Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution

Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution

Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.

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.

Centimeter-scale nanomechanical resonators with low dissipation

High-aspect-ratio mechanical resonators are pivotal in precision sensing, from macroscopic gravitational wave detectors to nanoscale acoustics. However, fabrication challenges and high computational costs have limited the length-to-thickness ratio of these devices, leaving a largely unexplored regime in nano-engineering. We present nanomechanical resonators that extend centimeters in length yet retain nanometer thickness. We explore this expanded design space using an optimization approach which judiciously employs fast millimeter-scale simulations to steer the more computationally intensive centimeter-scale design optimization. By employing delicate nanofabrication techniques, our approach ensures high-yield realization, experimentally confirming room-temperature quality factors close to theoretical predictions. The synergy between nanofabrication, design optimization guided by machine learning, and precision engineering opens a solid-state path to room-temperature quality factors approaching 10 billion at kilohertz mechanical frequencies - comparable to the performance of leading cryogenic resonators and levitated nanospheres, even under significantly less stringent temperature and vacuum conditions.

Ultrasensitive optomechanical strain sensor

We demonstrate an ultrasensitive optomechanical strain sensor based on a SiN membrane and a Fabry-Perot cavity, enabling the measurements of both static and dynamic strain by monitoring reflected light fluctuations using a single-frequency laser. The SiN membrane offers high-quality-factor mechanical resonances that are sensitive to minute strain fluctuations. The two-beam Fabry-Perot cavity is constructed to interrogate the motion state of the SiN membrane. A static strain resolution of 4.00 nɛ is achieved by measuring mechanical resonance frequency shifts of the SiN membrane. The best dynamic resolution is 4.47 pɛHz-1/2, which is close to that of the sensor using high-finesse cavity and optical frequency comb, overcoming the dependence of ultrasensitive strain sensors on narrow-linewidth laser and high-finesse cavity with frequency locking equipment. This work opens up a promising avenue for a new generation of ultrasensitive strain sensors.

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.

Long-lived and Efficient Optomechanical Memory for Light

We demonstrate a memory for light based on optomechanically induced transparency. We achieve a long storage time by leveraging the ultralow dissipation of a soft-clamped mechanical membrane resonator, which oscillates at MHz frequencies. At room temperature, we demonstrate a lifetime T_{1}≈23  ms and a retrieval efficiency η≈40% for classical coherent pulses. We anticipate the storage of quantum light to be possible at moderate cryogenic conditions (T≈10  K). Such systems could find applications in emerging quantum networks, where they can serve as long-lived optical quantum memories by storing optical information in a phononic mode.

Beating the spectroscopic Rayleigh limit via post-processed heterodyne detection

Quantum-inspired superresolution methods surpass the Rayleigh limit in imaging, or the analogous Fourier limit in spectroscopy. This is achieved by carefully extracting the information carried in the emitted optical field by engineered measurements. An alternative to complex experimental setups is to use simple homodyne detection and customized data analysis. We experimentally investigate this method in the time-frequency domain and demonstrate the spectroscopic superresolution for two distinct types of light sources: thermal and phase-averaged coherent states. The experimental results are backed by theoretical predictions based on estimation theory.

High-Strength Amorphous Silicon Carbide for Nanomechanics

For decades, mechanical resonators with high sensitivity have been realized using thin-film materials under high tensile loads. Although there are remarkable strides in achieving low-dissipation mechanical sensors by utilizing high tensile stress, the performance of even the best strategy is limited by the tensile fracture strength of the resonator materials. In this study, a wafer-scale amorphous thin film is uncovered, which has the highest ultimate tensile strength ever measured for a nanostructured amorphous material. This silicon carbide (SiC) material exhibits an ultimate tensile strength of over 10 GPa, reaching the regime reserved for strong crystalline materials and approaching levels experimentally shown in graphene nanoribbons. Amorphous SiC strings with high aspect ratios are fabricated, with mechanical modes exceeding quality factors 108 at room temperature, the highest value achieves among SiC resonators. These performances are demonstrated faithfully after characterizing the mechanical properties of the thin film using the resonance behaviors of free-standing resonators. This robust thin-film material has significant potential for applications in nanomechanical sensors, solar cells, biological applications, space exploration, and other areas requiring strength and stability in dynamic environments. The findings of this study open up new possibilities for the use of amorphous thin-film materials in high-performance applications.

Room-temperature quantum optomechanics using an ultralow noise cavity

At room temperature, mechanical motion driven by the quantum backaction of light has been observed only in pioneering experiments in which an optical restoring force controls the oscillator stiffness1,2. For solid-state mechanical resonators in which oscillations are controlled by the material rigidity, the observation of these effects has been hindered by low mechanical quality factors, optical cavity frequency fluctuations3, thermal intermodulation noise4,5 and photothermal instabilities. Here we overcome these challenges with a phononic-engineered membrane-in-the-middle system. By using phononic-crystal-patterned cavity mirrors, we reduce the cavity frequency noise by more than 700-fold. In this ultralow noise cavity, we insert a membrane resonator with high thermal conductance and a quality factor (Q) of 180 million, engineered using recently developed soft-clamping techniques6,7. These advances enable the operation of the system within a factor of 2.5 of the Heisenberg limit for displacement sensing8, leading to the squeezing of the probe laser by 1.09(1) dB below the vacuum fluctuations. Moreover, the long thermal decoherence time of the membrane oscillator (30 vibrational periods) enables us to prepare conditional displaced thermal states of motion with an occupation of 0.97(2) phonons using a multimode Kalman filter. Our work extends the quantum control of solid-state macroscopic oscillators to room temperature.

Research on Fabrication of Phononic Crystal Soft-Supported Graphene Resonator

In aviation, aerospace, and other fields, nanomechanical resonators could offer excellent sensing performance. Among these, graphene resonators, as a new sensitive unit, are expected to offer very high mass and force sensitivity due to their extremely thin thickness. However, at present, the quality factor of graphene resonators at room temperature is generally low, which limits the performance improvement and further application of graphene resonators. Enhancing the quality factor of graphene resonators has emerged as a pressing research concern. In a previous study, we have proposed a new mechanism to reduce the energy dissipation of graphene resonators by utilizing phononic crystal soft-supported structures. We verified its feasibility through theoretical analysis and simulations. This article focuses on the fabrication of a phononic crystal soft-supported graphene resonator. In order to address the issues of easy fracture, deformation, and low success rate in the fabrication of phononic crystal soft-supported graphene resonators, we have studied key processes for graphene suspension release and focused ion beam etching. Through parameter optimization, finally, we have obtained phononic crystal soft-supported graphene resonators with varying cycles and pore sizes. Finally, we designed an optical excitation and detection platform based on Fabry-Pérot interference principle and explored the impact of laser power and spot size on phononic crystal soft-supported graphene resonators.

Direct laser-written optomechanical membranes in fiber Fabry-Perot cavities

Integrated micro- and nanophotonic optomechanical experiments enable the manipulation of mechanical resonators on the single phonon level. Interfacing these structures requires elaborate techniques limited in tunability, flexibility, and scaling towards multi-mode systems. Here, we demonstrate a cavity optomechanical experiment using 3D-laser-written polymer membranes inside fiber Fabry-Perot cavities. Vacuum coupling rates of g0/2π ≈ 30 kHz to the fundamental megahertz mechanical mode are reached. We observe optomechanical spring tuning of the mechanical resonator frequency by tens of kilohertz exceeding its linewidth at cryogenic temperatures. The direct fiber coupling, its scaling capabilities to coupled resonator systems, and the potential implementation of dissipation dilution structures and integration of electrodes make it a promising platform for fiber-tip integrated accelerometers, optomechanically tunable multi-mode mechanical systems, and directly fiber-coupled systems for microwave to optics conversion.

Integrated microcavity optomechanics with a suspended photonic crystal mirror above a distributed Bragg reflector

Increasing the interaction between light and mechanical resonators is an ongoing endeavor in the field of cavity optomechanics. Optical microcavities allow for boosting the interaction strength through their strong spatial confinement of the optical field. In this work, we follow this approach by realizing a sub-wavelength-long, free-space optomechanical microcavity on-chip fabricated from an (Al,Ga)As heterostructure. A suspended GaAs photonic crystal mirror is acting as a highly reflective mechanical resonator, which together with a distributed Bragg (DBR) reflector forms an optomechanical microcavity. We demonstrate precise control over the microcavity resonance by change of the photonic crystal parameters. We find that the microcavity mode can strongly couple to the transmissive modes of the DBR. The interplay between the microcavity mode and a guided resonance of the photonic crystal modifies the cavity response and results in a stronger dynamical backaction on the mechanical resonator compared to conventional optomechanical dynamics.

Active-feedback quantum control of an integrated low-frequency mechanical resonator

Preparing a massive mechanical resonator in a state with quantum limited motional energy provides a promising platform for studying fundamental physics with macroscopic systems and allows to realize a variety of applications, including precise sensing. While several demonstrations of such ground-state cooled systems have been achieved, in particular in sideband-resolved cavity optomechanics, for many systems overcoming the heating from the thermal bath remains a major challenge. In contrast, optomechanical systems in the sideband-unresolved limit are much easier to realize due to the relaxed requirements on their optical properties, and the possibility to use a feedback control schemes to reduce the motional energy. The achievable thermal occupation is ultimately limited by the correlation between the measurement precision and the back-action from the measurement. Here, we demonstrate measurement-based feedback cooling on a fully integrated optomechanical device fabricated using a pick-and-place method, operating in the deep sideband-unresolved limit. With the large optomechanical interaction and a low thermal decoherence rate, we achieve a minimal average phonon occupation of 0.76 when pre-cooled with liquid helium and 3.5 with liquid nitrogen. Significant sideband asymmetry for both bath temperatures verifies the quantum character of the mechanical motion. Our method and device are ideally suited for sensing applications directly operating at the quantum limit, greatly simplifying the operation of an optomechanical system in this regime.

Optomechanically induced optical trapping system based on photonic crystal cavities

Optical trapping has proven to be a valuable experimental technique for precisely controlling small dielectric objects. However, due to their very nature, conventional optical traps are diffraction limited and require high intensities to confine the dielectric objects. In this work, we propose a novel optical trap based on dielectric photonic crystal nanobeam cavities, which overcomes the limitations of conventional optical traps by significant factors. This is achieved by exploiting an optomechanically induced backaction mechanism between a dielectric nanoparticle and the cavities. We perform numerical simulations to show that our trap can fully levitate a submicron-scale dielectric particle with a trap width as narrow as 56 nm. It allows for achieving a high trap stiffness, therefore, a high Q-frequency product for the particle's motion while reducing the optical absorption by a factor of 43 compared to the cases for conventional optical tweezers. Moreover, we show that multiple laser tones can be used further to create a complex, dynamic potential landscape with feature sizes well below the diffraction limit. The presented optical trapping system offers new opportunities for precision sensing and fundamental quantum experiments based on levitated particles.

Phononically shielded photonic-crystal mirror membranes for cavity quantum optomechanics

We present a highly reflective, sub-wavelength-thick membrane resonator featuring high mechanical quality factor and discuss its applicability for cavity optomechanics. The 88.5 nm thin stoichiometric silicon-nitride membrane, designed and fabricated to combine 2D-photonic and phononic crystal patterns, reaches reflectivities up to 99.89 % and a mechanical quality factor of 2.9 × 10⁷ at room temperature. We construct a Fabry-Perot-type optical cavity, with the membrane forming one terminating mirror. The optical beam shape in cavity transmission shows a stark deviation from a simple Gaussian mode-shape, consistent with theoretical predictions. We demonstrate optomechanical sideband cooling to mK-mode temperatures, starting from room temperature. At higher intracavity powers we observe an optomechanically induced optical bistability. The demonstrated device has potential to reach high cooperativities at low light levels desirable, for example, for optomechanical sensing and squeezing applications or fundamental studies in cavity quantum optomechanics; and meets the requirements for cooling to the quantum ground state of mechanical motion from room temperature.

Mechanical Mode Imaging of a High-Q Hybrid hBN/Si3N4 Resonator

We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si₃N₄ membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si₃N₄ membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si₃N₄ membrane, the quality factors and the motional mass of the hBN drum modes can be shifted by orders of magnitude. This effect could be exploited to engineer hybrid drum/membrane modes that combine the low motional mass of 2D materials with the high quality factor of Si₃N₄ membranes for optomechanical or sensing applications.

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.

Diamond Nanomechanical Resonators Protected by a Phononic Band Gap

We report the design, fabrication, and characterization of diamond cantilevers attached to a phononic square lattice. We show that the robust protection of mechanical modes by phononic band gaps leads to a three-orders-of-magnitude increase in mechanical Q-factors, with the Q-factors exceeding 10⁶ at frequencies as high as 100 MHz. Temperature-dependent studies indicate that the Q-factors obtained at a few Kelvin are still limited by the materials loss. The high-Q diamond nanomechanical resonators provide a promising hybrid quantum system for spin-mechanics studies.

Enhancement of Optomechanical Squeezing of Light Using the Optical Coherent Feedback

A coherent feedback scheme is used to enhance the degree of squeezing of the output field in a cavity optomechanical system. In the feedback loop, a beam splitter (BS) plays the roles of both a feedback controller and an input-output port. To realize effective enhancement, the output quadrature should take the same form as the input quadrature, and the system should operate at the deamplification situation in the meantime. This can be realized by choosing an appropriate frequency-dependent phase angle for the generalized quadrature. Additionally, both the transmissivity of the BS and the phase factor induced by time delays in the loop affect optical squeezing. For the fixed frequency, the optimal values of transmissivity and phase factor can be used to achieve the enhanced optical squeezing. The effect of optical losses on squeezing is also discussed. Optical squeezing is degraded by the introduced vacuum noise owing to the inefficient transmission in the loop. We show that the enhancement of squeezing is achievable with the parameters of the current experiments.

Sliding nanomechanical resonators

The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding motion. Surprisingly, the resonant frequency of vibrations draws a loop as a tuning gate voltage is cycled. This behavior indicates that sliding is accompanied by a delayed frequency response of the resonators, making their dynamics richer than that of resonators with fixed clamping points. Our work elucidates the dynamics of nanomechanical resonators with unconventional boundary conditions, and offers opportunities for studying friction at the nanoscale from resonant frequency measurements.

The motion of a vibrating object is set by the way it is held. Here, the authors show a nanomechanical resonator reversibly slides on its supporting substrate as it vibrates and exploit this unconventional dynamics to quantify friction at the nanoscale.

A wave-confining metasphere beamforming acoustic sensor for superior human-machine voice interaction

Highly sensitive, source-tracking acoustic sensing is essential for effective and natural human-machine interaction based on voice. It is a known challenge to omnidirectionally track sound sources under a hypersensitive rate with low noise interference using a compact sensor. Here, we present a unibody acoustic metamaterial spherical shell with equidistant defected piezoelectric cavities, referred to as the metasphere beamforming acoustic sensor (MBAS). It demonstrates a wave-confining capability and low self-noise, simultaneously achieving an outstanding intrinsic signal-to-noise ratio (72 dB) and an ultrahigh sensitivity (137 mV_pp/Pa or -26.3 dBV), with a range spanning the daily phonetic frequencies (0 to 1500 Hz) and omnidirectional beamforming for the perception and spatial filtering of sound sources. Moreover, the MBAS-based auditory system is shown for high-performance audio cloning, source localization, and speech recognition in a noisy environment without any signal enhancement, revealing its promising applications in various voice interaction systems.

Excitation and detection of acoustic phonons in nanoscale systems

Phonons play a key role in the physical properties of materials, and have long been a topic of study in physics. While the effects of phonons had historically been considered to be a hindrance, modern research has shown that phonons can be exploited due to their ability to couple to other excitations and consequently affect the thermal, dielectric, and electronic properties of solid state systems, greatly motivating the engineering of phononic structures. Advances in nanofabrication have allowed for structuring and phonon confinement even down to the nanoscale, drastically changing material properties. Despite developments in fabricating such nanoscale devices, the proper manipulation and characterization of phonons continues to be challenging. However, a fundamental understanding of these processes could enable the realization of key applications in diverse fields such as topological phononics, information technologies, sensing, and quantum electrodynamics, especially when integrated with existing electronic and photonic devices. Here, we highlight seven of the available methods for the excitation and detection of acoustic phonons and vibrations in solid materials, as well as advantages, disadvantages, and additional considerations related to their application. We then provide perspectives towards open challenges in nanophononics and how the additional understanding granted by these techniques could serve to enable the next generation of phononic technological applications.

Integrated optical-readout of a high-Q mechanical out-of-plane mode

The rapid development of high-Q_M macroscopic mechanical resonators has enabled great advances in optomechanics. Further improvements could allow for quantum-limited or quantum-enhanced applications at ambient temperature. Some of the remaining challenges include the integration of high-Q_M structures on a chip, while simultaneously achieving large coupling strengths through an optical read-out. Here, we present a versatile fabrication method, which allows us to build fully integrated optomechanical structures. We place a photonic crystal cavity directly above a mechanical resonator with high-Q_M fundamental out-of-plane mode, separated by a small gap. The highly confined optical field has a large overlap with the mechanical mode, enabling strong optomechanical interaction strengths. Furthermore, we implement a novel photonic crystal design, which allows for a very large cavity photon number, a highly important feature for optomechanical experiments and sensor applications. Our versatile approach is not limited to our particular design but allows for integrating an out-of-plane optical read-out into almost any device layout. Additionally, it can be scaled to large arrays and paves the way to realizing quantum experiments and applications with mechanical resonators based on high-Q_M out-of-plane modes alike.

Mechanical Bistability in Kerr-modified Cavity Magnomechanics

Bistable mechanical vibration is observed in a cavity magnomechanical system, which consists of a microwave cavity mode, a magnon mode, and a mechanical vibration mode of a ferrimagnetic yttrium-iron-garnet sphere. The bistability manifests itself in both the mechanical frequency and linewidth under a strong microwave drive field, which simultaneously activates three different kinds of nonlinearities, namely, magnetostriction, magnon self-Kerr, and magnon-phonon cross-Kerr nonlinearities. The magnon-phonon cross-Kerr nonlinearity is first predicted and measured in magnomechanics. The system enters a regime where Kerr-type nonlinearities strongly modify the conventional cavity magnomechanics that possesses only a radiation-pressure-like magnomechanical coupling. Three different kinds of nonlinearities are identified and distinguished in the experiment. Our Letter demonstrates a new mechanism for achieving mechanical bistability by combining magnetostriction and Kerr-type nonlinearities, and indicates that such Kerr-modified cavity magnomechanics provides a unique platform for studying many distinct nonlinearities in a single experiment.

Soft-Clamped Silicon Nitride String Resonators at Millikelvin Temperatures

We demonstrate that soft-clamped silicon nitride strings with a large aspect ratio can be operated at mK temperatures. The quality factors (Q) of two measured devices show consistent dependency on the cryostat temperature, with soft-clamped mechanical modes reaching Q>10^{9} at roughly 46 mK. For low optical readout power, Q is found to saturate, indicating good thermalization between the sample and the stage it is mounted on. Our best device exhibits a calculated force sensitivity of 9.6  zN/sqrt[Hz] and a thermal decoherence time of 0.38 s, which bode well for future applications such as nanomechanical force sensing.

High Quality Factors in Superlattice Ferroelectric Hf0.5Zr0.5O2 Nanoelectromechanical Resonators

The discovery of ferroelectricity and advances in creating polar structures in atomic-layered hafnia-zirconia (Hf_xZr_1-xO₂) films spur the exploration of using the material for novel integrated nanoelectromechanical systems (NEMS). Despite its popularity, the approach to achieving high quality factors (Qs) in resonant NEMS made of Hf_xZr_1-xO₂ thin films remains unexplored. In this work, we investigate the realization of high Qs in Hf_0.5Zr_0.5O₂ nanoelectromechanical resonators by stress engineering via the incorporation of alumina (Al₂O₃) interlayers. We fabricate nanoelectromechanical resonators out of the Hf_0.5Zr_0.5O₂-Al₂O₃ superlattices, from which we measure Qs up to 171,000 and frequency-quality factor products (f × Q) of >10¹¹ Hz through electrical excitation and optical detection schemes at room temperature in vacuum. The analysis suggests that clamping loss and surface loss are the limiting dissipation sources and f × Q > 10¹² Hz is achievable through further engineering of anchor structure and built-in stress.

Structural Optimization of Graphene Triangular Lattice Phononic Crystal Based on Dissipation Dilution Theory

Nanomechanical resonators offer brilliant mass and force sensitivity applied in many fields, owing to a low mass m and high-quality factor Q. However, in vibrating process, resonant energy is inevitably dissipated. Typically, quality factor does not surpass the inverse of the material loss angle φ. Recently, some exceptions emerged in the use of highly stressed silicon nitride material. As yet, it is interpreted that the pre-stress seems to "dilute" the intrinsic energy dissipation according to the Zener model. Is there any other material that could further break the 1/φ limit and achieve higher quality factors? In our previous research, through theoretical calculation and finite element simulation, we have proved that graphene's quality factor is two orders of magnitude larger than silicon nitride, on account of the extremely thin thickness of graphene. Based on this, we further optimize the structure of phononic crystals to achieve higher quality factors, in terms of duty cycle and cell size. Through simulation analysis, the quality factor could improve with a larger duty cycle and bigger cell size of triangular lattice phononic crystal. Unexpectedly, the Q amplification coefficient of the 3 × 5-cell structure, which is the least number to compose a phononic crystal with a central defect area, is the highest. In contrast, the minimal cell-number structure in hexagonal lattice could not achieve the brilliant dissipation dilution effect as well as the triangular one. Then we consider how overall size and stress influence quality factor and, furthermore, compare theoretical calculation and finite simulation. Lastly, we start from the primitive 3 × 5 cells, constantly adding cells to the periphery. Through simulation, to our surprise, the largest Q amplification coefficient does not belong to the largest structure, instead originating from the moderate one consisting of 7 × 13 cells.

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/Hz^1/2 at room temperature and 90 zN/Hz^1/2 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.

Low dissipation of fundamental mode is a determinant factor in nanomechanical resonator design. Here the authors realize soft clamping for the fundamental mode in a nanomechanical tensile structure achieving low loss, low mass, and low resonance frequency that render it a perfect force sensor.

Ground state cooling of an ultracoherent electromechanical system

Cavity electromechanics relies on parametric coupling between microwave and mechanical modes to manipulate the mechanical quantum state, and provide a coherent interface between different parts of hybrid quantum systems. High coherence of the mechanical mode is of key importance in such applications, in order to protect the quantum states it hosts from thermal decoherence. Here, we introduce an electromechanical system based around a soft-clamped mechanical resonator with an extremely high Q-factor (>10⁹) held at very low (30 mK) temperatures. This ultracoherent mechanical resonator is capacitively coupled to a microwave mode, strong enough to enable ground-state-cooling of the mechanics (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{n}}_{\min }=0.76\pm 0.16$$\end{document}n¯min=0.76±0.16). This paves the way towards exploiting the extremely long coherence times (t_coh > 100 ms) offered by such systems for quantum information processing and state conversion.

’Systems with long coherence times are extremely important for the processing of quantum information. To this end the authors present a system able to cool down a resonator to its quantum mechanical ground state harnessing the large coupling between an ultra-coherent mechanical resonator and a superconducting circuit.’

Strong Parametric Coupling between Two Ultracoherent Membrane Modes

We demonstrate parametric coupling between two modes of a silicon nitride membrane. We achieve the coupling by applying an oscillating voltage to a sharp metal tip that approaches the membrane surface to within a few 100 nm. When the voltage oscillation frequency is equal to the mode frequency difference, the modes exchange energy periodically and faster than their free energy decay rate. This flexible method can potentially be useful for rapid state control and transfer between modes, and is an important step toward parametric spin sensing experiments with membrane resonators.

Femtometer-amplitude imaging of coherent super high frequency vibrations in micromechanical resonators

Dynamic measurement of femtometer-displacement vibrations in mechanical resonators at microwave frequencies is critical for a number of emerging high-impact technologies including 5G wireless communications and quantum state generation, storage, and transfer. However, the resolution of continuous-wave laser interferometry, the method most commonly used for imaging vibration wavefields, has been limited to vibration amplitudes just below a picometer at several gigahertz. This is insufficient for these technologies since vibration amplitudes precipitously decrease for increasing frequency. Here we present a stroboscopic optical sampling approach for the transduction of coherent super high frequency vibrations. Phase-sensitive absolute displacement detection with a noise floor of 55 fm/√Hz for frequencies up to 12 GHz is demonstrated, achieving higher bandwidth and significantly lower noise floor simultaneously compared to previous work. An acoustic microresonator with resonances above 10 GHz and displacements smaller than 70 fm is measured using the presented method to reveal complex mode superposition, dispersion, and anisotropic propagation.

Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators

Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich dynamical behavior, such as time-varying relaxation rates and signatures of nonergodicity in thermal equilibrium, revealed in the recent experimental and theoretical studies of micro- and nanomechanical resonators. However, a universal yet intuitive physical description for these diverse and sometimes contradictory experimental observations remains elusive. Here we experimentally reveal persistent nonlinear phase-locked states occurring at internal resonances and demonstrate that they are essential for understanding the transient dynamics of nonlinear systems with coupled eigenmodes. The measured dynamics of a fully observable micromechanical resonator system are quantitatively described by the lower-frequency mode entering, maintaining, and exiting a persistent phase-locked period-tripling state generated by the nonlinear driving force exerted by the higher-frequency mode. This model describes the observed phase-locked coherence times, the direction and magnitude of the energy exchange, and the resulting nonmonotonic mode energy evolution. Depending on the initial relative phase, the system selects distinct relaxation pathways, either entering or bypassing the locked state. The described persistent phase locking is not limited to particular frequency fractions or types of nonlinearities and may advance nonlinear resonator systems engineering across physical domains, including photonics as well as nanomechanics.

Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning

From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.

Optomechanical Anti-Lasing with Infinite Group Delay at a Phase Singularity

Singularities which symbolize abrupt changes and exhibit extraordinary behavior are of a broad interest. We experimentally study optomechanically induced singularities in a compound system consisting of a three-dimensional aluminum superconducting cavity and a metalized high-coherence silicon nitride membrane resonator. Mechanically induced coherent perfect absorption and anti-lasing occur simultaneously under a critical optomechanical coupling strength. Meanwhile, the phase around the cavity resonance undergoes an abrupt π-phase transition, which further flips the phase slope in the frequency dependence. The observed infinite discontinuity in the phase slope defines a singularity, at which the group velocity is dramatically changed. Around the singularity, an abrupt transition from an infinite group advance to delay is demonstrated by measuring a Gaussian-shaped waveform propagating. Our experiment may broaden the scope of realizing extremely long group delays by taking advantage of singularities.

Quantum-coherent nanoscience

For the past three decades nanoscience has widely affected many areas in physics, chemistry and engineering, and has led to numerous fundamental discoveries, as well as applications and products. Concurrently, quantum science and technology has developed into a cross-disciplinary research endeavour connecting these same areas and holds burgeoning commercial promise. Although quantum physics dictates the behaviour of nanoscale objects, quantum coherence, which is central to quantum information, communication and sensing, has not played an explicit role in much of nanoscience. This Review describes fundamental principles and practical applications of quantum coherence in nanoscale systems, a research area we call quantum-coherent nanoscience. We structure this Review according to specific degrees of freedom that can be quantum-coherently controlled in a given nanoscale system, such as charge, spin, mechanical motion and photons. We review the current state of the art and focus on outstanding challenges and opportunities unlocked by the merging of nanoscience and coherent quantum operations.

Quantum-dot-based deterministic photon-emitter interfaces for scalable photonic quantum technology

The scale-up of quantum hardware is fundamental to realize the full potential of quantum technology. Among a plethora of hardware platforms, photonics stands out: it provides a modular approach where the main challenges lie in the construction of high-quality building blocks and in the development of methods to interface the modules. The subsequent scale-up could exploit mature integrated photonics foundry technology to produce small-footprint quantum processors of immense complexity. Solid-state quantum emitters can realize a deterministic photon-emitter interface and enable key quantum photonic resources and functionalities, including on-demand single- and multi-photon-entanglement sources, as well as photon-photon nonlinear quantum gates. In this Review, we use the example of quantum dot devices to present the physics of deterministic photon-emitter interfaces, including the main photonic building blocks required to scale up, and discuss quantitative performance benchmarks. While our focus is on quantum dot devices, the presented methods also apply to other quantum-emitter platforms such as atoms, vacancy centres, molecules and superconducting qubits. We also identify applications within quantum communication and computing, presenting a route towards photonics with a genuine quantum advantage.

Graphene-Based Nanoelectromechanical Periodic Array with Tunable Frequency

Phononic crystals (PnCs) have attracted much attention due to their great potential for dissipation engineering and propagation manipulation of phonons. Notably, the excellent electrical and mechanical properties of graphene make it a promising material for nanoelectromechanical resonators. Transferring a graphene flake to a prepatterned periodic mechanical structure enables the realization of a PnC with on-chip scale. Here, we demonstrate a nanoelectromechanical periodic array by anchoring a graphene membrane to a 9 × 9 array of standing nanopillars. The device exhibits a quasi-continuous frequency spectrum with resonance modes distributed from ∼120 MHz to ∼980 MHz. Moreover, the resonant frequencies of these modes can be electrically tuned by varying the voltage applied to the gate electrode sitting underneath. Simulations suggest that the observed band-like spectrum provides an experimental evidence for PnC formation. Our architecture has large fabrication flexibility, offering a promising platform for investigations on PnCs with electrical accessibility and tunability.

Reaching silicon-based NEMS performances with 3D printed nanomechanical resonators

The extreme miniaturization in NEMS resonators offers the possibility to reach an unprecedented resolution in high-performance mass sensing. These very low limits of detection are related to the combination of two factors: a small resonator mass and a high quality factor. The main drawback of NEMS is represented by the highly complex, multi-steps, and expensive fabrication processes. Several alternatives fabrication processes have been exploited, but they are still limited to MEMS range and very low-quality factor. Here we report the fabrication of rigid NEMS resonators with high-quality factors by a 3D printing approach. After a thermal step, we reach complex geometry printed devices composed of ceramic structures with high Young’s modulus and low damping showing performances in line with silicon-based NEMS resonators ones. We demonstrate the possibility of rapid fabrication of NEMS devices that present an effective alternative to semiconducting resonators as highly sensitive mass and force sensors.

NEMS devices, nano-electro-mechanical systems, by virtue of their minute size, offer ultra-high sensitivity, though at the expense of manufacturing complexity. Here, Stassi et al succeed in manufacturing high quality factor NEMS devices using high resolution 3D printing.

Ultra-coherent nanomechanical resonators based on inverse design

Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute a promising platform for various quantum technologies and foundational research. Traditionally, the improvement of the resonator's performance through nanomechanical structural engineering has been driven by human intuition and insight. Such an approach is inefficient and leaves aside a plethora of unexplored mechanical designs that potentially achieve better performance. Here, we use a computer-aided inverse design approach known as topology optimization to structurally design mechanical resonators with optimized performance of the fundamental mechanical mode. Using the outcomes of this approach, we fabricate and characterize ultra-coherent nanomechanical resonators with, to the best of our knowledge, record-high Q ⋅ f products for their fundamental mode (where Q is the quality factor and f is the frequency). The proposed approach - which can also be used to improve phononic crystals and coupled-mode resonators - opens up a new paradigm for designing ultra-coherent micro- and nanomechanical resonators, enabling e.g. novel experiments in fundamental physics and extreme sensing.

Efficient Entanglement of Spin Qubits Mediated by a Hot Mechanical Oscillator

Localized electronic and nuclear spin qubits in the solid state constitute a promising platform for storage and manipulation of quantum information, even at room temperature. However, the development of scalable systems requires the ability to entangle distant spins, which remains a challenge today. We propose and analyze an efficient, heralded scheme that employs a parity measurement in a decoherence free subspace to enable fast and robust entanglement generation between distant spin qubits mediated by a hot mechanical oscillator. We find that high-fidelity entanglement at cryogenic and even ambient temperatures is feasible with realistic parameters and show that the entangled pair can be subsequently leveraged for deterministic controlled-NOT operations between nuclear spins. Our results open the door for novel quantum processing architectures for a wide variety of solid-state spin qubits.

Modeling and Observation of Nonlinear Damping in Dissipation-Diluted Nanomechanical Resonators

Dissipation dilution enables extremely low linear loss in stressed, high aspect ratio nanomechanical resonators, such as strings or membranes. Here, we report on the observation and theoretical modeling of nonlinear dissipation in such structures. We introduce an analytical model based on von Kármán theory, which can be numerically evaluated using finite-element models for arbitrary geometries. We use this approach to predict nonlinear loss and (Duffing) frequency shift in ultracoherent phononic membrane resonators. A set of systematic measurements with silicon nitride membranes shows good agreement with the model for low-order soft-clamped modes. Our analysis also reveals quantitative connections between these nonlinearities and dissipation dilution. This is of interest for future device design and can provide important insight when diagnosing the performance of dissipation dilution in an experimental setting.

Stimulated Raman Adiabatic Passage in Optomechanics

In multimode optomechanical systems, the mechanical modes can be coupled via the radiation pressure of the common optical mode, but the fidelity of the state transfer is limited by the optical cavity decay. Here we demonstrate stimulated Raman adiabatic passage (STIRAP) in optomechanics, where the optical mode is not populated during the coherent state transfer between the mechanical modes avoiding this decay channel. We show a state transfer of a coherent mechanical excitation between vibrational modes of a membrane in a high-finesse optical cavity with a transfer efficiency of 86%. Combined with exceptionally high mechanical quality factors, STIRAP between mechanical modes can enable generation, storage, and manipulation of long-lived mechanical quantum states, which is important for quantum information science and for the investigation of macroscopic quantum superpositions.

Tunable Graphene Phononic Crystal

In the field of phononics, periodic patterning controls vibrations and thereby the flow of heat and sound in matter. Bandgaps arising in such phononic crystals (PnCs) realize low-dissipation vibrational modes and enable applications toward mechanical qubits, efficient waveguides, and state-of-the-art sensing. Here, we combine phononics and two-dimensional materials and explore tuning of PnCs via applied mechanical pressure. To this end, we fabricate the thinnest possible PnC from monolayer graphene and simulate its vibrational properties. We find a bandgap in the megahertz regime within which we localize a defect mode with a small effective mass of 0.72 ag = 0.002 m_physical. We exploit graphene's flexibility and simulate mechanical tuning of a finite size PnC. Under electrostatic pressure up to 30 kPa, we observe an upshift in frequency of the entire phononic system by ∼350%. At the same time, the defect mode stays within the bandgap and remains localized, suggesting a high-quality, dynamically tunable mechanical system.

High-frequency broadband laser phase noise cancellation using a delay line

Laser phase noise remains a limiting factor in many experimental settings, including metrology, time-keeping, as well as quantum optics. Hitherto this issue was addressed at low frequencies ranging from well below 1 Hz to maximally 100 kHz. However, a wide range of experiments, such as, e.g., those involving nanomechanical membrane resonators, are highly sensitive to noise at higher frequencies in the range of 100 kHz to 10 MHz, such as nanomechanical membrane resonators. Here we employ a fiber-loop delay line interferometer optimized to cancel laser phase noise at frequencies around 1.5 MHz. We achieve noise reduction in 300 kHz-wide bands with a peak reduction of more than 10 dB at desired frequencies, reaching phase noise of less than -160 dB(rad²/Hz) with a Ti:Al₂O₃ laser. These results provide a convenient noise reduction technique to achieve deep ground-state cooling of mechanical motion.

Searching for Vector Dark Matter with an Optomechanical Accelerometer

We consider using optomechanical accelerometers as resonant detectors for ultralight dark matter. As a concrete example, we describe a detector based on a silicon nitride membrane fixed to a beryllium mirror, forming an optical cavity. The use of different materials gives access to forces proportional to baryon (B) and lepton (L) charge, which are believed to be coupling channels for vector dark matter particles ("dark photons"). The cavity meanwhile provides access to quantum-limited displacement measurements. For a centimeter-scale membrane precooled to 10 mK, we argue that sensitivity to vector B-L dark matter can exceed that of the Eöt-Wash experiment in integration times of minutes, over a fractional bandwidth of ∼0.1% near 10 kHz (corresponding to a particle mass of 10^{-10}  eV/c^{2}). Our analysis can be translated to alternative systems, such as levitated particles, and suggests the possibility of a new generation of tabletop experiments.

Electro-optic frequency combs for rapid interrogation in cavity optomechanics

Electro-optic frequency combs were employed to rapidly interrogate an optomechanical sensor, demonstrating spectral resolution substantially exceeding that possible with a mode-locked frequency comb. Frequency combs were generated using an integrated-circuit-based direct digital synthesizer and utilized in a self-heterodyne configuration. Unlike approaches based upon laser locking, the present approach allows rapid, parallel measurements of full optical cavity modes, large dynamic range of sensor displacement, and acquisition across a wide frequency range between DC and 500 kHz. In addition to being well suited to measurements of acceleration, this optical frequency comb-based approach can be utilized for interrogation in a wide range of cavity optomechanical sensors.