A multimode electromechanical parametric resonator array

Proliferation of unstable states and their impact on stochastic out-of-equilibrium dynamics in two coupled Kerr parametric oscillators

Networks of nonlinear parametric resonators are promising candidates as Ising machines for annealing and optimization. These many-body out-of-equilibrium systems host complex phase diagrams of coexisting stationary states. The plethora of states manifest via a series of bifurcations, including bifurcations that proliferate purely unstable solutions. Here we demonstrate that the latter take a fundamental role in the stochastic dynamics of the system. Specifically, they determine the switching paths and the switching rates between stable solutions. We demonstrate experimentally the impact of the added unstable states on noise-activated switching dynamics in a network of two coupled parametric resonators.

Dynamical response and noise limit of a parametrically pumped microcantilever sensor in a Phase-Locked Loop

We investigate the response of a digitally controlled and parametrically pumped microcantilever used for sensing in a Phase-Locked Loop (PLL). We develop an analytical model for its dynamical response and obtain an explicit dependence on the rheological parameters of the surrounding viscous medium. Linearization of this model allows to find improved responsivity to density variations in the case of parametric suppression. Experiments with a commercial microcantilever validate the model, but also reveal an increase of frequency noise in the PLL associated with the parametric gain and phase, which, in most cases, restricts the attainable limit of detection. The noise in open-loop is studied by measuring the random fluctuations of the noise-driven deflection of the microcantilever, and a model for the power spectral density of amplitude, phase and frequency noises is discussed and used to explain the frequency fluctuations in the closed-loop PLL. This work concludes that parametric pumping in a PLL does not improve the sensing performance in applications requiring detecting frequency shifts.

Mechanical memory operations in piezotransistive GaN microcantilevers using Au nanoparticle-enhanced photoacoustic excitation

Nonlinear oscillations in micro- and nanoelectromechanical systems have emerged as an exciting research area in recent years due to their promise in realizing low-power, scalable, and reconfigurable mechanical memory and logic devices. Here, we report ultralow-power mechanical memory operations utilizing the nonlinear oscillation regime of GaN microcantilevers with embedded piezotransistive AlGaN/GaN heterostructure field effect transistors as highly sensitive deflection transducers. Switching between the high and low oscillatory states of the nonlinear oscillation regime was demonstrated using a novel phase-controlled opto-mechanical excitation setup, utilizing a piezo actuator and a pulsed laser as the primary and secondary excitation sources, respectively. Laser-based photoacoustic excitation was amplified through plasmonic absorption in Au nanoparticles deposited on a transistor. Thus, the minimum switching energy required for reliable memory operations was reduced to less than a picojoule (pJ), which translates to one of the lowest ever reported, when normalized for mass.

Controllable multichannel acousto-optic modulator and frequency synthesizer enabled by nonlinear MEMS resonator

Nonlinear physics-based harmonic generators and modulators are critical signal processing technologies for optical and electrical communication. However, most optical modulators lack multi-channel functionality while frequency synthesizers have deficient control of output tones, and they additionally require vacuum, complicated setup, and high-power configurations. Here, we report a piezoelectrically actuated nonlinear Microelectromechanical System (MEMS) based Single-Input-Multiple-Output multi-domain signal processing unit that can simultaneously generate programmable parallel information channels (> 100) in both frequency and spatial domain. This significant number is achieved through the combined electromechanical and material nonlinearity of the Lead Zirconate Titanate thin film while still operating the device in an ambient environment at Complementary-Metal-Oxide-Semiconductor compatible voltages. By electrically detuning the operation point along the nonlinear regime of the resonator, the number of electrical and light-matter interaction signals generated based on higher-order non-Eigen modes can be controlled meticulously. This tunable multichannel generation enabled microdevice is a potential candidate for a wide variety of applications ranging from Radio Frequency communication to quantum photonics with an attractive MEMS-photonics monolithic integration ability.

Classical Many-Body Time Crystals

Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a many-body state, alongside several experimental realizations. In this work, we provide a simple and pedagogical framework by which to obtain many-body time crystals using parametrically coupled resonators. In our analysis, we use classical period-doubling bifurcation theory and present a clear distinction between single-mode time-translation symmetry breaking and a situation where an extensive number of degrees of freedom undergo the transition. We experimentally demonstrate this paradigm using coupled mechanical oscillators, thus providing a clear route for time crystal realizations in real materials.

Absolute Deflection Measurements in a Micro- and Nano-Electromechanical Fabry-Perot Interferometry System

Fabry-Perot laser interferometry is a common laboratory technique used to interrogate resonant micro- and nano-electromechanical systems (MEMS/NEMS). This method uses the substrate beneath a vibrating MEMS/NEMS device as a static reference mirror, encoding relative device motion in the reflected laser power. In this work, we present a general approach for calibrating these optical systems based on measurements of large-amplitude motion that exceeds one half of the laser wavelength. Utilizing the intrinsic nonlinearity of the optical transduction, our method enables the direct measurement of the system's transfer function (motion-to-detected-voltage). We experimentally demonstrate the use of this technique to measure vibration amplitudes and changes in the equilibrium position of a MEMS/NEMS device using monolithic silicon nitride and silicon cantilevers as sample systems. By scanning the laser along a cantilever surface, we spatially map static and dynamic deflection profiles simultaneously, and then compare the static profile against results from a commercial optical profilometer. We further demonstrate extension of our calibration technique to measurements taken at small amplitudes, where the optical transduction is linear, and to those taken in the frequency domain by a lock-in amplifier. Our aim is to present a robust calibration scheme that is independent of MEMS/NEMS materials and geometry, to completely negate the effects of nonlinear optical transduction, and to enable the assessment of excitation forces and MEMS/NEMS material properties through the accurate measurement of the MEMS/NEMS vibrational response.

Opto-thermally excited multimode parametric resonance in graphene membranes

In the field of nanomechanics, parametric excitations are of interest since they can greatly enhance sensing capabilities and eliminate cross-talk. Above a certain threshold of the parametric pump, the mechanical resonator can be brought into parametric resonance. Here we demonstrate parametric resonance of suspended single-layer graphene membranes by an efficient opto-thermal drive that modulates the intrinsic spring constant. With a large amplitude of the optical drive, a record number of 14 mechanical modes can be brought into parametric resonance by modulating a single parameter: the pre-tension. A detailed analysis of the parametric resonance allows us to study nonlinear dynamics and the loss tangent of graphene resonators. It is found that nonlinear damping, of the van der Pol type, is essential to describe the high amplitude parametric resonance response in atomically thin membranes.

Broadband reconfigurable logic gates in phonon waveguides

The high-quality-factor mechanical resonator in electromechanical systems has facilitated dynamic control of phonons via parametric nonlinear processes and paved the development of mechanical logic-elements. However, the narrow spectral bandwidth of the resonating element constrains the available nonlinear phenomena thus limiting the functionality of the device as well as the switching speeds. Here we have developed phonon waveguides, with a two-octave-wide phonon transmission band, in which mechanical four-wave-like mixing is demonstrated that enables the frequency of phonon waves to be converted over 1 MHz. We harness this platform to execute multiple binary mechanical logic gates in parallel, via frequency division multiplexing in this broadband, where each gate can be independently reconfigured. The fidelity of the binary gates is verified via temporal measurements yielding eye diagrams which confirm the availability of high speed logic operations. The phonon waveguide architecture thus offers the broadband functionality that is essential to realising mechanical signal processors.

Tunable nanoelectromechanical resonator for logic computations

There has been remarkable interest in nanomechanical computing elements that can potentially lead to a new era in computation due to their re-configurability, high integration density, and high switching speed. Here we present a nanomechanical device capable of dynamically performing logic operations (NOR, NOT, XNOR, XOR, and AND). The concept is based on the active tuning of the resonance frequency of a doubly-clamped nanoelectromechanical beam resonator through electro-thermal actuation. The performance of this re-configurable logic device is examined at elevated temperatures, ranging from 25 °C to 85 °C, demonstrating its resilience for most of the logic operations. The proposed device can potentially achieve switching rate in μs, switching energy in nJ, and an integration density up to 10⁶ per cm². The practical realization of this re-configurable device paves the way for nano-element-based mechanical computing.

Parametric Symmetry Breaking in a Nonlinear Resonator

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far-from-equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work unveils that the double hysteresis is a manifestation of an out-of-equilibrium symmetry breaking between parametric phase states. Such a fundamental phenomenon, in the most ubiquitous building block of nature, paves the way for the investigation of new dynamical phases of matter in parametrically driven many-body systems and motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

Microelectromechanical reprogrammable logic device

In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme.

High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions

Simultaneously measuring multiple eigenmode frequencies of nanomechanical resonators can determine the position and mass of surface-adsorbed proteins, and could ultimately reveal the mass tomography of nanoscale analytes. However, existing measurement techniques are slow (<1 Hz bandwidth), limiting throughput and preventing use with resonators generating fast transient signals. Here we develop a general platform for independently and simultaneously oscillating multiple modes of mechanical resonators, enabling frequency measurements that can precisely track fast transient signals within a user-defined bandwidth that exceeds 500 Hz. We use this enhanced bandwidth to resolve signals from multiple nanoparticles flowing simultaneously through a suspended nanochannel resonator and show that four resonant modes are sufficient for determining their individual position and mass with an accuracy near 150 nm and 40 attograms throughout their 150-ms transit. We envision that our method can be readily extended to other systems to increase bandwidth, number of modes, or number of resonators.

Parallel Transduction of Nanomechanical Motion Using Plasmonic Resonators

We demonstrate parallel transduction of thermally driven mechanical motion of an array of gold-coated silicon nitride nanomechanical beams, by using near-field confinement in plasmonic metal-insulator-metal resonators supported in the gap between the gold layers. The free-space optical readout, enabled by the plasmonic resonances, allows for addressing multiple mechanical resonators in a single measurement. Light absorbed in the metal layer of the beams modifies their mechanical properties, allowing photothermal tuning of the eigenfrequencies. The appearance of photothermally driven parametric amplification indicates the possibility of plasmonic mechanical actuation.