Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical Resonator.

Hexagonal boron nitride (hBN) is a van der Waals material with excellent mechanical properties hosting quantum emitters and optically active spin defects, with several of them being sensitive to strain. Establishing optomechanical control of hBN will enable hybrid quantum devices that combine the spin degree of freedom with the cavity optomechanical toolbox. In this Letter, we report the first observation of radiation pressure backaction at telecom wavelengths with a hBN drum-head mechanical resonator. The thermomechanical motion of the resonator is coupled to the optical mode of a high finesse fiber-based Fabry-Pérot microcavity in a membrane-in-the-middle configuration. We are able to resolve the optical spring effect and optomechanical damping with a single photon coupling strength of g0/2π = 1200 Hz. Our results pave the way for tailoring the mechanical properties of hBN resonators with light.

Iterative Adaptive Spectroscopy of Short Signals.

We develop an iterative, adaptive frequency sensing protocol based on Ramsey interferometry of a two-level system. Our scheme allows one to estimate unknown frequencies with a high precision from short, finite signals consisting of only a small number of Ramsey fringes. It avoids several issues related to processing of decaying signals and reduces the experimental overhead related to sampling. High precision is achieved by enhancing the Ramsey sequence to prepare with high fidelity both the sensing and readout state and by using an iterative procedure built to mitigate systematic errors when estimating frequencies from Fourier transforms. A comparison with state-of-the-art dynamical decoupling techniques reveals a significant speedup of the frequency estimation without loss of precision.

Persistent Response in an Ultrastrongly Driven Mechanical Membrane Resonator.

We study experimentally and theoretically the phenomenon of "persistent response" in ultrastrongly driven membrane resonators. The term persistent response denotes the development of a vibrating state with nearly constant amplitude over an extreme wide frequency range. We reveal the underlying mechanism by directly imaging the vibrational state using advanced optical interferometry. We argue that this state is related to the nonlinear interaction between higher-order flexural modes and higher-order overtones of the driven mode. Finally, we propose a stability diagram for the different vibrational states that the membrane can adopt.

Resonantly Induced Friction and Frequency Combs in Driven Nanomechanical Systems.

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

Spatial Modulation of Nonlinear Flexural Vibrations of Membrane Resonators.

We study the vibrational motion of mechanical resonators under strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular silicon nitride membrane resonators and by analyzing the frequency response using optical interferometry, we show that, upon increasing the driving strength, the membrane adopts a peculiar deflection pattern formed by concentric rings superimposed onto the drum head shape of the fundamental mode. Such a circular symmetry cannot be described as a superposition of a small number of excited linear eigenmodes. Furthermore, different parts of the membrane vibrate at different multiples of the drive frequency, an observation that we denominate as "localization of overtones." We introduce a phenomenological model that is based on the coupling of a small number of effective nonlinear resonators, representing the different parts of the membrane, and that describes the experimental observations correctly.

Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes.

We study locking phenomena of two strongly coupled, high quality factor nanomechanical resonator modes to a common parametric drive at a single drive frequency in different parametric driving regimes. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via nondegenerate parametric two-mode oscillation is observed. Broadband frequency tuning of the very narrow linewidth signal and idler resonances is demonstrated. When the resonance frequencies of the signal and idler get closer to each other, partial injection locking, injection pulling, and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically offset from the signal and idler by their beat note, are observed, which can be attributed to degenerate four-wave mixing in the highly nonlinear mechanical oscillations.

Universal transduction scheme for nanomechanical systems based on dielectric forces.

Any polarizable body placed in an inhomogeneous electric field experiences a dielectric force. This phenomenon is well known from the macroscopic world: a water jet is deflected when approached by a charged object. This fundamental mechanism is exploited in a variety of contexts-for example, trapping microscopic particles in an optical tweezer, where the trapping force is controlled via the intensity of a laser beam, or dielectrophoresis, where electric fields are used to manipulate particles in liquids. Here we extend the underlying concept to the rapidly evolving field of nanoelectromechanical systems (NEMS). A broad range of possible applications are anticipated for these systems, but drive and detection schemes for nanomechanical motion still need to be optimized. Our approach is based on the application of dielectric gradient forces for the controlled and local transduction of NEMS. Using a set of on-chip electrodes to create an electric field gradient, we polarize a dielectric resonator and subject it to an attractive force that can be modulated at high frequencies. This universal actuation scheme is efficient, broadband and scalable. It also separates the driving scheme from the driven mechanical element, allowing for arbitrary polarizable materials and thus potentially ultralow dissipation NEMS. In addition, it enables simple voltage tuning of the mechanical resonance over a wide frequency range, because the dielectric force depends strongly on the resonator-electrode separation. We use the modulation of the resonance frequency to demonstrate parametric actuation. Moreover, we reverse the actuation principle to realize dielectric detection, thus allowing universal transduction of NEMS. We expect this combination to be useful both in the study of fundamental principles and in applications such as signal processing and sensing.

Thermoelastic damping in MEMS gyroscopes at high frequencies.

Microelectromechanical systems (MEMS) gyroscopes are widely used, e.g., in modern automotive and consumer applications, and require signal stability and accuracy in rather harsh environmental conditions. In many use cases, device reliability must be guaranteed under large external loads at high frequencies. The sensitivity of the sensor to such external loads depends strongly on the damping, or rather quality factor, of the high-frequency mechanical modes of the structure. In this paper, we investigate the influence of thermoelastic damping on several high-frequency modes by comparing finite element simulations with measurements of the quality factor in an application-relevant temperature range. We measure the quality factors over different temperatures in vacuum, to extract the relevant thermoelastic material parameters of the polycrystalline MEMS device. Our simulation results show a good agreement with the measured quantities, therefore proving the applicability of our method for predictive purposes in the MEMS design process. Overall, we are able to uniquely identify the thermoelastic effects and show their significance for the damping of the high-frequency modes of an industrial MEMS gyroscope. Our approach is generic and therefore easily applicable to any mechanical structure with many possible applications in nano- and micromechanical systems.

Optical instability and self-pulsing in silicon nitride whispering gallery resonators.

We report time domain observations of optical instability in high Q silicon nitride whispering gallery disk resonators. At low laser power the transmitted optical power through the disk looks chaotic. At higher power, the optical output settles into a stable self-pulsing regime with periodicity ranging from hundreds of milliseconds to hundreds of seconds. This phenomenon is explained by the interplay between a fast thermo-optic nonlinearity within the disk and a slow thermo-mechanic nonlinearity of the structure. A model for this interplay is developed which provides good agreement with experimental data and points out routes to control this instability.

Nonadiabatic dynamics of two strongly coupled nanomechanical resonator modes.

The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here, we present a classical mechanical model system exhibiting analogous behavior using two inversely tunable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.

Observing polarization patterns in the collective motion of nanomechanical arrays.

In recent years, nanomechanics has evolved into a mature field, 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 can be effectively treated as scalar fields on a lattice. Moving to a scenario where the vector character of the fields becomes important would unlock a whole host of conceptually interesting additional phenomena, including the physics of polarization patterns in wave fields and their associated topology. Here we introduce a new platform, a two-dimensional array of coupled nanomechanical pillar resonators, whose orthogonal vibration directions encode a mechanical polarization degree of freedom. We demonstrate direct optical imaging of the collective dynamics, enabling us to analyze the emerging polarization patterns, follow their evolution with drive frequency, and identify topological polarization singularities.

Fluctuating nanomechanical system in a high finesse optical microcavity.

The idea of extending cavity quantum electrodynamics experiments to sub-wavelength sized nanomechanical systems has been recently proposed in the context of optical cavity cooling and optomechanics of deformable cavities. Here we present an experiment involving a single nanorod consisting of about 10(9) atoms precisely positioned into the confined mode of a miniature high finesse Fabry-Pérot microcavity. We show that the optical transmission of the cavity is affected not only by the static position of the nanorod but also by its vibrational fluctuation. The Brownian motion of the nanorod is resolved with a displacement sensitivity of 200 fm/square root Hz at room temperature. Besides a broad range of sensing applications, cavity-induced manipulation of optomechanical nanosystems and back-action is anticipated.

Energy losses of nanomechanical resonators induced by atomic force microscopy-controlled mechanical impedance mismatching.

Clamping losses are a widely discussed damping mechanism in nanoelectromechanical systems, limiting the performance of these devices. Here we present a method to investigate this dissipation channel. Using an atomic force microscope tip as a local perturbation in the clamping region of a nanoelectromechanical resonator, we increase the energy loss of its flexural modes by at least one order of magnitude. We explain this by a transfer of vibrational energy into the cantilever, which is theoretically described by a reduced mechanical impedance mismatch between the resonator and its environment. A theoretical model for this mismatch, in conjunction with finite element simulations of the evanescent strain field of the mechanical modes in the clamping region, allows us to quantitatively analyse data on position and force dependence of the tip-induced damping. Our experiments yield insights into the damping of nanoelectromechanical systems with the prospect of engineering the energy exchange in resonator networks.

Ultrasonically driven nanomechanical single-electron shuttle.

The single-electron transistor is the fastest and most sensitive electrometer available today. Single-electron pumps and turnstiles are also being explored as part of the global effort to redefine the ampere in terms of the fundamental physical constants. However, the possibility of electrons tunnelling coherently through these devices, a phenomenon known as co-tunnelling, imposes a fundamental limit on device performance. It has been predicted that it should be possible to completely suppress co-tunnelling in mechanical versions of the single-electron transistor, which would allow mechanical devices to outperform conventional single-electron transistors in many applications. However, the mechanical devices developed so far are fundamentally limited by unwanted interactions with the electrical mechanisms that are used to excite the devices. Here we show that it is possible to overcome this problem by using ultrasonic waves rather than electrical currents as the excitation mechanism, which we demonstrate at low temperatures. This is a significant step towards the development of high-performance devices.