating term in the linear coupling. The scheme can be compared with laser cooling for the atomic systems and can be realized in…
We study the optical properties of quantum dipole emitters coupled to hyperbolic metamaterial nano-resonators using a semi-analytical quasinormal mode approach. We show that coupling to metamaterial nano-resonators can lead to significant Purcell enhancements that are nearly an order of magnitude larger than those of plasmonic resonators with comparable geometry. However, the associated single photon output $β$-factors are extremely low (around 10$\%$), far smaller than those of comparable sized metallic resonators (70$\%$). Using a quasinormal mode expansion of the photon Green function, we d…
We consider a theoretical model for a nonlinear nanomechanical resonator coupled to a superconducting microwave resonator. The nanomechanical resonator is driven parametrically at twice its resonance frequency, while the superconducting microwave resonator is driven with two tones that differ in frequency by an amount equal to the parametric driving frequency. We show that the semi-classical approximation of this system has an interesting fixed point bifurcation structure. In the semi-classical dynamics a transition from stable fixed points to limit cycles is observed as one moves from positiv…
Strong Stokes and anti-Stokes one-photon luminescence from single gold nanorods is measured in experiments. It is found that the intensity and polarization of the Stokes and anti-Stokes emissions are in strong correlation. Our experimental observation discovered a coherent process in light emission from single gold nanorods. We present a theoretical mode, based on the concept of cavity resonance, for consistently understanding both Stokes and anti-Stokes photoluminescence. Our theory is in good agreement of all our measurements.
We study a system of two nanomechanical resonators embedded in a dc SQUID. We show that the inductively-coupled resonators can be treated as two entangled quantum memory elements with states that can be read from, or written on by employing the SQUID as a displacement detector or switching additional external magnetic fields, respectively. We present a scheme to squeeze the even modeof the state of the resonators and consequently reduce the noise in the measurement of the magnetic flux threading the SQUID. Wefinally analyze the effect of dissipation on the squeezing using the quantum master eq…
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of spin-mechanical resonators and discuss both the cavity-QED-like and the trapped-ion-like spin-mechanical coupling processes. The implementation of these processes using negatively charged nitrogen vacancy and silicon vacancy centers in diamond is reviewed. Prospects for reaching the full quantum regime of spin-mechanics, in which quantum control can occur at t…
We have used nanoelectromechanical resonators to probe superfluid $^4$He at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant contributions to damping and the shift of the resonance frequency: tunneling two level systems at the lowest temperatures, ballistic phonons and rotons at few hundred mK, and laminar drag in the two-fluid regime below the superfluid transition temperature as well as in the normal fluid. Immersing the nanoelectromechanical resonators in fluid increases their effec…
In this work we present the fabrication and characterization of superconducting nano-mechanical resonators made from nanocrystalline boron doped diamond (BDD). The oscillators can be driven and read out in their superconducting state and show quality factors as high as 40,000 at a resonance frequency of around 10 MHz. Mechanical damping is studied for magnetic fields up to 3 T where the resonators still show superconducting properties. Due to their simple fabrication procedure, the devices can easily be coupled to other superconducting circuits and their performance is comparable with state-of…
