Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity

Magnetic-field-direction-controlled slow light and second-order sidebands in a cavity-magnon optomechanical system

We theoretically study how the magnetic field direction controls both the transmission rate and the group delay of the signal, as well as the second-order sideband process in a hybrid cavity-magnon optomechanical system. By tuning the direction of the bias magnetic field, either a positive or negative magnon Kerr coefficient can be achieved, leading to a corresponding shift in the magnon frequency. As a result, the transmission rate can be significantly modified, resulting in a Fano-like transparency spectrum governed by the magnetic field direction, along with a slow-to-fast light switch also influenced by that direction. Moreover, we study the impact of magnetic field direction on the second-order sidebands, revealing that the enhancement of the second-order sideband effect is dependent on this direction. These findings pave the way to engineering magnon Kerr nonlinearity-assisted optomechanical devices for applications in signal propagation and storage.

Unveiling the tradeoff between device scale and surface nonidealities for an optimized quality factor at room temperature in 2D MoS2 nanomechanical resonators

A high quality (Q) factor is essential for enhancing the performance of resonant nanoelectromechanical systems (NEMS). NEMS resonators based on two-dimensional (2D) materials such as molybdenum disulfide (MoS2) have high frequency tunability, large dynamic range, and high sensitivity, yet room-temperature Q factors are typically less than 1000. Here, we systematically investigate the effects of device size and surface nonidealities on Q factor by measuring 52 dry-transferred fully clamped circular MoS2 NEMS resonators with diameters ranging from 1 μm to 8 μm, and optimize the Q factor by combining these effects with the strain-modulated dissipation model. We find that Q factor first increases and then decreases with diameter, with an optimized room-temperature Q factor up to 3315 ± 115 for a 2-μm-diameter device. Through extensive characterization and analysis using Raman spectroscopy, atomic force microscopy, and scanning electron microscopy, we demonstrate that surface nonidealities such as wrinkles, residues, and bubbles are especially significant for decreasing Q factor, especially for larger suspended membranes, while resonators with flat and smooth surfaces typically have larger Q factors. To further optimize Q factors, we measure and model Q factor dependence on the gate voltage, showing that smaller DC and radio-frequency (RF) driving voltages always lead to a higher Q factor, consistent with the strain-modulated dissipation model. This optimization of the Q factor delineates a straightforward and promising pathway for designing high-Q 2D NEMS resonators for ultrasensitive transducers, efficient RF communications, and low-power memory and computing.

Two-color electromagnetically induced transparency generated slow light in double-mechanical-mode coupling carbon nanotube resonators

We theoretically propose a multiple-mode-coupling hybrid quantum system comprising two-mode-coupling nanomechanical carbon nanotube (CNT) resonators realized by a phase-dependent phonon-exchange interaction interacting with the same nitrogen-vacancy (NV) center in diamond. We investigate the coherent optical responses of the NV center under the condition of resonance and detuning. In particular, two-color electromagnetically induced transparency (EIT) can be achieved by controlling the system parameters and coupling regimes. Combining the spin-phonon interactions and phonon-phonon coupling with the modulation phase, the switching of one and two EIT windows has been demonstrated, which generates a light delay or advance. The slow-to-fast and fast-to-slow light transitions have been studied in different coupling regimes, and the switch between slow and fast light can be controlled periodically by tuning the modulation phase. The study can be applied to phonon-mediated optical information storage or information processing with spin qubits based on multiple-mode hybrid quantum systems.

Superconducting Cavity-Based Sensing of Band Gaps in 2D Materials

The superconducting coplanar waveguide (SCPW) cavity plays an essential role in various areas like superconducting qubits, parametric amplifiers, radiation detectors, and studying magnon-photon and photon-phonon coupling. Despite its wide-ranging applications, the use of SCPW cavities to study various van der Waals 2D materials has been relatively unexplored. The resonant modes of the SCPW cavity exquisitely sense the dielectric environment. In this work, we measure the charge compressibility of bilayer graphene coupled to a half-wavelength SCPW cavity. Our approach provides a means to detect subtle changes in the capacitance of the bilayer graphene heterostructure, which depends on the compressibility of bilayer graphene, manifesting as shifts in the resonant frequency of the cavity. This method holds promise for exploring a wide class of van der Waals 2D materials, including transition metal dichalcogenides (TMDs) and their moiré, where DC transport measurement is challenging.

Bogoliubov polaritons mediated strong indirect interaction between distant whispering-gallery-mode resonators

We propose a method to achieve a strong indirect interaction between two distant whispering-gallery-mode (WGM) resonators in a hybrid quantum system at room temperature, even when the distance between them exceeds 40 wavelengths. By exploiting the quantum critical point, we can greatly enhance both the effective damping rate and the coupling strengths between a WGM resonator and a low-frequency polariton. We introduce a large effective frequency detuning to suppress the effective damping rate while maintaining the enhanced coupling strength. The strong indirect interaction between separated WGM resonators is mediated by a far-off-resonant low-frequency polariton through virtual excitations in a process similar to Raman process. This proposal provides a viable approach to building a quantum network based on strongly coupled WGM resonators.

Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes

We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.

Tunable couplings between location-insensitive emitters mediated by an epsilon-near-zero plasmonic waveguide

This work demonstrates the efficient tuning of incoherent and coherent coupling between emitters embedded in an epsilon-near-zero (ENZ) waveguide coated with a multilayer graphene. As a result, a tunable two-qubit quantum phase gate based on the ENZ waveguide is realized at the cutoff frequency. Furthermore, due to the vanishingly small permittivity of the ENZ waveguide, all incoherent coupling between any two identical emitters located in the central area of the slit approaches a maximum, enabling near-ideal bipartite and multipartite entanglement. The coherent coupling between emitters is much larger at an operating frequency far from the ENZ resonance frequency than at the cutoff frequency, and the coherent coupling and resulting energy transfer efficiency can also be effectively tuned by the Fermi level of graphene. These results demonstrate an efficiently tunable electro-optical platform for quantum devices.

Radiation Pressure Backaction on a Hexagonal Boron Nitride Nanomechanical Resonator

Hexagonal boron nitride (hBN) is a van der Waals material with excellent mechanical properties hosting quantum emitters and optically active spin defects, with several of them being sensitive to strain. Establishing optomechanical control of hBN will enable hybrid quantum devices that combine the spin degree of freedom with the cavity optomechanical toolbox. In this Letter, we report the first observation of radiation pressure backaction at telecom wavelengths with a hBN drum-head mechanical resonator. The thermomechanical motion of the resonator is coupled to the optical mode of a high finesse fiber-based Fabry-Pérot microcavity in a membrane-in-the-middle configuration. We are able to resolve the optical spring effect and optomechanical damping with a single photon coupling strength of g₀/2π = 1200 Hz. Our results pave the way for tailoring the mechanical properties of hBN resonators with light.

2D-materials-integrated optoelectromechanics: recent progress and future perspectives

The discovery of two-dimensional (2D) materials has gained worldwide attention owing to their extraordinary optical, electrical, and mechanical properties. Due to their atomic layer thicknesses, the emerging 2D materials have great advantages of enhanced interaction strength, broad operating bandwidth, and ultralow power consumption for optoelectromechanical coupling. The van der Waals (vdW) epitaxy or multidimensional integration of 2D material family provides a promising platform for on-chip advanced nano-optoelectromechanical systems (NOEMS). Here, we provide a comprehensive review on the nanomechanical properties of 2D materials and the recent advances of 2D-materials-integrated nano-electromechanical systems and nano-optomechanical systems. By utilizing active nanophotonics and optoelectronics as the interface, 2D active NOEMS and their coupling effects are particularly highlighted at the 2D atomic scale. Finally, we share our viewpoints on the future perspectives and key challenges of scalable 2D-materials-integrated active NOEMS for on-chip miniaturized, lightweight, and multifunctional integration applications.

From cavity optomechanics to cavity-less exciton optomechanics: a review

Cavity optomechanical coupling based on radiation pressure, photothermal forces and the photoelastic effect has been investigated widely over the past few decades, including optical measurements of mechanical vibration, dynamic backaction damping and amplification, nonlinear dynamics, quantum state transfer and so on. However, the delicate cavity operation, including cavity stabilization, fine detuning, tapered fibre access etc., limits the integration of cavity optomechanical devices. Dynamic backaction damping and amplification based on cavity-less exciton optomechanical coupling in III-V semiconductor nanomechanical systems, semiconductor nanoribbons and monolayer transition metal dichalcogenides have been demonstrated in recent years. The cavity-less exciton optomechanical systems interconnect photons, phonons and excitons in a highly integrable platform, opening up the development of integrable optomechanics. Furthermore, the highly tunable exciton resonance enables the exciton optomechanical coupling strength to be tuned. In this review, the mechanisms of cavity optomechanical coupling, the principles of exciton optomechanical coupling and the recent progress of cavity-less exciton optomechanics are reviewed. Moreover, the perspectives for exciton optomechanical devices are described.

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.

Nanomechanical Resonators: Toward Atomic Scale

The quest for realizing and manipulating ever smaller man-made movable structures and dynamical machines has spurred tremendous endeavors, led to important discoveries, and inspired researchers to venture to previously unexplored grounds. Scientific feats and technological milestones of miniaturization of mechanical structures have been widely accomplished by advances in machining and sculpturing ever shrinking features out of bulk materials such as silicon. With the flourishing multidisciplinary field of low-dimensional nanomaterials, including one-dimensional (1D) nanowires/nanotubes and two-dimensional (2D) atomic layers such as graphene/phosphorene, growing interests and sustained effort have been devoted to creating mechanical devices toward the ultimate limit of miniaturization─genuinely down to the molecular or even atomic scale. These ultrasmall movable structures, particularly nanomechanical resonators that exploit the vibratory motion in these 1D and 2D nano-to-atomic-scale structures, offer exceptional device-level attributes, such as ultralow mass, ultrawide frequency tuning range, broad dynamic range, and ultralow power consumption, thus holding strong promises for both fundamental studies and engineering applications. In this Review, we offer a comprehensive overview and summary of this vibrant field, present the state-of-the-art devices and evaluate their specifications and performance, outline important achievements, and postulate future directions for studying these miniscule yet intriguing molecular-scale machines.

A monolithically sculpted van der Waals nano-opto-electro-mechanical coupler

The nano-opto-electro-mechanical systems (NOEMS) are a class of hybrid solid devices that hold promises in both classical and quantum manipulations of the interplay between one or more degrees of freedom in optical, electrical and mechanical modes. To date, studies of NOEMS using van der Waals (vdW) heterostructures are very limited, although vdW materials are known for emerging phenomena such as spin, valley, and topological physics. Here, we devise a universal method to easily and robustly fabricate vdW heterostructures into an architecture that hosts opto-electro-mechanical couplings in one single device. We demonstrated several functionalities, including nano-mechanical resonator, vacuum channel diodes, and ultrafast thermo-radiator, using monolithically sculpted graphene NOEMS as a platform. Optical readout of electric and magnetic field tuning of mechanical resonance in a CrOCl/graphene vdW NOEMS is further demonstrated. Our results suggest that the introduction of the vdW heterostructure into the NOEMS family will be of particular potential for the development of novel lab-on-a-chip systems.

Superconducting Vortex-Charge Measurement Using Cavity Electromechanics

As the magnetic field penetrates the surface of a superconductor, it results in the formation of flux vortices. It has been predicted that the flux vortices will have a charged vortex core and create a dipolelike electric field. Such a charge trapping in vortices is particularly enhanced in high-T_c superconductors (HTS). Here, we integrate a mechanical resonator made of a thin flake of HTS Bi₂Sr₂CaCu₂O_8+δ into a microwave circuit to realize a cavity-electromechanical device. Due to the exquisite sensitivity of cavity-based devices to the external forces, we directly detect the charges in the flux vortices by measuring the electromechanical response of the mechanical resonator. Our measurements reveal the strength of surface electric dipole moment due to a single vortex core to be approximately 30 |e|a_B, equivalent to a vortex charge per CuO₂ layer of 3.7 × 10^-2|e|, where a_B is the Bohr radius and e is the electronic charge.

Strain-Modulated Dissipation in Two-Dimensional Molybdenum Disulfide Nanoelectromechanical Resonators

Resonant nanoelectromechanical systems (NEMS) based on two-dimensional (2D) materials such as molybdenum disulfide (MoS₂) are interesting for highly sensitive mass, force, photon, or inertial transducers, as well as for fundamental research approaching the quantum limit, by leveraging the mechanical degree of freedom in these atomically thin materials. For these mechanical resonators, the quality factor (Q) is essential, yet the mechanism and tuning methods for energy dissipation in 2D NEMS resonators have not been fully explored. Here, we demonstrate that by tuning static strain and vibration-induced strain in suspended MoS₂ using gate voltages, we can effectively tune the Q in 2D MoS₂ NEMS resonators. We further show that for doubly clamped resonators, the Q increases with larger DC gate voltage, while fully clamped drumhead resonators show the opposite trend. Using DC gate voltages, we can tune the Q by ΔQ/Q = 448% for fully clamped resonators, and by ΔQ/Q = 369% for doubly clamped resonators. We develop the strain-modulated dissipation model for these 2D NEMS resonators, which is verified against our measurement data for 8 fully clamped resonators and 7 doubly clamped resonators. We find that static tensile strain decreases dissipation while vibration-induced strain increases dissipation, and the actual dependence of Q on DC gate voltage depends on the competition between these two effects, which is related to the device boundary condition. Such strain dependence of Q is useful for optimizing the resonance linewidth in 2D NEMS resonators toward low-power, ultrasensitive, and frequency-selective devices for sensing and signal processing.

Mechanical frequency control in inductively coupled electromechanical systems

Nano-electromechanical systems implement the opto-mechanical interaction combining electromagnetic circuits and mechanical elements. We investigate an inductively coupled nano-electromechanical system, where a superconducting quantum interference device (SQUID) realizes the coupling. We show that the resonance frequency of the mechanically compliant string embedded into the SQUID loop can be controlled in two different ways: (1) the bias magnetic flux applied perpendicular to the SQUID loop, (2) the magnitude of the in-plane bias magnetic field contributing to the nano-electromechanical coupling. These findings are quantitatively explained by the inductive interaction contributing to the effective spring constant of the mechanical resonator. In addition, we observe a residual field dependent shift of the mechanical resonance frequency, which we attribute to the finite flux pinning of vortices trapped in the magnetic field biased nanostring.

Fabry-Perot interferometric calibration of van der Waals material-based nanomechanical resonators

One of the challenges in integrating nanomechanical resonators made from van der Waals materials in optoelectromechanical technologies is characterizing their dynamic properties from vibrational displacement. Multiple calibration schemes using optical interferometry have tackled this challenge. However, these techniques are limited only to optically thin resonators with an optimal vacuum gap height and substrate for interferometric detection. Here, we address this limitation by implementing a modeling-based approach via multilayer thin-film interference for in situ, non-invasive determination of the resonator thickness, gap height, and motional amplitude. This method is demonstrated on niobium diselenide drumheads that are electromotively driven in their linear regime of motion. The laser scanning confocal configuration enables a resolution of hundreds of picometers in motional amplitude for circular and elliptical devices. The measured thickness and spacer height, determined to be in the order of tens and hundreds of nanometers, respectively, are in excellent agreement with profilometric measurements. Moreover, the transduction factor estimated from our method agrees with the result of other studies that resolved Brownian motion. This characterization method, which applies to both flexural and acoustic wave nanomechanical resonators, is robust because of its scalability to thickness and gap height, and any form of reflecting substrate.

Thermal hysteresis controlled reconfigurable MoS2 nanomechanical resonators

Two-dimensional (2D) structures from layered materials have enabled a number of novel devices including resonant nanoelectromechanical systems (NEMS). 2D NEMS resonators are highly responsive to strain, allowing their resonance frequencies to be efficiently tuned over broad ranges, which is a feature difficult to attain in conventional micromachined resonators. In electrically configured and tuned devices, high external voltages are typically required to set and maintain different frequencies, limiting their applications. Here we experimentally demonstrate molybdenum disulfide (MoS₂) nanomechanical resonators that can be reconfigured between different frequency bands with zero maintaining voltage in a non-volatile fashion. By leveraging the thermal hysteresis in these 2D resonators, we use heating and cooling pulses to reconfigure the device frequency, with no external voltage required to maintain each frequency. We further show that the frequency spacing between the bands can be tuned by the thermal pulse strength, offering full control over the programmable operation. Such reconfigurable MoS₂ resonators may provide an alternative pathway toward small-form-factor and low-power tunable devices in future reconfigurable radio-frequency circuits with multi-band capability.

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.

Single pixel wide gamut dynamic color modulation based on a graphene micromechanical system

Dynamic color modulation in the composite structure of a graphene microelectromechanical system (MEMS)-photonic crystal microcavity is investigated in this work. The designed photonic crystal microcavity has three resonant standing wave modes corresponding to the three primary colors of red (R), green (G) and blue (B), forming strong localization of light in three modes at different positions of the microcavity. Once graphene is added, it can govern the transmittance of three modes. When graphene is located in the antinode of the standing wave, it has strong light absorption and therefore the structure's transmittance is lower, and when graphene is located in the node of the standing wave, it has weak light absorption and therefore the structure's transmittance is higher. Therefore, the graphene absorption of different colors of light can be regulated dynamically by applying voltages to tune the equilibrium position of the graphene MEMS in the microcavity, consequently realizing the output of vivid monochromatic light or multiple mixed colors of light within a single pixel, thus greatly improving the resolution. Our work provides a route to dynamic color modulation with graphene and provides guidance for the design and manufacture of high resolution, fast modulation and wide color gamut interferometric modulator displays.

Imaging Off-Resonance Nanomechanical Motion as Modal Superposition

Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion can be obtained by also looking at modal responses at frequencies in between resonances. Here, an imaging of the modal responses for a nanomechanical drum driven off resonance is presented. By using the frequency modal analysis, these shapes are described as a superposition of resonance modes. It is found that the spatial distribution of the oscillating component of the driving force, which is affected by both the shape of the actuating electrode and inherent device properties such as asymmetry and initial slack, greatly influences the modal weight or participation. This modal superposition analysis elucidates the dynamics of any nanomechanical system through modal weights. This aids in optimizing mode-specific designs for force sensing and integration with other systems.

Tunable parametric amplification of a graphene nanomechanical resonator in the nonlinear regime

Parametric amplification is widely used in nanoelectro-mechanical systems to enhance the transduced mechanical signals. Although parametric amplification has been studied in different mechanical resonator systems, the nonlinear dynamics involved receives less attention. Taking advantage of the excellent electrical and mechanical properties of graphene, we demonstrate electrical tunable parametric amplification using a doubly clamped graphene nanomechanical resonator. By applying external microwave pumping with twice the resonant frequency, we investigate parametric amplification in the nonlinear regime. We experimentally show that the extracted coefficient of the nonlinear Duffing force α and the nonlinear damping coefficient η vary as a function of external pumping power, indicating the influence of higher-order nonlinearity beyond the Duffing (∼x ³) and van der Pol (∼[Formula: see text]) types in our device. Even when the higher-order nonlinearity is involved, parametric amplification still can be achieved in the nonlinear regime. The parametric gain increases and shows a tendency of saturation with increasing external pumping power. Further, the parametric gain can be electrically tuned by the gate voltage with a maximum gain of 10.2 dB achieved at the gate voltage of 19 V. Our results will benefit studies on nonlinear dynamics, especially nonlinear damping in graphene nanomechanical resonators that has been debated in the community over past decade.

Mode Localization and Eigenfrequency Curve Veerings of Two Overhanged Beams

Overhang provides a simple but effective way of coupling (sub)structures, which has been widely adopted in the applications of optomechanics, electromechanics, mass sensing resonators, etc. Despite its simplicity, an overhanging structure demonstrates rich and complex dynamics such as mode splitting, localization and eigenfrequency veering. When an eigenfrequency veering occurs, two eigenfrequencies are very close to each other, and the error associated with the numerical discretization procedure can lead to wrong and unphysical computational results. A method of computing the eigenfrequency of two overhanging beams, which involves no numerical discretization procedure, is analytically derived. Based on the method, the mode localization and eigenfrequency veering of the overhanging beams are systematically studied and their variation patterns are summarized. The effects of the overhang geometry and beam mechanical properties on the eigenfrequency veering are also identified.

Dynamically-enhanced strain in atomically thin resonators

Graphene and related two-dimensional (2D) materials associate remarkable mechanical, electronic, optical and phononic properties. As such, 2D materials are promising for hybrid systems that couple their elementary excitations (excitons, phonons) to their macroscopic mechanical modes. These built-in systems may yield enhanced strain-mediated coupling compared to bulkier architectures, e.g., comprising a single quantum emitter coupled to a nano-mechanical resonator. Here, using micro-Raman spectroscopy on pristine monolayer graphene drums, we demonstrate that the macroscopic flexural vibrations of graphene induce dynamical optical phonon softening. This softening is an unambiguous fingerprint of dynamically-induced tensile strain that reaches values up to ≈4 × 10⁻⁴ under strong non-linear driving. Such non-linearly enhanced strain exceeds the values predicted for harmonic vibrations with the same root mean square (RMS) amplitude by more than one order of magnitude. Our work holds promise for dynamical strain engineering and dynamical strain-mediated control of light-matter interactions in 2D materials and related heterostructures.

Here, the authors use Raman spectroscopy on circular graphene drums to demonstrate dynamical softening of optical phonons induced by the macroscopic flexural motion of graphene, and find evidence that the strain in graphene is enhanced under non-linear driving.

Dissipative bosonic squeezing via frequency modulation and its application in optomechanics

The dissipative squeezing mechanism is an effective method to generate the strong squeezing, which is important in the precision metrology. Here, we propose a practical method to achieve arbitrary bosonic squeezing via introducing frequency modulation into the coupled harmonic resonator model. We analyze the effect of frequency modulation and give the analytical and numerical squeezing results, respectively. To measure the accurate dynamic squeezing in our proposal, we give a more general defination of the relative squeezing degree. Finally, the proposed method is extended to generate the strong mechanical squeezing (>3 dB) in a practical optomechanical system consisting of a graphene mechanical oscillator coupled to a superconducting microwave cavity. The result indicates that the strong mechanical squeezing can be effectively achieved even when the mechanical oscillator is not initially in its ground state. The proposed method expands the study on nonclassical state and does not need the bichromatic microwave driving technology.

Cavity electromechanics with parametric mechanical driving

Microwave optomechanical circuits have been demonstrated to be powerful tools for both exploring fundamental physics of macroscopic mechanical oscillators, as well as being promising candidates for on-chip quantum-limited microwave devices. In most experiments so far, the mechanical oscillator is either used as a passive element and its displacement is detected using the superconducting cavity, or manipulated by intracavity fields. Here, we explore the possibility to directly and parametrically manipulate the mechanical nanobeam resonator of a cavity electromechanical system, which provides additional functionality to the toolbox of microwave optomechanics. In addition to using the cavity as an interferometer to detect parametrically modulated mechanical displacement and squeezed thermomechanical motion, we demonstrate that this approach can realize a phase-sensitive parametric amplifier for intracavity microwave photons. Future perspectives of optomechanical systems with a parametrically driven mechanical oscillator include exotic bath engineering with negative effective photon temperatures, or systems with enhanced optomechanical nonlinearities.

Microwave circuits are interesting tools for microwave optomechanics and quantum information processing. Here, the authors demonstrate a phase-sensitive microwave amplifier by using parametric frequency modulation of a MHz mechanical nanobeam integrated in a superconducting microwave cavity.

Single-photon quantum regime of artificial radiation pressure on a surface acoustic wave resonator

Electromagnetic fields carry momentum, which upon reflection on matter gives rise to the radiation pressure of photons. The radiation pressure has recently been utilized in cavity optomechanics for controlling mechanical motions of macroscopic objects at the quantum limit. However, because of the weakness of the interaction, attempts so far had to use a strong coherent drive to reach the quantum limit. Therefore, the single-photon quantum regime, where even the presence of a totally off-resonant single photon alters the quantum state of the mechanical mode significantly, is one of the next milestones in cavity optomechanics. Here we demonstrate an artificial realization of the radiation pressure of microwave photons acting on phonons in a surface acoustic wave resonator. The order-of-magnitude enhancement of the interaction strength originates in the well-tailored, strong, second-order nonlinearity of a superconducting Josephson junction circuit. The synthetic radiation pressure interaction adds a key element to the quantum optomechanical toolbox and can be applied to quantum information interfaces between electromagnetic and mechanical degrees of freedom.

The radiation pressure of light on a mechanical oscillator can be used to manipulate mechanical degrees of freedom in the quantum regime. Noguchi et al. use Josephson junctions to realize an artificial system where the radiation pressure of a single photon is stronger than the effect of dissipation.

A Review on the Development of Tunable Graphene Nanoantennas for Terahertz Optoelectronic and Plasmonic Applications

Exceptional advancement has been made in the development of graphene optical nanoantennas. They are incorporated with optoelectronic devices for plasmonics application and have been an active research area across the globe. The interest in graphene plasmonic devices is driven by the different applications they have empowered, such as ultrafast nanodevices, photodetection, energy harvesting, biosensing, biomedical imaging and high-speed terahertz communications. In this article, the aim is to provide a detailed review of the essential explanation behind graphene nanoantennas experimental proofs for the developments of graphene-based plasmonics antennas, achieving enhanced light-matter interaction by exploiting graphene material conductivity and optical properties. First, the fundamental graphene nanoantennas and their tunable resonant behavior over THz frequencies are summarized. Furthermore, incorporating graphene-metal hybrid antennas with optoelectronic devices can prompt the acknowledgment of multi-platforms for photonics. More interestingly, various technical methods are critically studied for frequency tuning and active modulation of optical characteristics, through in situ modulations by applying an external electric field. Second, the various methods for radiation beam scanning and beam reconfigurability are discussed through reflectarray and leaky-wave graphene antennas. In particular, numerous graphene antenna photodetectors and graphene rectennas for energy harvesting are studied by giving a critical evaluation of antenna performances, enhanced photodetection, energy conversion efficiency and the significant problems that remain to be addressed. Finally, the potential developments in the synthesis of graphene material and technological methods involved in the fabrication of graphene-metal nanoantennas are discussed.

Manufacture and characterization of graphene membranes with suspended silicon proof masses for MEMS and NEMS applications

Graphene's unparalleled strength, chemical stability, ultimate surface-to-volume ratio and excellent electronic properties make it an ideal candidate as a material for membranes in micro- and nanoelectromechanical systems (MEMS and NEMS). However, the integration of graphene into MEMS or NEMS devices and suspended structures such as proof masses on graphene membranes raises several technological challenges, including collapse and rupture of the graphene. We have developed a robust route for realizing membranes made of double-layer CVD graphene and suspending large silicon proof masses on membranes with high yields. We have demonstrated the manufacture of square graphene membranes with side lengths from 7 µm to 110 µm, and suspended proof masses consisting of solid silicon cubes that are from 5 µm × 5 µm × 16.4 µm to 100 µm × 100 µm × 16.4 µm in size. Our approach is compatible with wafer-scale MEMS and semiconductor manufacturing technologies, and the manufacturing yields of the graphene membranes with suspended proof masses were >90%, with >70% of the graphene membranes having >90% graphene area without visible defects. The measured resonance frequencies of the realized structures ranged from tens to hundreds of kHz, with quality factors ranging from 63 to 148. The graphene membranes with suspended proof masses were extremely robust, and were able to withstand indentation forces from an atomic force microscope (AFM) tip of up to ~7000 nN. The proposed approach for the reliable and large-scale manufacture of graphene membranes with suspended proof masses will enable the development and study of innovative NEMS devices with new functionalities and improved performances.

Phase-controlled amplification and slow light in a hybrid optomechanical system

We theoretically investigate the transmission and group delay of a probe field incident on a hybrid optomechanical system, which consists of a mechanical resonator simultaneously coupled to an optical cavity and a two-level system (qubit). The cavity field is driven by a strong red-detuned control field, and a weak coherent mechanical driving field is applied to the mechanical resonator. With the assistance of additional mechanical driving field, it is shown that double optomechanically induced transparency can be switched into absorption due to destructive interference or amplification because of constructive interference, which depends on the phase difference of the applied fields. We study in detail how to control the probe transmission by tuning the parameters of the optical and mechanical driving fields. Furthermore, we find that the group delay of the transmitted probe field can be prolonged by the tuning the amplitude and phase of the mechanical driving field.

Gate Tunable Cooperativity between Vibrational Modes

Coupling between a mechanical resonator and optical cavities, microwave resonators, or other mechanical resonators have been used to observe interesting effects from sideband cooling to coherent manipulation of phonons. Here we demonstrate strong coupling between different vibrational modes of MoS₂ drum resonators at room temperature. We observe intermodal as well as intramodal coupling. Cooperativity, a measure of coupling between the two modes, can be tuned by more than an order of magnitude by changing the direct current gate bias. The large measured cooperativity of about 900 at room temperature indicates that the phonon population can be coherently transferred between the modes for more than 500 cycles. This coherent oscillation is of great interest in studying quantum effects in macroscopic objects.

Two-dimensional layered materials: from mechanical and coupling properties towards applications in electronics

With the increasing interest in nanodevices based on two-dimensional layered materials (2DLMs) after the birth of graphene, the mechanical and coupling properties of these materials, which play an important role in determining the performance and life of nanodevices, have drawn increasingly more attention. In this review, both experimental and simulation methods investigating the mechanical properties and behaviour of 2DLMs have been summarized, which is followed by the discussion of their elastic properties and failure mechanisms. For further understanding and tuning of their mechanical properties and behaviour, the influence factors on the mechanical properties and behaviour have been taken into consideration. In addition, the coupling properties between mechanical properties and other physical properties are summarized to help set up the theoretical blocks for their novel applications. Thus, the understanding of the mechanical and coupling properties paves the way to their applications in flexible electronics and novel electronics, which is demonstrated in the last part. This review is expected to provide in-depth and comprehensive understanding of mechanical and coupling properties of 2DLMs as well as direct guidance for obtaining satisfactory nanodevices from the aspects of material selection, fabrication processes and device design.

Misfit strain-induced energy dissipation for graphene/MoS2 heterostructure nanomechanical resonators

Misfit strain is inevitable in various heterostructures like the graphene/MoS₂ van der Waals heterostructure. Although the misfit strain effect on electronic and other physical properties have been well studied, it is still unclear how the misfit strain will affect the performance of the nanomechanical resonator based on the graphene/MoS₂ heterostructure. By performing molecular dynamics simulations, we disclose a misfit strain-induced decoupling phenomenon between the graphene layer and the MoS₂ layer during the resonant oscillation of the heterostructure. A direct relationship between the misfit strain and the decoupling mechanism is successfully established through the retraction force analysis. We further suggest to use the graphene/MoS₂/graphene sandwich heterostructure for the nanomechanical resonator application, which is able to prevent the misfit strain-related decoupling phenomenon. These results provide valuable information for the future application of the graphene/MoS₂ heterostructure in the nanomechanical resonator field.

Optomechanical Measurement of Thermal Transport in Two-Dimensional MoSe2 Lattices

Nanomechanical resonators have emerged as sensors with exceptional sensitivities. These sensing capabilities open new possibilities in the studies of the thermodynamic properties in condensed matter. Here, we use mechanical sensing as a novel approach to measure the thermal properties of low-dimensional materials. We measure the temperature dependence of both the thermal conductivity and the specific heat capacity of a transition metal dichalcogenide monolayer down to cryogenic temperature, something that has not been achieved thus far with a single nanoscale object. These measurements show how heat is transported by phonons in two-dimensional systems. Both the thermal conductivity and the specific heat capacity measurements are consistent with predictions based on first-principles.

The effect of strain on effective Duffing nonlinearity in the CVD-MoS2 resonator

We demonstrate all electrical measurements on NEMS devices fabricated using CVD grown monolayer MoS2. The as-grown monolayer film of MoS2 on top of the SiO2/Si wafer is processed to fabricate arrays and individual NEMS devices without the complex pick and transfer techniques associated with graphene. The electromechanical properties of the devices are on par with those fabricated using the exfoliation method. The frequency response of these devices is then used as a probe to estimate the linear thermal expansion coefficient of the material and evaluate the effect of strain on the effective Duffing nonlinearity in the devices.

Giant, Voltage Tuned, Quality Factors of Single Wall Carbon Nanotubes and Graphene at Room Temperature

Mastering dissipation in graphene-based nanostructures is still the major challenge in most fundamental and technological exploitations of these ultimate mechanical nanoresonators. Although high quality factors have been measured for carbon nanotubes (>10⁶) and graphene (>10⁵) at cryogenic temperatures, room-temperature values are orders of magnitude lower (≃10²). We present here a controlled quality factor increase of up to ×10³ for these basic carbon nanostructures when externally stressed like a guitar string. Quantitative agreement is found with theory attributing this decrease in dissipation to the decrease in viscoelastic losses inside the material, an effect enhanced by tunable "soft clamping". Quality factors exceeding 25 000 for SWCNTs and 5000 for graphene were obtained on several samples, reaching the limits of the graphene material itself. The combination of ultralow size and mass with high quality factors opens new perspectives for atomically localized force sensing and quantum computing as the coherence time exceeds state-of-the-art cryogenic devices.

GHz nanomechanical resonator in an ultraclean suspended graphene p-n junction

We demonstrate high-frequency mechanical resonators in ballistic graphene p-n junctions. Fully suspended graphene devices with two bottom gates exhibit ballistic bipolar behavior after current annealing. We determine the graphene mass density and built-in tension for different current annealing steps by comparing the measured mechanical resonant response to a simplified membrane model. In a graphene membrane with high built-in tension, but still of macroscopic size with dimensions 3 × 1 μm2, a record resonance frequency of 1.17 GHz is observed after the final current annealing step. We further compare the resonance response measured in the unipolar with the one in the bipolar regime. Remarkably, the resonant signals are strongly enhanced in the bipolar regime.

Cavity-enhanced optical controlling based on three-wave mixing in cavity-atom ensemble system

Cavity-enhanced optical controlling is experimentally observed with a low-control laser power in a cavity-atom ensemble system. Here, the three-level atoms are coupled with two optical modes of a Fabry-Perot cavity, where a new theoretical model is developed to describe the effective three-wave mixing process between spin-wave and optical modes. By adjusting either temperature or cavity length, we demonstrate the precise frequency tuning of the hybrid optical-atomic resonances. When the doubly-resonant condition is satisfied, the probe laser can be easily modulated by a control laser. In addition, interesting non-Hermitian physics are predicted theoretically and demonstrated experimentally, and all-optical switching is also achieved. Such a doubly-resonant cavity-atom ensemble system without a specially designed cavity can be used for future applications, such as optical signal storage and microwave-to-optical frequency conversion.

Quantum Effects in a Mechanically Modulated Single-Photon Emitter

Recent observation of quantum emitters in monolayers of hexagonal boron nitride (h-BN) has provided a novel platform for optomechanical experiments where the single-photon emitters can couple to the motion of a freely suspended h-BN membrane. Here, we propose a scheme where the electronic degree of freedom (d.o.f.) of an embedded color center is coupled to the motion of the hosting h-BN resonator via dispersive forces. We show that the coupling of membrane vibrations to the electronic d.o.f. of the emitter can reach the strong regime. By suitable driving of a three-level Λ-system composed of two spin d.o.f. in the electronic ground state as well as an isolated excited state of the emitter, a multiple electromagnetically induced transparency spectrum becomes available. The experimental feasibility of the efficient vibrational ground-state cooling of the membrane via quantum interference effects in the two-color drive scheme is numerically confirmed. More interestingly, the emission spectrum of the defect exhibits a frequency comb with frequency spacings as small as the fundamental vibrational mode, which finds applications in high-precision spectroscopy.

Anomalous scaling of flexural phonon damping in nanoresonators with confined fluid

Various one and two-dimensional (1D and 2D) nanomaterials and their combinations are emerging as next-generation sensors because of their unique opto-electro-mechanical properties accompanied by large surface-to-volume ratio and high quality factor. Though numerous studies have demonstrated an unparalleled sensitivity of these materials as resonant nanomechanical sensors under vacuum isolation, an assessment of their performance in the presence of an interacting medium like fluid environment is scarce. Here, we report the mechanical damping behavior of a 1D single-walled carbon nanotube (SWCNT) resonator operating in the fundamental flexural mode and interacting with a fluid environment, where the fluid is placed either inside or outside of the SWCNT. A scaling study of dissipation shows an anomalous behavior in case of interior fluid where the dissipation is found to be extremely low and scaling inversely with the fluid density. Analyzing the sources of dissipation reveals that (i) the phonon dissipation remains unaltered with fluid density and (ii) the anomalous dissipation scaling in the fluid interior case is solely a characteristic of the fluid response under confinement. Using linear response theory, we construct a fluid damping kernel which characterizes the hydrodynamic force response due to the resonant motion. The damping kernel-based analysis shows that the unexpected behavior stems from time dependence of the hydrodynamic response under nanoconfinement. Our systematic dissipation analysis helps us to infer the origin of the intrinsic dissipation. We also emphasize on the difference in dissipative response of the fluid under nanoconfinement when compared to a fluid exterior case. Our finding highlights a unique feature of confined fluid-structure interaction and evaluates its effect on the performance of high-frequency nanoresonators.

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.

Magnon-Photon-Phonon Entanglement in Cavity Magnomechanics

We show how to generate tripartite entanglement in a cavity magnomechanical system which consists of magnons, cavity microwave photons, and phonons. The magnons are embodied by a collective motion of a large number of spins in a macroscopic ferrimagnet, and are driven directly by an electromagnetic field. The cavity photons and magnons are coupled via magnetic dipole interaction, and the magnons and phonons are coupled via magnetostrictive (radiation pressurelike) interaction. We show optimal parameter regimes for achieving the tripartite entanglement where magnons, cavity photons, and phonons are entangled with each other, and we further prove that the steady state of the system is a genuinely tripartite entangled state. The entanglement is robust against temperature. Our results indicate that cavity magnomechanical systems could provide a promising platform for the study of macroscopic quantum phenomena.

Motion Transduction with Thermo-mechanically Squeezed Graphene Resonator Modes

There is a recent surge of interest in amplification and detection of tiny motion in the growing field of opto- and electromechanics. Here, we demonstrate widely tunable, broad bandwidth, and high gain all-mechanical motion amplifiers based on graphene/silicon nitride (SiNx) hybrids. In these devices, a tiny motion of a large-area SiNx membrane is transduced to a much larger motion in a graphene drum resonator coupled to SiNx. Furthermore, the thermal noise of graphene is reduced (squeezed) through parametric tension modulation. The parameters of the amplifier are measured by photothermally actuating SiNx and interferometrically detecting graphene displacement. We obtain a displacement power gain of 38 dB and demonstrate 4.7 dB of squeezing, resulting in a detection sensitivity of 3.8 [Formula: see text], close to the thermal noise limit of SiNx.

Tunable slow and fast light in parity-time-symmetric optomechanical systems with phonon pump

We study the response of parity-time (PT)-symmetric optomechanical systems with tunable gain and loss to the weak probe field in the presence of a strong control field and a coherent phonon pump. We show that the probe transmission can exceed unity at low control power due to the optical gain of the cavity and it can be further enhanced or suppressed by tuning the amplitude and phase of the phonon pump. Furthermore, the phase dispersion of the transmitted probe field is modified by controlling the applied fields, which allows one to tune the group delay of the probe field. Based on this optomechianical system, we can realize a tunable switch between slow and fast light effect by adjusting the gain-to-loss ratio, power of the control field as well as the amplitude and phase of the phonon pump. Our work provides a platform to control the light propagation in a more flexible way.

Hybrid Systems for the Generation of Nonclassical Mechanical States via Quadratic Interactions

We present a method to implement two-phonon interactions between mechanical resonators and spin qubits in hybrid setups, and show that these systems can be applied for the generation of nonclassical mechanical states even in the presence of dissipation. In particular, we demonstrate that the implementation of a two-phonon Jaynes-Cummings Hamiltonian under coherent driving of the qubit yields a dissipative phase transition with similarities to the one predicted in the model of the degenerate parametric oscillator: beyond a certain threshold in the driving amplitude, the driven-dissipative system sustains a mixed steady state consisting of a "jumping cat," i.e., a cat state undergoing random jumps between two phases. We consider realistic setups and show that, in samples within reach of current technology, the system features nonclassical transient states, characterized by a negative Wigner function, that persist during timescales of fractions of a second.

Quantum nondemolition measurement of mechanical motion quanta

The fields of optomechanics and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to make the detection of the mechanical mode occupation difficult, typically requiring the single-photon strong-coupling regime. Here, we propose and analyse an electromechanical setup, which allows us to overcome this limitation and resolve the energy levels of a mechanical oscillator. We found that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups.

Although electro-and optomechanics has recently moved towards the quantum regime, the quantized energy spectrum of a mechanical oscillator has not been directly observed. Here Dellantonio et al. propose an electromechanical setup with a membrane resonator that could enable phonon number measurements.