Nanomechanical Resonators Research Articles

THE CARBON NANOTUBE-EMBEDDED BOUNDARY LAYER THEORY FOR ENERGY HARVESTING

Single-walled carbon nanotubes (SWNTs) and multi-walled nanotubes (MWNTs) are gaining appeal in mechanical engineering and industrial applications due to their direct influence on enhancing the thermal conductivity of base fluids. With such intriguing properties of carbon nanotubes in mind, our goal in this work is to investigate radiation effects on the flow of carbon nanotube suspended nanofluids in the presence of a magnetic field past a stretched sheet impacted by slip state. CNTs flow and heat transmission are frequently modelled in practice using nonlinear differential equation systems. This system has been precisely solved, and an accurate analytical expression for the fluid velocity in terms of an exponential function has been derived, while the temperature distribution is stated in terms of a confluent hypergeometric function. The impact of the radiation parameter, slip parameter, sloid volume fraction, magnetic parameter, Eckart and Prandtl numbers on the velocity, temperature, and heat transfer rate profiles are demonstrated using a parametric analysis. When compared to the two types of nanoparticles (Cooper and Silver) in earlier published articles, temperature profiles for single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs) are revealed to be particularly sensitive to radiation, solid volume fraction, and slip parameters. Nanomechanical gears, nanosensors, nanocomposite materials, resonators, and thermal materials are only a few of the present problem's technical applications.

Mechanical dissipation by substrate–mode coupling in SiN resonators

State-of-the-art nanomechanical resonators are heralded as a central component for next-generation clocks, filters, resonant sensors, and quantum technologies. To practically build these technologies will require monolithic integration of microchips, resonators, and readout systems. While it is widely seen that mounting microchip substrates into a system can greatly impact the performance of high-Q resonators, a systematic study has remained elusive, owing to the variety of physical processes and factors that influence the dissipation. Here, we analytically analyze a mechanism by which substrates couple to resonators manufactured on them and experimentally demonstrate that this coupling can increase the mechanical dissipation of nanomechanical resonators when resonance frequencies of resonator and substrate coincide. More generally, we then show that a similar coupling mechanism can exist between two adjacent resonators. Since the substrate–mode coupling mechanism strongly depends on both the resonator position on the substrate and the mounting of the substrate, this work provides key design guidelines for high-precision nanomechanical technologies.

Optoelectrical Nanomechanical Resonators Made from Multilayered Two-Dimensional Materials

Studies involving nanomechanical motion have evolved from the detection and understanding of its fundamental aspects to its promising practical utility as an integral component of hybrid systems. The nanomechanical resonators’ indispensable role as transducers between optical and microwave fields in hybrid systems, such as quantum communications interfaces, have elevated their importance in recent years. It is therefore crucial to determine which among the family of nanomechanical resonators is more suitable for this role. Most of the studies revolve around nanomechanical resonators of ultrathin structures because of their inherently large mechanical amplitude due to their very low mass. Here, we argue that the underutilized nanomechanical resonators made from multilayered two-dimensional (2D) materials are the better fit for this role because of their comparable electrostatic tunability and potential for larger optomechanical responsivity. To show this, we first demonstrate the electrostatic tunability of mechanical modes of a multilayered nanomechanical resonator made from graphite. We also show that the optimal values of optomechanical responsivities are obtained for multilayered devices, particularly when the Fabry–Perot gap is close to half the detection wavelength. Finally, by using the multilayered model and comparing this device with the reported ones, we find that the electrostatic tunability of devices of intermediate thickness is not significantly lower than that of ultrathin ones. Together with the practicality in terms of fabrication ease and design predictability, we contend that multilayered 2D nanomechanical resonators are the optimal choice for the electromagnetic interface in integrated quantum systems.

Properly-tuned continuum and atomistic models for vibrational analysis of the silicon nanoplates

The high computational costs of atomistic simulations for the investigation of nanostructures, despite their accuracy, necessitate efforts to develop efficient continuum models. Since the classical continuum mechanics assume the matter as continuous and ignore the size dependency of material properties, these theories fail to capture the behavior of materials at the nanoscale. Size-dependencies of nanostructures could result in the emergence of surface effects. This paper, for the first time, aims to develop and tune surface-enhanced continuum models to predict the vibrational properties of nanoplates which are inherently discrete at the nanoscale. Regarding this aim, we use a composite core-shell modeling scheme for integrating Kirchhoff and Mindlin plate theories with the surface effects. We have performed Molecular Dynamics (MD) simulations to determine the accurate vibrational behavior of silicon nanoplates. We present a systematic procedure for obtaining continuum model parameters, including the surface elastic parameters and surface-induced stress, from our MD simulation results. In doing so, this simulation method benefits from the merits of both continuum- and atomistic-based modeling. We further examine the validity of the developed continuum models by comparing the results achieved using calibrated continuum models and the validation set of MD results. It is demonstrated that properly tuned continuum models, especially the Mindlin plate theory with surface effects, can accurately predict the vibrational behavior of ultrathin Si nanoplates. Furthermore, our calibrated continuum models based on the Mindlin plate theory offer an effective tool for capturing higher natural frequencies of Si nanoplates, introducing new paradigms in nanomechanical resonators.

On-Chip Microwave Frequency Combs in a Superconducting Nanoelectromechanical Device.

Nanomechanical resonances coupled to microwave cavities can be excited, measured, and controlled simultaneously using electromechanical back-action phenomena. Examples of these effects include sideband cooling and amplification, which are commonly described through linear equations of motion governed by an effective optomechanical Hamiltonian. However, this linear approximation is invalid when the pump-induced cavity microwave field is large enough to trigger optomechanical nonlinearities, resulting in phenomena like frequency combs. Here, we employ a niobium-based superconducting electromechanical device to explore the generation of microwave frequency combs. We observe the formation of combs around a microwave resonant frequency (3.78 GHz) with 8-MHz frequency spacing, equal to the mechanical resonant frequency. We investigate their dynamics for different optomechanical parameters, including detuning, pump powers, and cavity decay rates. Our experimental results show excellent agreement with numerical modeling. These electromechanical frequency combs can be beneficial in nanomechanical sensing applications that require precise electrical tracking of mechanical resonant frequencies.

Nanomechanical probing and strain tuning of the Curie temperature in suspended Cr2Ge2Te6-based heterostructures

Two-dimensional magnetic materials with strong magnetostriction are attractive systems for realizing strain-tuning of the magnetization in spintronic and nanomagnetic devices. This requires an understanding of the magneto-mechanical coupling in these materials. In this work, we suspend thin Cr2Ge2Te6 layers and their heterostructures, creating ferromagnetic nanomechanical membrane resonators. We probe their mechanical and magnetic properties as a function of temperature and strain by observing magneto-elastic signatures in the temperature-dependent resonance frequency near the Curie temperature, TC. We compensate for the negative thermal expansion coefficient of Cr2Ge2Te6 by fabricating heterostructures with thin layers of WSe2 and antiferromagnetic FePS3, which have positive thermal expansion coefficients. Thus we demonstrate the possibility of probing multiple magnetic phase transitions in a single heterostructure. Finally, we demonstrate a strain-induced enhancement of TC in a suspended Cr2Ge2Te6-based heterostructure by 2.5 ± 0.6 K by applying a strain of 0.026% via electrostatic force.

Acute entanglement and Photon/Phonons statistics in a balanced/unbalanced [formula omitted]-symmetry systems

We study the significance of Photon/Phonons bunching and antibunching on the dynamics of the quantum entanglement in the presence of coupled PT-symmetry systems with balanced/unbalanced gain and loss. We suggest a hybrid electromechanical system to realize a strong and tunable coupling between a Coplanar-Waveguide (CPW) microwave cavity and a nanomechanical resonator (NAMR) via a superconducting Transmon qubit. The hybrid electromechanical system consists of a non-hermitian Hamiltonian with balanced/unbalanced gain and loss. The interplay between the quantum entanglement and the PT-symmetry systems is also thoroughly investigated. We frame a connection between Number operators, Photon/Phonons antibunching, and entanglement. It has been observed that the relative Photon/Phonons numbers play a key role in the quantum entanglement dynamics. Furthermore, we study that quantum entanglement can be characterized by defining a Photon/Phonons antibunching. The Photon/Phonons antibunching is strongly dependent on the initial squeezed state and the rate of balanced/unbalanced gain and loss of the system.

Hierarchical tensile structures with ultralow mechanical dissipation

Structural hierarchy is found in myriad biological systems and has improved man-made structures ranging from the Eiffel tower to optical cavities. In mechanical resonators whose rigidity is provided by static tension, structural hierarchy can reduce the dissipation of the fundamental mode to ultralow levels due to an unconventional form of soft clamping. Here, we apply hierarchical design to silicon nitride nanomechanical resonators and realize binary tree-shaped resonators with room temperature quality factors as high as 7.8 × 108 at 107 kHz frequency (1.1 × 109 at T = 6 K). The resonators’ thermal-noise-limited force sensitivities reach 740 zN/Hz1/2 at room temperature and 90 zN/Hz1/2 at 6 K, surpassing state-of-the-art cantilevers currently used for force microscopy. Moreover, we demonstrate hierarchically structured, ultralow dissipation membranes suitable for interferometric position measurements in Fabry-Pérot cavities. Hierarchical nanomechanical resonators open new avenues in force sensing, signal transduction and quantum optomechanics, where low dissipation is paramount and operation with the fundamental mode is often advantageous.

Measurement-based preparation of multimode mechanical states.

Nanomechanical resonators are a key tool for future quantum technologies, such as quantum force sensors and interfaces, and for studies of macroscopic quantum physics. The ability to prepare room temperature nonclassical states is a major outstanding challenge. It has been suggested that this could be achieved using a fast continuous measurement to break the usual symmetry between position and momentum. Here, we demonstrate this symmetry breaking and use it to prepare a thermally squeezed mechanical state. Our experiments take advantage of collective measurements on multiple mechanical modes, which we show can increase the measurement speed and improve state preparation. Theoretically, we show that this result extends to the quantum regime, relaxing the requirements to generate nonclassical states. We predict that multimode conditioning can enable room temperature quantum squeezing with existing technology. Our work paves the way toward room temperature quantum nanomechanical devices and toward their application in quantum technology and fundamental science.

Highly sensitive vibration measurement method of nanomechanical resonators using a convolutional neural network

Nanomechanical resonators can detect various small physical quantities. It is necessary to increase the sensitivity of nanomechanical resonators. In this study, a deep learning-based method is developed for sensitive detection of vibration states of nanomechanical resonators. It enables one to explore the most highly sensitive vibration states without missing targets while conventional methods focus only on the resonant frequency. The proposed method was evaluated with laser intensity. Sensitive measurement of laser intensity has the potential for applications in laser wavelength measurement. The proposed method could identify laser intensity at intervals of 0.03 mW at which the resonance frequency did not shift. Grad-CAM was used to clarify features on the vibration spectra used in the convolutional neural network. Frequency bands other than the resonance frequency band were used for the laser intensity measurement. This result implies that there is a possibility that highly sensitive vibration behavior exists outside the resonance frequency.

Determining Young's modulus via the eigenmode spectrum of a nanomechanical string resonator

We present a method for the in-situ determination of Young's modulus of a nanomechanical string resonator subjected to tensile stress. It relies on measuring a large number of harmonic eigenmodes and allows to access Young's modulus even for the case of a stress-dominated frequency response. We use the proposed framework to obtain the Young's modulus of four different wafer materials, comprising the three different material platforms amorphous silicon nitride, crystalline silicon carbide and crystalline indium gallium phosphide. The resulting values are compared with theoretical and literature values where available, revealing the need to measure Young's modulus on the sample material under investigation for precise device characterization.

Surface acoustic wave coupling between micromechanical resonators

The coupling of micro- or nanomechanical resonators via a shared substrate is intensively exploited to built systems for fundamental studies and practical applications. So far, the focus has been on devices operating in the kHz regime with a spring-like coupling. At resonance frequencies above several 10 MHz, wave propagation in the solid substrate becomes relevant. The resonators act as sources for surface acoustic waves (SAWs), and it is unknown how this affects the coupling between them. Here, we present a model for MHz frequency resonators interacting by SAWs, which agrees well with finite element method simulations and recent experiments of coupled micro-pillars. In contrast to the well-known strain-induced spring-like coupling, the coupling via SAWs is not only dispersive but also dissipative. This can be exploited to realize high quality phonon cavities, an alternative to acoustic radiation shielding by, e.g. phononic crystals.

Phonon transport in the gigahertz to terahertz range: Confinement, topology, and second sound

Transport of heat and hypersound with gigahertz (GHz) to terahertz (THz) phonons is crucial for heat management in electronics, mediating signal processing with microwave radiation, thermoelectrics, and various types of sensors based on nanomechanical resonators. Efficient control of heat and sound transport requires new materials, novel experimental techniques, and a detailed knowledge of the interaction of phonons with other elementary excitations. Wave-like heat transport, also known as second sound, has recently attracted renewed attention since it provides several opportunities for overcoming some of the limitations imposed by diffusive transport (Fourier’s regime). The frequency-domain detection of GHz-to-THz phonons can be carried out in a remote, non-destructive, and all-optical manner. The ongoing development of nanodevices and metamaterials made of low-dimensional nanostructures will require spatially resolved, time-resolved, and anisotropic measurements of phonon-related properties. These tasks can be accomplished with Brillouin light scattering (BLS) and various newly developed variants of this method, such as pumped-BLS. In the near future, pumped-BLS is expected to become useful for characterizing GHz topological nanophononics. Finally, second-sound phenomena can be observed with all-optical methods like frequency-domain thermoreflectance.

Frequency Scaling, Elastic Transition, and Broad-Range Frequency Tuning in WSe2Nanomechanical Resonators

Nanomechanical resonators based on atomic layers of tungsten diselenide (WSe2) offer intriguing prospects for enabling novel sensing and signal processing functions. The frequency scaling law of such resonant devices is critical for designing and realizing these high-frequency circuit components. Here, we elucidate the frequency scaling law for WSe2 nanomechanical resonators by studying devices of one-, two-, three-, to more than 100-layer thicknesses and different diameters. We observe resonant responses in both mechanical limits and clear elastic transition in between, revealing intrinsic material properties and devices parameters such as Young's modulus and pretension. We further demonstrate a broad frequency tuning range (up to 230%) with a high tuning efficiency (up to 23% V-1). Such tuning efficiency is among the highest in resonators based on two-dimensional (2D) layered materials. Our findings can offer important guidelines for designing high-frequency WSe2 resonant devices.

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.

Controllable Phononic Low-Pass Filter via Optomechanical Interactions

We present an experimental demonstration of an optically controllable phononic low-pass filter in a multimode optomechanical system. By coupling two spatially separated nanomechanical resonators via optomechanical interactions, the phononic signal below a cutoff frequency can be transferred between mechanical resonators, while the signal above the cutoff frequency is attenuated, which resembles an electronic low-pass filter. Moreover, the cutoff frequency is controllable by tuning the optomechanical interaction via the intracavity field. Our results provide an essential element in phononic circuits and have potential applications for information processing in hybrid quantum systems.

Multi-outlet single photon quantum router between optics and microwave based on a hybrid optomechanical system

A Multi-outlet single photon quantum router between microwave and optical frequency domain is investigated in a system consisting of a superconducting microwave cavity and an optical nanomechanical cavity coupled to a commom nanomechanical resonator (NAMR). It is demonstration that the single-photon of optical frequency can be routed into three different output ports by adjusting microwave power. More importantly, the two output signals can be selected according to microwave power. Meanwhile, we also show that thermal noise will be insignificant for the optical performance of the single-photon router at temperature of the order of 20 mK. Our proposal may have paved a new avenue towards multi-channel router and quantum network.

Quantum state preparation and tomography of entangled mechanical resonators.

Precisely engineered mechanical oscillators keep time, filter signals and sense motion, making them an indispensable part of the technological landscape of today. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors1-3. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout4,5, phonon number resolution6,7 and phonon-mediated qubit-qubit interactions8,9. At present, these acoustic platforms lack processors capable of controlling the quantum states of several mechanical oscillators with a single qubit and the rapid quantum non-demolition measurements of mechanical states needed for error correction. Here we use a superconducting qubit to control and read out the quantum state of a pair of nanomechanical resonators. Our device is capable of fast qubit-mechanics swap operations, which we use to deterministically manipulate the mechanical states. By placing the qubit into the strong dispersive regime with both mechanical resonators simultaneously, we determine the phonon number distributions of the resonators by means of Ramsey measurements. Finally, we present quantum tomography of the prepared nonclassical and entangled mechanical states. Our result represents a concrete step towards feedback-based operation of a quantum acoustic processor.

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.

Manipulation of the topology and solid-state spin using a mechanic-based hybrid system

In this paper, a three-body hybrid quantum system with the solid-state spin and topological qubit both mediated by a torsional nanomechanical resonator (NMR) is built by taking advantage of two different coupling mechanisms, the so-called strain and the magnetism, respectively. Two basic quantum manipulation (QM) schemes with respect to the quantum interface for arbitrary-state transfer and two-qubit Mølmer–Sørensen (MS) gate are also studied here. Then the efficiency for both QM processes is also systematically estimated, even under the influence of all kinds of adverse factors such as dissipation, decoherence and dephasing. This work may provide an extensible route towards a wider range of applications in quantum manipulation.