Mechanical Oscillator Research Articles

Elastic metasurfaces for Scholte-Stoneley wave control.

In this work, we investigate the dynamics of Scholte-Stoneley waves (SSWs) travelling along elastic metasurfaces, e.g. thin resonant structures embedding mechanical oscillators, placed at the interface between solid and fluid. To this purpose, an analytical dispersion law, valid in the long-wavelength regime, is derived and used to reveal the hybridization of SSWs with the collective resonance of the mechanical oscillators and the conversion of SSWs into leaky modes within the fluid. The analytical predictions are validated through numerical simulations that include both dispersive and harmonic analysis. Our findings disclose the capabilities of elastic metasurfaces in filtering, trapping and converting SSWs along fluid-solid interfaces, thus supporting the design of novel devices for solid-fluid interaction across various engineering applications, including microfluidics. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Nonclassical coincidences of atomic and mechanical excitations

Hybrid systems hold promise to provide an advantage in future quantum technology. Operating such systems outside the classical regime is crucially important to fully realize their potential. We investigate a pulsed quantum nondemolition gate between a cloud of atoms and a mechanical oscillator in distant cavities and demonstrate that this gate is capable of producing nonclassical coincidences of excitations in the disparate subsystems interacting by light. The nonclassicality is justified by evaluation of excitations created simultaneously in both modes beyond any joint classical states of such subsystems. To test the result, we use a nonclassicality witness based on available homodyne tomography of the atomic and mechanical states. Using feasible parameters, we show that it is possible to turn the pulsed dynamics of the state-of-the-art systems into nonclassical coincidences, and illustrate it for the cases of the atom-light, optomechanical, and atom-mechanical hybrid interactions. These tests are necessary to open full investigation of quantum correlations in hybrid systems. Published by the American Physical Society 2024

The role of dynamic friction in the appearance of periodic oscillations in mechanical systems

This article investigates the appearance of periodic mechanical oscillations associated with the transition between static and dynamic friction regimes. The study employs a mechanical system with one degree of freedom and a friction model recently proposed by Brown and McPhee, whose continuity and differentiability properties make it particularly appropriate for an analytical treatment of the equations. A bifurcation study of the system, including stability analysis, transformation to normal form and numerical continuation techniques, reveals that stable periodic orbits can be created either by a supercritical Hopf bifurcation or by a saddle-node bifurcation of limit cycles. The influence of all system parameters on the appearance of periodic oscillations is investigated in detail. In particular, the effect of the friction model parameters (static-to-dynamic friction ratio and transition speed between the static and dynamic regimes) on the bifurcation behavior of the system is addressed.

Investigating the nonlinear dynamics of photosensitive Belousov-Zhabotinsky gels via bifurcation analyses.

Controlling the dynamics of active stimuli-responsive smart materials is essential to replicate the biomimetic functionalities at different length scales for a variety of biological systems-based applications. Photosensitive Belousov-Zhabotinsky (BZ) gels, powered by a nonlinear chemical oscillator, called a BZ reaction are one of the stimuli-responsive smart materials in demand due to their ability to continuously transduce chemical oscillations into mechanical deformations. The chemical oscillations in a BZ reaction and subsequent mechanical oscillations in photosensitive BZ gels occur due to the redox cycle of photosensitive ruthenium complex-based catalysts. In this work, our objective is to identify how the behavior of photosensitive BZ gels can be tuned and used for biomimetic applications by investigating its dynamical characteristics using bifurcation analyses. Specifically, we use the normal form approach and perform linear and nonlinear stability analyses to identify high-order bifurcations by computing higher-order Lyapunov and frequency coefficients. We revealed the existence of domains that encompass coexisting stable and unstable limit cycles (LCs), which merge to form a semi-stable LC at the limit point of cycle (LPC). Their existence shows how a slight variation in the BZ gel recipe can significantly alter its dynamics. Subsequently, we quantify the amplitude and frequency of oscillations in different domains under the effect of variation of BZ reaction formulations. We believe that the outcomes of our work serve as an efficient template for the design and control of BZ gel-based applications. The usage of a normal form and a systematic representation of nonlinear dynamics allow our framework to be extended for other nonlinear dynamical systems.

Wilberforce-like Larmor Magnetic Moment and Spin Precession.

In a Wilberforce pendulum, two mechanical oscillators are coupled: one pertains to the longitudinal (tension) motion and the other to the rotational (twisting) motion. It is shown that the longitudinal magnetic moment of circular currents, and similarly the magnetic moment of a spin-chain, can exhibit a Wilberforce-like vibration. The longitudinal oscillation is related to the Langevin diamagnetism, while the twisting motion is superimposed on the magnetic moment and spin precession. The calculations show that the coupling term is nonlinear in this (longitudinal) vibrating and (magnetic moment) precession system. By increasing the strength of the coupling we arrive at a spectrum, where further vibrational modes can be associated with the rotation of the precession. This means that the extent of the change in coherence can be demonstrated. Since the coupling strength can be different due to local effects, this can be an important factor from the point of view of signal propagation and in preserving signal shapes. The amount specifying the dissipation is introduced to express the degree of deviation. A relationship exists between the parameter characteristic of the coupling strength and how its quantity influences decoherence and dissipation.

Optical frequency comb significantly spanned to broadband by an optomechanical resonance

An optical frequency comb, as a spectrum made of discrete and equally spaced spectral lines, is a light source with essential applications in modern technology. Cavity optomechanical systems were found to be a feasible candidate for realizing an on-chip frequency comb with low repetition rate. However, it was difficult to increase the comb line numbers of this type of frequency combs because the mechanical oscillation amplitude of such a system, which determines the frequency comb bandwidth, cannot quickly increase with pump laser power. Here, we develop a new approach to generate a broadband optomechanical frequency comb by employing a different mechanism to enhance the mechanical oscillation. Two pump tones with their frequency difference matching the mechanical frequency will drive the system into a self-organized nonlinear resonance and thus tremendously transfer the energy to the mechanical resonator. As a result, more than 10,000 or even more comb lines become available under the pump laser power of the order of milliwatts. A unique feature of the self-organized resonance is the mechanical frequency locking so that, within a certain range of the frequency difference between two drive tones, the distance between comb teeth can be locked by the two drive tones and becomes independent of any change of pump power. This property guarantees a stable repetition rate of the generated frequency comb.

Ground-state cooling of a mechanical oscillator by a noisy environment

Dissipation and the accompanying fluctuations are often seen as detrimental for quantum systems since they are associated with fast relaxation and loss of phase coherence. However, it has been proposed that a pure state can be prepared if external noise induces suitable downwards transitions, while exciting transitions are blocked. We demonstrate such a refrigeration mechanism in a cavity optomechanical system, where we prepare a mechanical oscillator in its ground state by injecting strong electromagnetic noise at frequencies around the red mechanical sideband of the cavity. The optimum cooling is reached with a noise bandwidth smaller than but on the order of the cavity decay rate. At higher bandwidths, cooling is less efficient as suitable transitions are not effectively activated. In the opposite regime where the noise bandwidth becomes comparable to the mechanical damping rate, damping follows the noise amplitude adiabatically, and the cooling is also suppressed.

High-Resolution Drift Tube Ion Mobility Spectrometer with Ultra-Fast Polarity Switching.

Besides safety and security applications, ion mobility spectrometry (IMS) is increasingly used in other fields such as medicine, environmental monitoring and food quality analysis. However, some applications require gas chromatographic separation before analysis by IMS. Furthermore, different compounds in the sample may form positive or negative ions during ionization and therefore simultaneous detection of both ion polarities is highly beneficial to avoid two chromatographic runs of the same sample. This can be achieved by ultra-fast polarity switching of a single drift tube IMS, allowing for quasi-simultaneous detection of both ion polarities. By using a ramped aperture voltage during the switching process, we overcome the issue of excessive displacement currents at the detector during polarity switching, which usually lead to overdriving the output signal of the high-gain transimpedance amplifier. Furthermore, mechanical aperture grid oscillations caused by polarity switching were also reduced through the ramped aperture voltage. This enables a polarity switching time of only 7 ms at a drift voltage of 8 kV and a drift length of 103 mm, leading to a high resolving power of RP = 117. Requiring 50 ms to acquire a pair of positive and negative spectrum, the IMS achieves an acquisition rate of 20 Hz. It reaches limits of detection of 20 pptv for dimethyl methylphosphonate and 40 pptv for methyl salicylate. For demonstration, different hop varieties were investigated and could be clearly differentiated by considering both, the positive and negative spectra.

Double-coupled slotted photonic crystal slab cavities through a high-frequency mechanical oscillator

Double-coupled slotted photonic crystal slab cavities through a high-frequency mechanical oscillator

Thermodynamic sensing of quantum nonlinear noise correlations

Abstract We put forth the concept of quantum noise sensing in nonlinear two-mode interferometers coupled to mechanical oscillators. These autonomous machines are capable of sensing quantum nonlinear correlations of two-mode noisy fields via their thermodynamic variable of extractable work, alias work capacity (WC) or ergotropy. The fields are formed by thermal noise input via its interaction with multi-level systems inside the interferometer. Such interactions amount to the generation of two-mode quantum nonlinear gauge fields that may be partly unknown. We show that by monitoring a mechanical oscillator coupled to the interferometer, one can sense the WC of one of the output field modes and thereby reveal the quantum nonlinear correlations of the field. The proposed quantum sensing method can provide an alternative to quantum multiport interferometry where the output field is unraveled by tomography. This method may advance the simulation and control of multimode quantum nonlinear gauge fields.

Identifying tinnitus in mice by tracking the motion of body markers in response to an acoustic startle.

Rodent models of tinnitus are commonly used to study its mechanisms and potential treatments. Tinnitus can be identified by changes in the gap-induced prepulse inhibition of the acoustic startle (GPIAS), most commonly by using pressure detectors to measure the whole-body startle (WBS). Unfortunately, the WBS habituates quickly, the measuring system can introduce mechanical oscillations and the response shows considerable variability. We have instead used a motion tracking system to measure the localized motion of small reflective markers in response to an acoustic startle reflex in guinea pigs and mice. For guinea pigs, the pinna had the largest responses both in terms of displacement between pairs of markers and in terms of the speed of the reflex movement. Smaller, but still reliable responses were observed with markers on the thorax, abdomen and back. The peak speed of the pinna reflex was the most sensitive measure for calculating GPIAS in the guinea pig. Recording the pinna reflex in mice proved impractical due to removal of the markers during grooming. However, recordings from their back and tail allowed us to measure the peak speed and the twitch amplitude (area under curve) of reflex responses and both analysis methods showed robust GPIAS. When mice were administered high doses of sodium salicylate, which induces tinnitus in humans, there was a significant reduction in GPIAS, consistent with the presence of tinnitus. Thus, measurement of the peak speed or twitch amplitude of pinna, back and tail markers provides a reliable assessment of tinnitus in rodents.

Dual-driving parametric locking of GHz phonon sources to sub-hertz linewidth in optomechanical systems

In the exploration of collective dynamics and advanced information processing, synchronization and frequency locking of mechanical oscillations are cornerstone phenomena. Traditional synchronization techniques, which typically involve a single mechanical mode, are limited by their inability to distinguish between intrinsic mechanical oscillations and external signals after locking. Addressing this challenge, we introduce a parametric approach that enables simultaneous frequency locking of two gigahertz mechanical modes within an optomechanical crystal cavity. By modulating the pump light to match the sum and difference frequencies of the mechanical modes, we significantly narrow their linewidths from tens of kilohertz to below 1 Hz at room temperature and ambient pressure. This dual-locking scheme also drastically reduces the phase noise of the mechanical modes by 76.6 dBc/Hz at a 100 Hz offset, while allowing flexible tuning of the locked modes’ frequencies via input signal adjustments. Our method not only facilitates direct observation of mechanical oscillations under the locking regime but also enriches the understanding of coherent phonons in multimode regimes, opening new avenues for optomechanical applications in signal processing.

Correlated qubit coherences stimulated by thermal energy

Abstract Quantum coherence, the ability of a system to be in a quantum superposition of pure states, is a distinct feature of quantum mechanics that has no direct analog in classical mechanics. Quantum states that possess coherence efficiently outperform their classical counterparts in fundamental science and practical applications, including quantum metrology, computation, and simulation. Generation of coherence without the need to employ strong classical drives remains a challenging and not yet experimentally explored task. Beyond individual thermally-induced coherences already proposed for different experiments, correlated quantum coherences of multiple qubits represent a new target. We prove that correlated qubit coherence emerges thermally stimulated from incoherent states in hybrid superconducting and solid-state systems comprising non-interacting qubits coupled only via Dicke-type interaction to a shared thermal mechanical oscillator, exhibits coherences beyond the Tavis–Cummings coupling and, moreover, can be advantageous in quantum sensing.

Compact inertial sensors for measuring external disturbances of physics experiments

Compact, high-precision inertial sensors are needed in the control schemes of many modern physics experiments to isolate them from disturbances caused by seismic motion. We present an inertial sensor whose mechanical oscillator fits on a one-inch diameter optic. The oscillators achieve a mechanical Quality factor of a fundamental oscillation mode of 600,000 and a resonance frequency of 50 Hz, giving them a suspension thermal noise floor lower than all commercially available inertial sensors. The motion of this fundamental mode is suitable to encode inertial motion into the sensor readout. The oscillator is combined with an optical resonator readout scheme that achieves a displacement noise of 100 fm/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext{Hz}}$$\\end{document} above 0.2 Hz. We validate the sensors’ noise floor using a huddle test. Below 20 Hz, the sensor offers comparable performance to the best inertial sensors available today while being a fraction of the size. Above 20 Hz, the sensor is, to the author’s knowledge, the best demonstrated in the literature to date for such a sensor, with a self-noise floor of 0.1 ng/Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\ ext{Hz}}$$\\end{document}. The excellent performance of the sensors across seismically relevant frequencies, vacuum compatibility, and compact size make it a prime candidate for integration into sophisticated seismic isolation schemes, such as those used by gravitational wave detectors.

Coherent coupling and non-destructive measurement of trapped-ion mechanical oscillators

Coherent coupling and non-destructive measurement of trapped-ion mechanical oscillators

Observation of a phase transition from a continuous to a discrete time crystal

Discrete (DTCs) and continuous time crystals (CTCs) are novel dynamical many-body states, that are characterized by robust self-sustained oscillations, emerging via spontaneous breaking of discrete or continuous time translation symmetry. DTCs are periodically driven systems that oscillate with a subharmonic of the external drive, while CTCs are continuously driven and oscillate with a frequency intrinsic to the system. Here, we explore a phase transition from a continuous time crystal to a discrete time crystal. A CTC with a characteristic oscillation frequency ωCTC is prepared in a continuously pumped atom-cavity system. Modulating the pump intensity of the CTC with a frequency ωdr close to 2ωCTC leads to robust locking of ωCTC to ωdr/2 , and hence a DTC arises. This phase transition in a quantum many-body system is related to subharmonic injection locking of non-linear mechanical and electronic oscillators or lasers.

Thermo-mechanical investigation of a friction oscillator under high-frequency excitation

The frictional behavior, temperature evolution, and system dynamics in tribological systems are closely coupled. However, in many cases, at least one of the mentioned phenomena is neglected or not modeled consistently. This paper presents a model of a thermo-mechanically coupled oscillator, where the reduction of friction force due to high-frequency excitation is analyzed. The oscillator’s equation of motion, the impulse balance, and the heat equation for the thermo-mechanical continuum are evaluated so that a set of nonlinear equations describes the coupled system. Using specific mathematical procedures like Laplace-transformation and a particular transformation ansatz for integral equations, the system can be transformed into a set of ordinary differential equations, enabling efficient simulation. Based on this equation set, an averaging method is applied to eliminate the fast time scale of the mechanical oscillation due to high-frequency excitation so that only the averaged influence of the motion goes into the heat evolution. This procedure leads to concise expressions to determine the stationary state of the system, and the quantities of interest can be calculated conveniently. These equations yield parameter combinations where the friction force can be reduced due to the high-frequency excitation, even though thermal expansion is considered. However, there are also parameter regions where the excitation yields a significantly larger friction force.

Design of a Two-Degree-of-Freedom Mechanical Oscillator for Multidirectional Vibration Energy Harvesting to Power Wireless Sensor Nodes.

Converting otherwise wasted kinetic energy present in the environment into usable electrical energy to power wireless sensor nodes, is a green strategy to avoid the use of batteries and wires. Most of the energy harvesters presented in the literature are based on the exploitation of a one-degree-of-freedom arrangement, consisting of a tuned spring-mass system oscillating in the main direction of the exciting vibration source. However, if the direction of excitation changes, the efficiency of the harvester decreases. This paper thus proposes the idea of a curved cantilever beam with a two-degree-of-freedom arrangement, where the two bending natural frequencies of the mechanical resonator are designed to be equal. This is thought to lead to a configuration design that can be used in practical circumstances where excitation varies its direction in the plane. This, in turn, may possibly lead to a more effective energy-harvesting solution to power nodes in a wireless sensor network.

Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - [formula omitted] chain

It is known that for the Heisenberg XXZ spin - 12 chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.

Solar-Powered Molecular Crystal Motor Based on an Anthracene-Thiazolidinedione Photoisomerization Reaction.

Assembling molecular machines into crystals provides a way to harness their power on large length scales, but the development of a crystal analogue to a molecular motor remains a challenge. The molecule (Z)-5-(anthracen-9-ylmethylene)-3-butylthiazolidine-2,4-dione (C4-ATD) has E and Z isomers with strongly overlapping absorption spectra. This spectroscopic property allows both Z → E and E → Z photoisomerization reactions to be driven by a single light source, and simulations indicate this property can provide a route to robust oscillatory motion. Reprecipitation in an aqueous surfactant enables the growth of single crystal microwires that exhibit continuous mechanical oscillations under a wide range of illumination conditions, including ambient solar irradiation. Molecular crystal motors provide a new approach for transforming continuous light into oscillatory mechanical motion.