We propose and study a spin-orbit interaction based mechanism to actively cool down the torsional vibration of a nanomechanical resonator made by semiconductor materials. We show that the spin-orbit interactions of electrons can induce a coherent coupling between the electron spins and the torsional modes of nanomechanical vibration. This coherent coupling leads to an active cooling for the torsional modes via the dynamical thermalization of the resonator and the spin ensemble.
The interaction between spin and nanomechanical degrees of freedom attracts interest from the viewpoint of basic science and device applications. We study the magnon current induced by the torsional oscillation of ferromagnetic nanomechanical cantilever. We find that a finite Dzyaloshinskii-Moriya (DM) interaction emerges by the torsional oscillation, which is described by the spin gauge field, and the DM interaction leads to the detectably-large magnon current with frequency same as that of the torsional oscillation. Our theory paves the way for studying torsional spin-nanomechanical phenomen…
Torsional oscillations of a free-standing semiconductor beam are shown to cause spin-dependent oscillating potentials that spin-polarize an applied charge current in the presence of intentional or disorder scattering potentials. We propose several realizations of mechanical spin generators and manipulators based on this piezo-spintronic effect.
We demonstrate that a supercurrent can pump energy from a battery that provides a voltage bias into nanomechanical vibrations. Using a device containing a nanowire Josephson weak link as an example we show that a nonlinear coupling between the supercurrent and a static external magnetic field leads to a Lorentz force that excites bending vibrations of the wire at resonance conditions. We also demonstrate the possibility to achieve more than one regime of stationary nonlinear vibrations and how to detect them via the associated dc Josephson currents and we discuss possible applications of such …
State of the art nanomechanical resonators present quality factors Q ~ 10^3 - 10^5, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the dissipation mechanism that arises in nanomechanical beam-structures due to the tunneling of mesoscopic phonons between the beam and its supports (known as clamping losses). We derive the environmental force spectral density that determines the quantum Brownian motion of a given resonance. Our treatment is valid for low frequencies and provides the leading contribution in the aspect ra…
We propose a scheme of strong and tunable coupling between a superconducting phase qubit and nanomechanical torsional resonator. In our scheme the torsional resonator directly modulates the largest energy scale (the Josephson coupling energy) of the phase qubit, and the coupling strength is very large. We analyze the quantum correlation effects in the torsional resonator as a result of the strong coupling to the phase qubit.
An optically levitated nanoparticle in vacuum is a paradigm optomechanical system for sensing and studying macroscopic quantum mechanics. While its center-of-mass motion has been investigated intensively, its torsional vibration has only been studied theoretically in limited cases. Here we report the first experimental observation of the torsional vibration of an optically levitated nonspherical nanoparticle in vacuum. We achieve this by utilizing the coupling between the spin angular momentum of photons and the torsional vibration of a nonspherical nanoparticle whose polarizability is a tenso…
Nanomechanics has brought mesoscopic physics into the world of vibrations. Because nanomechanical systems are small, fluctuations are significant, the vibrations become nonlinear already for comparatively small amplitudes, and new mechanisms of dissipation come into play. At the same time, the exquisite control of these systems makes them a platform for studying many problems of classical and quantum physics far from thermal equilibrium in a well-characterized setting. This review describes, at a conceptual level, basic theoretical ideas and explicative experiments pertaining to mesoscopic phy…
The nonlinear interactions between flexural and torsional modes of a microcantilever are experimentally studied. The coupling is demonstrated by measuring the frequency response of one mode, which is sensitive to the motion of another resonance mode. The flexural-flexural, torsional-torsional and flexural-torsional modes are coupled due to nonlinearities, which affect the dynamics at high vibration amplitudes and cause the resonance frequency of one mode to depend on the amplitude of the other modes. We also investigate the nonlinear dynamics of torsional modes, which cause a frequency stiffen…
We propose a model for a molecular junction with internal anharmonic torsional vibrations interacting with an electric current. The Wangsness-Bloch-Redfield master equation approach is used to determine the stationary reduced density matrix of the molecule. The dependence of the current, excitation energy and angular momentum of the junction on the applied voltage is studied. Negative differential conductance is observed in the current-voltage characteristics. It is shown that a model with vibrationally dependent coupling to the electrodes, asymmetric with respect to the interchanging of elect…
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.
We consider a new type of cooling mechanism for a suspended nanowire acting as a weak link between two superconductive electrodes. By applying a bias voltage over the system, we show that the system can be viewed as a refrigerator for the nanomechanical vibrations, where energy is continuously transferred from the vibrational degrees of freedom to the extended quasiparticle states in the leads through the periodic modulation of the inter-Andreev level separation. The necessary coupling between the electronic and mechanical degrees of freedom responsible for this energy-transfer can be achieved…
The electrical response of two-dimensional electron gas to vibrations of a nanomechanical cantilever containing it is studied. Vibrations of perpendicularly oriented cantilevers are experimentally shown to change oppositely the conductivity near their bases. This indicates the piezoelectric nature of electromechanical coupling. A physical model is developed, which quantitatively explains the experiment. It shows that the main origin of the conductivity change is a rapid change in the mechanical stress on the boundary between suspended and non-suspended areas, rather than the stress itself.
Software-defined radio dongles are small and inexpensive receivers well known to amateur radio enthusiasts. When connected to an antenna, they enable monitoring of a wide range of the radio spectrum by conditioning the input signal and transferring a downconverted version of it to a personal computer for software processing. Here, we employ a composite of two such dongles, interfaced with codes written in MATLAB and GNU Radio, as a measuring instrument to study the flexural vibrations of a few-layer graphene nanomechanical resonator. Instead of an antenna, we connect the dongles to the split o…
We study the effect of the electron-phonon coupling on vibrational eigenmodes of nano- and micro-mechanical systems made of semiconductors with equivalent energy valleys. We show that the coupling can lead to a strong mode nonlinearity. The mechanism is the lifting of the valley degeneracy by the strain. The redistribution of the electrons between the valleys is controlled by a large ratio of the electron-phonon coupling constant to the electron chemical potential or temperature. We find the quartic in the strain terms in the electron free energy, which determine the amplitude dependence of th…
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 discuss two theoretical proposals for controlling the nonequilibrium steady state of nanomechanical resonators using quantum electronic transport. Specifically?, we analyse two approaches to achieve the ground-state cooling of the mechanical vibration coupled to a quantum dot embedded between (i) spin-polarised contacts or (ii) a normal metal and a superconducting contact. Assuming a suitable coupling between the vibrational modes and the charge or spin of the electrons in the quantum dot, we show that ground-state cooling of the mechanical oscillator is within the state of the art for susp…
We study the response of a weakly damped vibrational mode of a nanostring resonator to a moderately strong resonant driving force. Because of the geometry of the experiment, the studied flexural vibrations lack inversion symmetry. As we show, this leads to a nontrivial dependence of the vibration amplitude on the force parameters. For a comparatively weak force, the response has the familiar Duffing form, but for a somewhat stronger force, it becomes significantly different. Concurrently there emerge vibrations at twice the drive frequency, a signature of the broken symmetry. Their amplitude a…
We consider a nanoelectromechanical system composed of a carbon nanotube suspended between two normal leads and coupled to a superconducting scanning tunneling microscope (STM) tip via vacuum tunnel barrier. Treating the nanotube as a single-level quantum dot, it is shown that an applied voltage between the superconducting STM tip and normal leads gives rise to a pumping or a cooling of the mechanical subsystem depending on the direction of the electronic flow. It is also demonstrated that the transition between these two regimes is controlled by the strength of the tunnel coupling between the…
A nanoelectromechanical weak link composed of a carbon nanotube suspended between two normal electrodes in a gap between two superconducting leads is considered. The nanotube is treated as a movable single-level quantum dot in which the position-dependent superconducting order parameter is induced due to the Cooper pair tunneling. We show that electron tunneling processes significantly affect the state of the mechanical subsystem. We found that at a given direction of the applied voltage between the electrodes, the stationary state of the mechanical subsystem has a Boltzmann form with an effec…
We study a system consisting of a particle adsorbed on a carbon nanotube resonator. The particle is allowed to diffuse along the resonator, in order to enable study of e.g. room temperature mass sensing devices. The system is initialized in a state where only the fundamental vibration mode is excited, and the ring-down of the system is studied by numerically and analytically solving the stochastic equations of motion. We find two mechanisms of dissipation, induced by the diffusing adsorbate. First, short-time correlations between particle and resonator motions means that the net effect of the …
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the anomalously strong and nonmonotonic dependence of the decay rate of the low frequency mode on its amplitude, if the decay rate of the high-frequency mode is comparatively large. In this case the low-frequency mode driven close to resonance can have several branches of steady-state vibrations with constant amplitude. If the decay rates of the both modes are smal…
We develop a simple continuum model to analyze the vibrational modes of a nanomechanical multi-element structure. In this model, arrays of sub-micron cantilevers located symmetrically on both sides of the central clamped-clamped nanobeam are replaced by a continuum. In this approach, the punctual shear forces exerted by the cantilevers on the central beam are smoothed out and the equations of motion of the structure become exactly solvable. Our analytical results capture the main features of the vibrational modes observed both numerically and experimentally. Furthermore, using a perturbative a…
Reminiscent of the bound character of a qubit's dynamics confined on the Bloch sphere, the observation of a Mollow triplet in the resonantly driven qubit fluorescence spectrum represents one of the founding signatures of Quantum Electrodynamics. Here we report on its observation in a hybrid spin-nanomechanical system, where a Nitro-gen Vacancy spin qubit is magnetically coupled to the vibrations of a Silicon Carbide nanowire. A resonant microwave field turns the originally parametric hybrid interac-tion into a resonant process, where acoustic phonons are now able to induce transitions between …
The efficient cooling of the nanomechanical resonators is essential to exploration of quantum properties of the macroscopic or mesoscopic systems. We propose such a laser-cooling scheme for a nanomechanical cantilever, which works even for the low-frequency mechanical mode and under weak cooling lasers. The cantilever is attached by a diamond nitrogen-vacancy center under a strong magnetic field gradient and the cooling is assisted by a dynamical Stark-shift gate. Our scheme can effectively enhance the desired cooling efficiency by avoiding the off-resonant and unexpected carrier transitions, …
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and nonlinear properties. For large vibration amplitudes the system develops spontaneous oscillations of amplitude modulation that also show period doubling transitions and chaos. The complex nonlinear dynamics are quantitatively predicted by a simple theoretical model.
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…
Torsional oscillation of carbon nanotubes driven by electron spins
University of Tokyo（东京大学）；Tohoku University（东北大学）；University of Chinese Academy of Sciences（中国科学院大学）；Japan Atomic Energy Agency（日本原子能研究开发机构）；RIKEN（理化学研究所）
The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding m…
Energy decay plays a central role in a wide range of phenomena, such as optical emission, nuclear fission, and dissipation in quantum systems. Energy decay is usually described as a system leaking energy irreversibly into an environmental bath. Here, we report on energy decay measurements in nanomechanical systems based on multi-layer graphene that cannot be explained by the paradigm of a system directly coupled to a bath. As the energy of a vibrational mode freely decays, the rate of energy decay switches abruptly to a lower value. This finding can be explained by a model where the measured m…
We show that torsion resonators can experience massive dissipation dilution due to nanoscale strain, and draw a connection to a century-old theory from the torsion balance community which suggests that a simple torsion ribbon is naturally soft-clamped. By disrupting a commonly held belief in the nanomechanics community, our findings invite a rethinking of strategies towards quantum experiments and precision measurement with nanomechanical resonators. For example, we revisit the optical lever technique for monitoring displacement, and find that the rotation of a strained nanobeam can be resolve…
The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2 π) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electr…
We show that the vibrations of a nanomechanical resonator can be cooled to near its quantum ground state by tunnelling injection of electrons from an STM tip. The interplay between two mechanisms for coupling the electronic and mechanical degrees of freedom results in a bias-voltage dependent difference between the probability amplitudes for vibron emission and absorption during tunneling. For a bias voltage just below the Coulomb blockade threshold we find that absorption dominates, which leads to cooling corresponding to an average vibron population of the fundamental bending mode of 0.2.
We propose a general one-dimensional {\em continuous} formulation to analyze the vibrational modes of antenna-like nanomechanical resonators consisting of two symmetric arrays of cantilevers affixed to a central nano-beam. The cantilever arrays can have arbitrary density and length profile along the beam. We obtain the secular equation that allows for the determination of their frequency spectrum and illustrate the results on the particular examples of structures with constant or alternating cantilever length profiles. We show that our analytical results capture the vibration spectrum of such …
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 d…
We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to th…
I study dephasing of an underdamped nanomechanical resonator subject to random mass loading of small particles. I present a frequency noise model which describes dephasing due to attachment and detachment of particles at random points and particle diffusion along the resonator. This situation is commonly encountered in current mass measurement experiments using NEM resonators. I discuss the conditions which can lead to inhomogeneous broadening and fine structure in the modes absorption spectra. I also show that the spectra of the higher order cumulants of the (complex) vibrational mode amplitu…
We study the nonequilibrium steady state of a mechanical resonator in the quantum regime realized by a suspended carbon nanotube quantum dot contacted by two ferromagnets. Because of the spin-orbit interaction and/or an external magnetic field gradient, the spin on the dot couples directly to the flexural eigenmodes. Accordingly, the nanomechanical motion induces inelastic spin flips of the tunneling electrons. A spin-polarized current at finite bias voltage causes either heating or active cooling of the mechanical modes. We show that maximal cooling is achieved at resonant transport when the …
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…
Nanomechanical resonators have recently been highlighted because of their remarkable ability to perform the sensing and detection. Since the nanomechanical resonators are characterized by large surface-to-volume ratio, it is implied that the surface effect plays a substantial role on not only the resonance but also the sensing performance of nanomechanical resonators. In this work, we have studied the role of surface effect on the detection sensitivity of a nanoresonator that undergoes either harmonic vibration or nonlinear oscillation based on the continuum elastic model such as beam model. I…
We show that nitrogen-vacancy (NV) centers in diamond interfaced with a suspended carbon nanotube carrying a dc current can facilitate a spin-nanomechanical hybrid device. We demonstrate that strong magnetomechanical interactions between a single NV spin and the vibrational mode of the suspended nanotube can be engineered and dynamically tuned by external control over the system parameters. This spin-nanomechanical setup with strong, \emph{intrinsic} and \emph{tunable} magnetomechanical couplings allows for the construction of hybrid quantum devices with NV centers and carbon-based nanostructu…
In the context of a recoil damping analysis, we have designed and produced a membrane resonator equipped with a specific on-chip structure working as a "loss shield" for a circular membrane. In this device the vibrations of the membrane, with a quality factor of $10^7$, reach the limit set by the intrinsic dissipation in silicon nitride, for all the modes and regardless of the modal shape, also at low frequency. Guided by our theoretical model of the loss shield, we describe the design rationale of the device, which can be used as effective replacement of commercial membrane resonators in adva…
We investigate the torsional vibrations in biphenyl-like molecular junctions and transport properties in the presence of an external THz field. Ab-initio calculations including external electric fields show that the torsional angle ϕ of a thiolated biphenyl junction exhibits virtually no response. However, if functional groups are added to the molecule, creating a dipole moment in each of the rings, an external field becomes more effective for changing ϕ. A model based on the cos2ϕ dependence of the current is proposed for the biphenyl-like molecular junctions in presence of an external THz fi…
We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances, that either tune to higher or to lower frequencies when increasing the dc voltage on the back-gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability.
We investigate the behaviour of two non-linearly coupled flexural modes of a doubly-clamped suspended beam (nanomechanical resonator). One of the modes is externally driven. We demonstrate that classically, the behavior of the non-driven mode is reminiscent of that of a parametrically driven linear oscillator: It exhibits a threshold behavior, with the amplitude of this mode below the threshold being exactly zero. Quantum-mechanically, we were able to access the dynamics of this mode below the classical parametric threshold. We show that whereas the mean displacement of this mode is still zero…
We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum dot with an odd number of electrons can serve as a realization of the Jaynes-Cummings model of quantum electrodynamics in the strong-coupling regime. A quantized flexural mode of the suspended tube plays the role of the optical mode and we identify two distinct two-level subspaces, at small and large magnetic field, which can be used as qubits in this setup. …
When a contaminant diffuses on the surface of a nanomechanical resonator, the motions of the two become correlated. Despite being a high-order effect in the resonator-particle coupling, such correlations affect the system dynamics by inducing dissipation of the resonator energy. Here, we consider this diffusion-induced dissipation in the cases of multiple particles adsorbed on carbon nanotube and graphene resonators. By solving the stochastic equations of motion, we simulate the ringdown of the resonator, in order to determine the resonator energy decay rate. We find two different scalings wit…
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 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…
Motivated by a recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] providing evidence for Majorana zero modes in iron chains on the superconducting Pb surface, in the present work, we theoretically propose an all-optical scheme to detect Majorana fermions, which is very different from the current tunneling measurement based on electrical means. The optical detection proposal consists of a quantum dot embedded in a nanomechanical resonator with optical pump-probe technology. With the optical means, the signal in the coherent optical spectrum presents a distinct signature for the exis…
In recent years, nanomechanics has evolved into a mature field, with wide-ranging impact from sensing applications to fundamental physics, and it has now reached a stage which enables the fabrication and study of ever more elaborate devices. This has led to the emergence of arrays of coupled nanomechanical resonators as a promising field of research, serving as model systems to study collective dynamical phenomena such as synchronization or topological transport. From a general point of view, the arrays investigated so far represent scalar fields on a lattice. Moving to a scenario where these …
From ultra-sensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exh…
We study a general model describing a self-detecting single electron transistor realized by a suspended carbon nanotube actuated by a nearby antenna. The main features of the device, recently observed in a number of experiments, are accurately reproduced. When the device is in a low current-carrying state, a peak in the current signals a mechanical resonance. On the contrary, a dip in the current is found in high current-carrying states. In the nonlinear vibration regime of the resonator, we are able to reproduce quantitatively the characteristic asymmetric shape of the current-frequency curve…
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 …
