Nanomechanical Oscillator Research Articles

Engineering error correcting dynamics in nanomechanical systems

Nanomechanical oscillators are an alternative platform for computation in harsh environments. However, external perturbations arising from such environments may hinder information processing by introducing errors into the computing system. Here, we simulate the dynamics of three coupled Duffing oscillators whose multiple equilibrium states can be used for information processing and storage. Our analysis reveals that, within experimentally relevant parameters, error correcting dynamics can emerge, wherein the system’s state is robust against random external impulses. We find that oscillators in this configuration have several surprising and attractive features, including dynamic isolation of resonators exposed to extreme impulses and the ability to correct simultaneous errors.

Studying phonon coherence with a quantum sensor

Nanomechanical oscillators offer numerous advantages for quantum technologies. Their integration with superconducting qubits shows promise for hardware-efficient quantum error-correction protocols involving superpositions of mechanical coherent states. Limitations of this approach include mechanical decoherence processes, particularly two-level system (TLS) defects, which have been widely studied using classical fields and detectors. In this manuscript, we use a superconducting qubit as a quantum sensor to perform phonon number-resolved measurements on a piezoelectrically coupled phononic crystal cavity. This enables a high-resolution study of mechanical dissipation and dephasing in coherent states of variable size (n¯≃1−10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{n}\\simeq 1-10$$\\end{document} phonons). We observe nonexponential relaxation and state size-dependent reduction of the dephasing rate, which we attribute to TLS. Using a numerical model, we reproduce the dissipation signatures (and to a lesser extent, the dephasing signatures) via emission into a small ensemble (N = 5) of rapidly dephasing TLS. Our findings comprise a detailed examination of TLS-induced phonon decoherence in the quantum regime.

Exploring regenerative coupling in phononic crystals for room temperature quantum optomechanics

Quantum technologies play a pivotal role in driving transformative advancements across diverse fields, surpassing classical approaches and empowering us to address complex challenges more effectively; however, the need for ultra-low temperatures limits the use of these technologies to particular fields. This work comes to alleviate this problem. We present a way of phononic bandgap engineering using FEM by which the radiative mechanical energy dissipation of a nanomechanical oscillator can be significantly suppressed through coupling with a complementary oscillating mode of a defect of the surrounding phononic crystal (PnC). Applied to an optomechanically coupled nanobeam resonator in the megahertz regime, we find a mechanical quality factor improvement of up to four orders of magnitude compared to conventional PnC designs. As this method is based on geometrical optimization of the PnC and frequency matching of the resonator and defect mode, it is applicable to a wide range of resonator types and frequency ranges. Taking advantage of the, hereinafter referred to as, “regenerative coupling” in phononic crystals, the presented device is capable of reaching f × Q products exceeding 10E16 Hz with only two rows of PnC shield. Thus, stable quantum states with mechanical decoherence times up to 700 μs at room temperature can be obtained, offering new opportunities for the optimization of mechanical resonator performance and advancing the room temperature quantum field across diverse applications.

Actively tunable laser action in GeSn nanomechanical oscillators.

Mechanical forces induced by high-speed oscillations provide an elegant way to dynamically alter the fundamental properties of materials such as refractive index, absorption coefficient and gain dynamics. Although the precise control of mechanical oscillation has been well developed in the past decades, the notion of dynamic mechanical forces has not been harnessed for developing tunable lasers. Here we demonstrate actively tunable mid-infrared laser action in group-IV nanomechanical oscillators with a compact form factor. A suspended GeSn cantilever nanobeam on a Si substrate is resonantly driven by radio-frequency waves. Electrically controlled mechanical oscillation induces elastic strain that periodically varies with time in the GeSn nanobeam, enabling actively tunable lasing emission at >2 μm wavelengths. By utilizing mechanical resonances in the radio frequency as a driving mechanism, this work presents wide-range mid-infrared tunable lasers with ultralow tuning power consumption.

Ultrahigh Quality Factor of a Levitated Nanomechanical Oscillator.

A levitated nanomechanical oscillator under ultrahigh vacuum is highly isolated from its environment. It has been predicted that this isolation leads to very low mechanical dissipation rates. However, a gap persists between predictions and experimental data. Here, we levitate a silica nanoparticle in a linear Paul trap at room temperature, at pressures as low as 7×10^{-11} mbar. We measure a dissipation rate of 2π×69(22) nHz, corresponding to a quality factor exceeding 10^{10}, more than 2 orders of magnitude higher than previously shown. A study of the pressure dependence of the particle's damping and heating rates provides insight into the relevant dissipation mechanisms.

Ultracoherent Nanomechanical Resonators Based on Density Phononic Crystal Engineering

Micromechanical and nanomechanical systems with exceptionally low dissipation rates are enabling the next-generation technologies of ultrasensitive detectors and quantum information systems. New techniques and methods for lowering the dissipation rate have in recent years been discovered and allowed for the engineering of mechanical oscillators with phononic modes that are extremely well isolated from the environment and thus possess quality factors close to and beyond 1×109. A powerful strategy for isolating and controlling a single phononic mode is based on phononic crystal engineering. Here we propose a new method for phononic crystal engineering of nanomechanical oscillators that is based on a periodic variation of the material density. To circumvent the introduction of additional bending losses resulting from the variation of material density, the added mass constitutes an array of nanopillars in which the losses will be diluted. Using this novel technique for phononic crystal engineering, we design and fabricate corrugated mechanical oscillators with quality factors approaching 1×109 in a room temperature environment. The flexibility space of these new phononic crystals is large and further advancement can be attained through optimized phononic crystal patterning and strain engineering via topology optimization. This will allow for the engineering of mechanical membranes with quality factors beyond 1×109 at room temperature. Such extremely low mechanical dissipation rates will enable the development of radically new technologies such as quantum-limited atomic force microscopy at room temperature, ultrasensitive detectors of dark matter, spontaneous waveform collapses, gravity, and high-efficiency quantum information transducers. Published by the American Physical Society 2024

Apparent nonlinear damping triggered by quantum fluctuations

Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or superconducting resonators, the origin of nonlinear damping is sometimes unclear. This presents a problem, as the damping rate is a key figure of merit in the application of these systems to extremely precise sensors or quantum computers. Through measurements of a superconducting resonator, we show that from the interplay of quantum fluctuations and the nonlinearity of a Josephson junction emerges a power-dependence in the resonator response which closely resembles nonlinear damping. The phenomenon can be understood and visualized through the flow of quasi-probability in phase space where it reveals itself as dephasing. Crucially, the effect is not restricted to superconducting circuits: we expect that quantum fluctuations or other sources of noise give rise to apparent nonlinear damping in systems with a similar conservative nonlinearity, such as nano-mechanical oscillators or even macroscopic systems.

Nonlinear nonlocal damping effects under magnetic loads of a ferromagnetic-viscoelastic nanotube exposed to a nonlinear elastic medium with nonlocal viscosity

This study presents innovative results on a nonlinear dynamic model of a ferromagnetic-viscoelastic nanotube (FVN) whose dissipation effects are captured by material behavior with a linear dissipation law operating in a nonlinear geometric regime. It investigates a possible system derived from a Kelvin–Voigt type dissipation model that describes internal viscoelastic damping in the form of a parallel spring and a dashpot. In addition, a class of losses by linear viscous media in local and nonlocal damping is presented in the modeling. Magnetic load effects are studied using axial rod theory regardless of rotational inertia and shear effects. The governing equation is derived by Hamilton's principle for the FVN subjected to a transverse magnetic field resting on a nonlinear elastic foundation with viscose effects. Formulas have been developed to obtain the nonlinear damping characteristics of a single-walled nanotube. Then, multiple scale method (MSM)-based solutions and Eringen elasticity theory are applied to demonstrate the aforementioned effects on a narrow clamped-clamped (CC) nanotube in detail. The approximate analytical solution is verified by numerical integration methods and a good agreement between the approximate analytical and numerical results is observed. The effect of all important parameters such as local and nonlocal viscosity damping, nonlinear damping coefficient, linear and nonlinear stiffness of the elastic medium due to changes in amplitude vibration of the magnetic field (AVMF) and displacement responses (DR) have been investigated. The original research proposed in this paper may enable the systematic study of nonlinear damping in nanomechanical oscillators, which may help to reveal the underlying physical mechanism.

Bayesian Estimation of Experimental Parameters in Stochastic Inertial Systems: Theory, Simulations, and Experiments with Objects Levitated in Vacuum

High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the interplay between acting external forces, viscous dissipation, and random driving by the thermal environment. The relevance of inertia then dictates that both position and momentum must, in principle, be known to fully describe the system, which makes its quantitative experimental characterization rather challenging. We introduce a general method of Bayesian inference of the force field and environmental parameters in stochastic inertial systems that operates solely on the time series of recorded noisy positions of the system. The method is first validated on simulated trajectories of model stochastic harmonic and anharmonic oscillators with damping. Subsequently, the method is applied to experimental trajectories of particles levitating in tailored optical fields and used to characterize the dynamics of particle motion in a nonlinear Duffing potential, a static or time-dependent double-well potential, and a nonconservative force field. The presented inference procedure does not make any simplifying assumptions about the nature or symmetry of the acting force field and provides robust results with trajectories 2 orders of magnitude shorter than those typically required by alternative inference schemes. In addition to being a powerful tool for quantitative data analysis, it can also guide experimentalists in choosing appropriate sampling frequency (at least 20 measured points per single characteristic period) and length of the measured trajectories (at least 10 periods) to estimate the force field and environmental characteristics with a desired accuracy and precision.

Nonlinear Oscillation States of Optomechanical Resonator for Reconfigurable Light‐Compatible Logic Functions

AbstractAn optomechanical scheme is reported to implement single devices combining an electromagnetic resonator with a strongly nonlinear nanomechanical oscillator in order to realize light‐controlled logic functions. In this scheme, the nonlinear mechanical oscillations, which can be well controlled by external drives, are revealed to be sensitive to incident light due to light–matter interactions enhanced by the resonator. As a result, one can adjust the initial mechanical configurations to obtain various on‐demand responses to input optical signals, and thus realize reconfigurable logic functions (NOT, XOR, OR, AND). The single optomechanical device reported here is designed to work at the terahertz (THz) frequency domain, which is the first demonstration of a THz‐compatible logic component that processes information encoded in modulated free‐space THz light, with operation rates reaching a few kilohertz. This device also can be integrated into other micro‐electromechanical systems as THz‐compatible actuators. Moreover, the optomechanical scheme proposed in this work is applicable to other frequency ranges, such as radio frequencies (RF) or the infrared.

Experimental Realization of Nonreciprocal Adiabatic Transfer of Phonons in a Dynamically Modulated Nanomechanical Topological Insulator.

High quality nanomechanical oscillators are promising platforms for quantum entanglement and quantum technology with phonons. Realizing coherent transfer of phonons between distant oscillators is a key challenge in phononic quantum information processing. Here, we report on the realization of robust unidirectional adiabatic pumping of phonons in a parametrically coupled nanomechanical system engineered as a one-dimensional phononic topological insulator. By exploiting three nearly degenerate local modes-two edge states and an interface state between them-and the dynamic modulation of their mutual couplings, we achieve nonreciprocal adiabatic transfer of phononic excitations from one edge to the other with near unit fidelity. We further demonstrate the robustness of such adiabatic transfer of phonons in the presence of various noises in the control signals. Our experiment paves the way toward nonreciprocal phonon dynamics via adiabatic pumping and is valuable for phononic quantum information processing.

High-precision multiparameter estimation of mechanical force by quantum optomechanics.

A nanomechanical oscillator can be used as a sensitive probe of a small linearized mechanical force. We propose a simple quantum optomechanical scheme using a coherent light mode in the cavity and weak short-pulsed light-matter interactions. Our main result is that if we transfer some displacement to the mechanical mode in an initialization phase, then a much weaker optomechanical interaction is enough to obtain a high-precision multiparameter estimation of the unknown force. This approach includes not only estimating the displacement caused by the force but also simultaneously observing the phase shift and squeezing of the mechanical mode. We show that the proposed scheme is robust against typical experimental imperfections and demonstrate the feasibility of our scheme using orders of magnitude weaker optomechanical interactions than in previous related works. Thus, we present a simple, robust estimation scheme requiring only very weak light-matter interactions, which could open the way to new nanomechanical sensors.

Energy Dissipation from Confined States in Nanoporous Molecular Networks.

Crystalline nanoporous molecular networks are assembled on the Ag(111) surface, where the pores confine electrons originating from the surface state of the metal. Depending on the pore sizes and their coupling, an antibonding level is shifted upward by 0.1-0.3 eV as measured by scanning tunneling microscopy. On molecular sites, a downshifted bonding state is observed, which is occupied under equilibrium conditions. Low-temperature force spectroscopy reveals energy dissipation peaks and jumps of frequency shifts at bias voltages, which are related to the confined states. The dissipation maps show delocalization on the supramolecular assembly and a weak distance dependence of the dissipation peaks. These observations indicate that two-dimensional arrays of coupled quantum dots are formed, which are quantitatively characterized by their quantum capacitances and resonant tunneling rates. Our work provides a method for studying the capacitive and dissipative response of quantum materials with nanomechanical oscillators.

Random number generation with a chaotic electromechanical resonator

Chaos enables the emergence of randomness in deterministic physical systems. Therefore it can be exploited for the conception of true random number generators mandatory in classical cryptography applications. Meanwhile, nanomechanical oscillators, at the core of many on-board functionalities such as sensing, reveal as excellent candidates to behave chaotically. This is made possible thanks to intrinsic mechanical nonlinearities emerging at the nanoscale. Here we present a platform gathering a nanomechanical oscillator and its integrated capacitive actuation. Using a modulation of the resonant force induced by the electrodes, we demonstrate chaotic dynamics and study how it depends on the dissipation of the system. The randomness of a binary sequence generated from a chaotic time trace is evaluated and discussed such that the generic parameters enabling successful random number generation can be established. This demonstration makes use of concepts which are sufficiently general to be applied to the next generation of nano-electro-optomechanical systems.

Nanomechanical cat states generated by a dc voltage-driven Cooper pair box qubit

We study a nanoelectromechanical system consisting of a Cooper pair box qubit performing nanomechanical vibrations between two bulk superconductors. We demonstrate that a bias voltage applied to the superconductors may generate states represented by entanglement between qubit states and quantum ’cat states’, i.e. a superposition of the coherent states of the nanomechanical oscillator. We characterize the formation and development of such states in terms of the corresponding Wigner function and entropy of entanglement. Also, we propose an experimentally feasible detection scheme for the effect, in which the average current that attains the specific features created by the entanglement is measured.

Amplitude stabilization in a synchronized nonlinear nanomechanical oscillator

In contrast to the well-known phenomenon of frequency stabilization in a synchronized noisy nonlinear oscillator, little is known about its amplitude stability. In this paper, we investigate experimentally and theoretically the amplitude evolution and stability of a nonlinear nanomechanical self-sustained oscillator that is synchronized with an external harmonic drive. We show that the phase difference between the tones plays a critical role on the amplitude level, and we demonstrate that in the strongly nonlinear regime, its amplitude fluctuations are reduced considerably. These findings bring to light a new facet of the synchronization phenomenon, extending its range of applications beyond the field of clock-references and suggesting a new means to enhance oscillator amplitude stability.

A High-Sensitivity Resonant Magnetic Sensor Based on Graphene Nanomechanical Resonator.

This paper presents a novel resonant magnetic sensor consisting of a graphene nanomechanical oscillator and magnetostrictive stress coupling structure, using Si/SiO2 substrate and Fe–Ga alloy, respectively. In this device, the deformation of the Fe–Ga alloy resulting from the external magnetic field changed the surface tension of the graphene, resulting in a significant change in the resonance frequency of graphene. Using the finite element analysis, it could be found that the response of the resonance frequency revealed a good linear relationship with the external magnetic field (along the x-axis) in the range of the 1 to 1.6 mT. By optimizing the sizes of each component of the magnetic sensor, such as the thickness of the Si/SiO2 substrate and the Fe–Ga alloy, and the length of the graphene, the sensitivity could even reach 834 kHz/mT, which is three orders of magnitude higher than conventional resonant magnetic devices. This provides a new method for highly sensitive and miniaturized magnetic sensors.

New Method of Chaos Generation by Using Nanomechanical Oscillator

New Method of Chaos Generation by Using Nanomechanical Oscillator

Self-sustaining MoS2 nanomechanical oscillators and feedback cooling

We report on the experimental demonstration of self-sustaining feedback oscillators referenced to ultrathin molybdenum disulfide (MoS2) nanomechanical resonators vibrating in the ∼10 to 20 MHz range. Based on comprehensive open-loop characterization of MoS2 resonators with dynamic ranges up to 85 dB, self-sustaining oscillators are constructed by incorporating the MoS2 resonators into an optoelectronic feedback circuitry. The prototyped MoS2 self-sustaining oscillators generate stable radio frequency waveforms with frequency stability (measured in Allan deviation) down to ∼2 × 10−5 and phase noise mainly limited by electronic thermal noise. Beyond self-sustaining oscillations, we demonstrate feedback cooling of thermomechanical motion of a bilayer (2L) MoS2 resonator from 300 K to 255 K by tuning the phase in the feedback, suppressing or “squashing” the noise level of the system.

Phonon-Laser Ultrasensitive Force Sensor

Developing nanomechanical oscillators for ultrasensitive force detection is very useful in exploring science. We report our achievement of ultrasensitive detection of the external force regarding the radiofrequency electric field by a nanosensor made of a single trapped ${}^{40}{\mathrm{Ca}}^{+}$ ion under injection locking, where squeezing is additionally applied to detection of the smallest force in the ion trap. The employed ion is confined stably in a surface electrode trap and works as a phonon laser that is very sensitive to the external disturbance. The injection locking drove the ion's oscillation with phase synchronization, yielding the force detection with sensitivity of 347 $\ifmmode\pm\else\textpm\fi{}50\phantom{\rule{0.2em}{0ex}}\mathrm{yN}/\sqrt{\mathrm{Hz}}$. Further with 3-dB squeezing applied on the oscillation phase variance, we achieve a successful detection of the smallest force to be $86.5\ifmmode\pm\else\textpm\fi{}70.1$ yN.