Nanomechanical Oscillator Research Articles

Slippage and boundary layer probed in an almost ideal gas by a nanomechanical oscillator.

We measure the interaction between ⁴He gas at 4.2 K and a high-quality nanoelectromechanical string device for its first three symmetric modes (resonating at 2.2, 6.7, and 11 MHz with quality factor Q>0.1×10⁶) over almost 6 orders of magnitude in pressure. This fluid can be viewed as the best experimental implementation of an almost ideal monoatomic and inert gas of which properties are tabulated. The experiment ranges from high pressure where the flow is of laminar Stokes-type presenting slippage down to very low pressures where the flow is molecular. In the molecular regime, when the mean-free path is of the order of the distance between the suspended nanomechanical probe and the bottom of the trench, we resolve for the first time the signature of the boundary (Knudsen) layer onto the measured dissipation. Our results are discussed in the framework of the most recent theories investigating boundary effects in fluids (both analytic approaches and direct simulation Monte Carlo methods).

Optical driving of macroscopic mechanical motion by a single two-level system

A quantum emitter coupled to a nanomechanical oscillator is a hybrid system where a macroscopic degree of freedom is coupled to a purely quantum system. Recent progress in nanotechnology has led to the realization of such devices by embedding single artificial atoms, such as quantum dots or superconducting qubits, into vibrating wires or membranes, opening up new perspectives for quantum information technologies and for the exploration of the quantum-classical boundary. In this paper, we show that the quantum emitter can be turned into a strikingly efficient light-controlled source of mechanical power by exploiting constructive interferences of classical phonon fields in the mechanical oscillator. We show that this mechanism can be exploited to carry out low-background nondestructive single-shot measurement of an optically active quantum bit state.

Long-time correlated quantum dynamics of phonon cooling

We investigate the steady-state cooling dynamics of vibrational degrees of freedom related to a nanomechanical oscillator coupled with a laser-pumped quantum dot in an optical resonator. Correlations between phonon-cooling and quantum-dot photon emission processes occur respectively when a photon laser absorption together with a vibrational phonon absorption is followed by photon emission in the optical resonator. Therefore, the detection of photons generated in the cavity mode concomitantly contribute to phonon cooling detection of the nanomechanical resonator.

Optomechanical sensing of spontaneous wave-function collapse.

Quantum experiments with nanomechanical oscillators are regarded as a test bed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macroscale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements.

Hybrid sensors based on colour centres in diamond and piezoactive layers.

The ability to measure weak signals such as pressure, force, electric field and temperature with nanoscale devices and high spatial resolution offers a wide range of applications in fundamental and applied sciences. Here we present a proposal for a hybrid device composed of thin film layers of diamond with colour centres and piezoactive elements for the transduction and measurement of physical signals. The magnetic response of a piezomagnetic layer to an external stress or a stress induced by a signal is shown to affect significantly the spin properties of nitrogen-vacancy centres in diamond. Under ambient conditions, realistic environmental noise and material imperfections, we show that this hybrid device can achieve significant improvements in sensitivity over the pure diamond-based approach in combination with nanometre-scale spatial resolution. Furthermore, the proposed hybrid architecture offers novel possibilities for engineering strong coherent couplings between nanomechanical oscillator and solid state spin qubits.

Teleportation-induced entanglement of two nanomechanical oscillators coupled to a topological superconductor

A one-dimensional topological superconductor features a single fermionic zero mode that is delocalized over two Majorana bound states located at the ends of the system. We study a pair of spatially separated nanomechanical oscillators tunnel-coupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electron-phonon coupling and a finite charging energy on the mesoscopic topological superconductor can lead to an effective superexchange between the oscillators via the non-local fermionic zero mode. We further show that this teleportation mechanism leads to entanglement of the two oscillators over distances that can significantly exceed the coherence length of the superconductor.

Radio-Wave Oscillations of Molecular-Chain Resonators

We report a new type of nanomechanical resonator system based on one-dimensional chains of only 4 to 7 weakly coupled small molecules. Experimental characterization of the truly nanoscopic resonators is achieved by means of a novel radio-frequency scanning tunneling microscopy detection technique at cryogenic temperatures. Above 20 K we observe concerted oscillations of the individual molecules in chains, reminiscent of the first and second eigenmodes of a one-dimensional harmonic resonator. Radio-frequency scanning tunneling microscopy based frequency measurement reveals a characteristic length dependence of the oscillation frequency (between 51 and 127 MHz) in reasonable agreement with one-dimensional oscillator models. Our study demonstrates a new strategy for investigating and controlling the resonance properties of nanomechanical oscillators.

Hardware for a quantum network

An optomechanical device has been designed that converts radio-frequency electrical signals into laser light. The system could allow computers to share data in a future quantum network based on optical fibres. See Letter p.81 Many applications, from medical imaging and radio astronomy to navigation and wireless communication, depend on the faithful transmission and detection of weak radio-frequency microwaves. Here Eugene Polzik and co-workers demonstrate a completely new capability in this area — the conversion of weak radio waves into laser signals using a nanomechanical oscillator. The oscillator, a membrane made from silicon nitride, can couple simultaneously to radio signals and light reflected off its surface and this feature can be used to measure the radio signals as optical phase shifts, with quantum-limited sensitivity. Compared to existing detectors, this approach has the advantage of working at room temperature, and the signals produced can be readily transferred into standard optical fibres.

Optical detection of radio waves through a nanomechanical transducer

Low-loss transmission and sensitive recovery of weak radio-frequency and microwave signals is a ubiquitous challenge, crucial in radio astronomy, medical imaging, navigation, and classical and quantum communication. Efficient up-conversion of radio-frequency signals to an optical carrier would enable their transmission through optical fibres instead of through copper wires, drastically reducing losses, and would give access to the set of established quantum optical techniques that are routinely used in quantum-limited signal detection. Research in cavity optomechanics has shown that nanomechanical oscillators can couple strongly to either microwave or optical fields. Here we demonstrate a room-temperature optoelectromechanical transducer with both these functionalities, following a recent proposal using a high-quality nanomembrane. A voltage bias of less than 10 V is sufficient to induce strong coupling between the voltage fluctuations in a radio-frequency resonance circuit and the membrane's displacement, which is simultaneously coupled to light reflected off its surface. The radio-frequency signals are detected as an optical phase shift with quantum-limited sensitivity. The corresponding half-wave voltage is in the microvolt range, orders of magnitude less than that of standard optical modulators. The noise of the transducer--beyond the measured 800 pV Hz-1/2 Johnson noise of the resonant circuit--consists of the quantum noise of light and thermal fluctuations of the membrane, dominating the noise floor in potential applications in radio astronomy and nuclear magnetic imaging. Each of these contributions is inferred to be 60 pV Hz-1/2 when balanced by choosing an electromechanical cooperativity of ~150 with an optical power of 1 mW. The noise temperature of the membrane is divided by the cooperativity. For the highest observed cooperativity of 6,800, this leads to a projected noise temperature of 40 mK and a sensitivity limit of 5 pV Hz-1/2. Our approach to all-optical, ultralow-noise detection of classical electronic signals sets the stage for coherent up-conversion of low-frequency quantum signals to the optical domain.

Novel spectral features of nanoelectromechanical systems.

Electron transport through a quantum dot or single molecule coupled to a quantum oscillator is studied by the Keldysh nonequilibrium Green's function formalism to obtain insight into the quantum dynamics of the electronic and oscillator degrees of freedom. We tune the electronic level of the quantum dot by a gate voltage, where the leads are kept at zero temperature. Due to the nonequilibrium distribution of the electrons in the quantum dot, the spectral function becomes a function of the gate voltage. Novel spectral features are identified for the ground and excited states of nanomechanical oscillators that can be used to enhance the measurement sensitivity.

Strong squeezing and robust entanglement in cavity electromechanics

We investigate nonlinear effects in an electromechanical system consisting of a superconducting charge qubit coupled to a transmission line resonator and a nanomechanical oscillator, which in turn is coupled to another transmission line resonator. The nonlinearities induced by the superconducting qubit and the optomechanical coupling play an important role in creating optomechanical entanglement as well as the squeezing of the transmitted microwave field. We show that strong squeezing of the microwave field and robust optomechanical entanglement can be achieved in the presence of moderate thermal decoherence of the mechanical mode. We also discuss the effect of the coupling of the superconducting qubit to the nanomechanical oscillator on the bistability behavior of the mean photon number.

Sensitivity to external signals and synchronization properties of a non-isochronous auto-oscillator with delayed feedback

For auto-oscillators of different nature (e.g. active cells in a human heart under the action of a pacemaker, neurons in brain, spin-torque nano-oscillators, micro and nano-mechanical oscillators, or generating Josephson junctions) a critically important property is their ability to synchronize with each other. The synchronization properties of an auto oscillator are directly related to its sensitivity to external signals. Here we demonstrate that a non-isochronous (having generation frequency dependent on the amplitude) auto-oscillator with delayed feedback can have an extremely high sensitivity to external signals and unusually large width of the phase-locking band near the boundary of the stable auto-oscillation regime. This property could be used for the development of synchronized arrays of non-isochronous auto-oscillators in physics and engineering, and, for instance, might bring a better fundamental understanding of ways to control a heart arrythmia in medicine.

Stabilization of a linear nanomechanical oscillator to its thermodynamic limit

The rapid development of micro- and nanomechanical oscillators in the past decade has led to the emergence of novel devices and sensors that are opening new frontiers in both applied and fundamental science. The potential of these devices is however affected by their increased sensitivity to external perturbations. Here we report a non-perturbative optomechanical stabilization technique and apply the method to stabilize a linear nanomechanical beam at its thermodynamic limit at room temperature. The reported ability to stabilize a nanomechanical oscillator to the thermodynamic limit can be extended to a variety of systems and increases the sensitivity range of nanomechanical sensors in both fundamental and applied studies.

Thermal nonlinearities in a nanomechanical oscillator

Nano- and micromechanical oscillators with high quality (Q) factors have gained much attention for their potential application as ultrasensitive detectors. In contrast to micro-fabricated devices, optically trapped nanoparticles in vacuum do not suffer from clamping losses, hence leading to much larger Q-factors. We find that for a levitated nanoparticle the thermal energy suffices to drive the motion of the nanoparticle into the nonlinear regime. First, we experimentally measure and fully characterize the frequency fluctuations originating from thermal motion and nonlinearities. Second, we demonstrate that feedback cooling can be used to mitigate these fluctuations. The high level of control allows us to fully exploit the force sensing capabilities of the nanoresonator. Our approach offers a force sensitivity of 20 zN $Hz^{-1/2}$, which is the highest value reported to date at room temperature, sufficient to sense ultra-weak interactions, such as non-Newtonian gravity-like forces.

Photonic Cavity Synchronization of Nanomechanical Oscillators

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 oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. In addition to the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.

Optomechanical generation of a photonic Bose-Einstein condensate

We propose to thermalize a low-dimensional photon gas and obtain photon Bose-Einstein condensation by optomechanical interactions in a microscopic optical cavity, with a single longitudinal mode and many transverse modes. The geometry of the short cavity is such that it provides a low-frequency cutoff at a photon energy far above the thermal energy, so that thermal emission of photons is suppressed and the photon number is conserved. While previous experiments on photon Bose-Einstein condensation have used dye molecules for photon gas thermalization, we here investigate thermalization owing to interactions with thermally fluctuating nanomechanical oscillators forming the cavity mirrors. In the quantum degenerate regime, the nanomechanical cavity converts broadband optical radiation into tuneable coherent radiation.

Entanglement of nanoelectromechanical oscillators by Cooper-pair tunneling

We demonstrate that entanglement of two macroscopic nanoelectromechanical resonators---coupled to each other via a common detector, a tunnel junction---can be generated by running a current through the device. We introduce a setup that overcomes generic limitations of proposals suggesting to entangle systems via a shared bath. At the heart of the proposal is an Andreev entangler setup, representing an experimentally feasible way of entangling two nanomechanical oscillators. Instead of relying on the coherence of a (fermionic) bath, in the Andreev entangler setup, a split Cooper pair that coherently tunnels to each oscillator mediates their coupling and thereby induces entanglement between them. Since entanglement is in each instance generated by Markovian and non-Markovian noisy open system dynamics in an out-of-equilibrium situation, we argue that the present scheme also opens up perspectives to observe dissipation-driven entanglement in a condensed-matter system.

Evanescently coupled optomechanical system with SiN nanomechanical oscillator and deformed silica microsphere

An evanescently coupled optomechanical system is developed, in which a SiN nanomechanical oscillator couples to the evanescent field of whispering gallery optical modes in a slightly deformed silica microsphere. The evanescent optomechanical coupling length varies strongly along the whispering gallery optical path, with the maximum coupling length nearly three times that of a regular optical resonator. The deformed resonator also allows efficient free-space evanescent excitation of whispering gallery optical modes. These unique features enable a relatively simple and robust implementation of evanescently coupled optomechanical systems.

Spinning oscillators

Coupled nanomechanical oscillators can show similar dynamics to two-level systems, and may eventually be used as quantum bits.

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

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