Coupled nanomechanical resonators are interesting for both fundamental studies and practical applications as they offer rich and tunable oscillation dynamics. At present, the mechanical coupling in such systems is often mediated by a fixed geometry, such as a joint clamping point of the resonators or a displacement-dependent force. Here we show a graphene-integrated electromechanical system consisting of two physically separated mechanical resonators -- a comb-drive actuator and a suspended silicon beam -- that are tunably coupled by a graphene membrane. The graphene membrane, moreover, provides a sensitive electrical read-out for the two resonating systems silicon structures showing 16 different modes in the frequency range from 0.4~to 24~MHz. In addition, by pulling on the graphene membrane with an electrostatic potential applied to one of the silicon resonators, we control the mechanical coupling, quantified by the $g$-factor, from 20 kHz to 100 kHz. Our results pave the way for coupled nanoelectromechanical systems requiring controllable mechanically coupled resonators.
We study the response of GaAs photonic crystal membrane resonators to thin film deposition. Slow spectral shifts of the cavity mode of several nanometers are observed at low temperatures, caused by cryo-gettering of background molecules. Heating the membrane resets the drift and shielding will prevent drift altogether. In order to explore the drift as a tool to detect surface layers, or to intentionally shift the cavity resonance frequency, we studied the effect of self-assembled monolayers of polypeptide molecules attached to the membranes. The 2 nm thick monolayers lead to a discrete step in…
Anisotropic phonon transport along different lattice directions of two-dimensional (2D) materials has been observed, however, the effect decreases with increasing the thickness beyond a few atomic layers. Here we establish a novel mechanism to induce anisotropic phonon transport in quasi-2D materials with isotropic symmetry. The phonon propagation is guided by resonance hybridization with surface nanostructures. We demonstrate that the thermal conductivity of 3 nm-thick silicon membrane with surface nanofins is greater by $\sim50\%$ parallel to the fins than that perpendicular to the fins.
Here, we demonstrate the fabrication of single-layer MoS2 mechanical resonators. The fabricated resonators have fundamental resonance frequencies in the order of 10 MHz to 30 MHz (depending on their geometry) and their quality factor is about ~55 at room temperature in vacuum. The dynamical properties clearly indicate that monolayer MoS2 membranes are in the membrane limit (i.e., tension dominated), in contrast to their thicker counterparts, which behave as plates. We also demonstrate clear signatures of nonlinear behaviour of our atomically thin membranes, thus providing a starting point for …
Silicon nitride (SiN) micro- and nanomechanical resonators have attracted a lot of attention in various research fields due to their exceptionally high quality factors ($Q$s). Despite their popularity, the origin of the limiting loss mechanisms in these structures has remained controversial. In this paper we propose an analytical model combining acoustic radiation loss with intrinsic loss. The model accurately predicts the resulting mode-dependent $Q$s of a low-stress silicon-rich and a high-stress stoichiometric SiN membrane. The large acoustic mismatch of the low-stress membrane to the subst…
We have fabricated suspended metal paddle resonators with carbon nanotubes functioning as self-detecting torsional springs. We observe gate-tunable resonances, that either tune to higher or to lower frequencies when increasing the dc voltage on the back-gate. We attribute the former modes to flexural vibrations of the paddle resonator, while the latter ones are identified as torsional vibrations. Compared to top-down silicon fabricated paddle resonators, nanotube springs have smaller torsional spring constants and provide a larger frequency tunability.
In the context of a recoil damping analysis, we have designed and produced a membrane resonator equipped with a specific on-chip structure working as a "loss shield" for a circular membrane. In this device the vibrations of the membrane, with a quality factor of $10^7$, reach the limit set by the intrinsic dissipation in silicon nitride, for all the modes and regardless of the modal shape, also at low frequency. Guided by our theoretical model of the loss shield, we describe the design rationale of the device, which can be used as effective replacement of commercial membrane resonators in adva…
A capacitive coupling between mechanical resonator and a microwave cavity enables readout and manipulation of the vibrations. We present a setup to carry out such experiments with aluminum membranes fabricated as stamps and transferred in place with micromanipulation. The membrane is held in place by van der Waals forces, and is supported by three microscopic points. We measure the lowest mechanical modes, and conclude the membrane vibrates as an essentially free-free resonator. Sliding clamping conditions are identified via a softening Duffing nonlinearity. The method will enable reduction of…
We study the vibrational motion of membrane resonators upon strong drive in the strongly nonlinear regime. By imaging the vibrational state of rectangular siliconnitride membrane resonators and by analyzing the frequency response using optical interferometry, we show that upon increasing the driving strength, the membrane adopts a peculiar deflection pattern formed by concentric rings superimposed onto the drum head shape of the fundamental mode. Such a circular symmetry cannot be described as a superposition of a small number of excited linear eigenmodes. Furthermore, the different parts of t…
We study mechanical dissipation of the fundamental mode of millimeter-sized, high quality-factor ($Q$) metalized silicon nitride membranes at temperatures down to 14 mK using a three-dimensional optomechanical cavity. Below 200 mK, high-$Q$ modes of the membranes show a diverging increase of $Q$ with decreasing temperature, reaching $Q=1.27\times10^8$ at 14 mK, an order of magnitude higher than reported before. The ultra-low dissipation makes the membranes highly attractive for the study of optomechanics in the quantum regime, as well as for other applications of optomechanics such as microwav…
Silicon membranes patterned by nanometer-scale pillars standing on the surface provide a practical platform for thermal conductivity reduction by resonance hybridization. Using molecular simulations, we investigate the effect of nanopillar size, unit-cell size, and finite-structure size on the net capacity of the local resonators in reducing the thermal conductivity of the base membrane. The results indicate that the thermal conductivity reduction increases as the ratio of the volumetric size of a unit nanopillar to that of the base membrane is increased, and the intensity of this reduction va…
Due to their exceptional mechanical and optical properties, dielectric silicon nitride (SiN) micromembrane resonators have become the centerpiece of many optomechanical experiments. Efficient capacitive coupling of the membrane to an electrical system would facilitate exciting hybrid optoelectromechanical devices. However, capacitive coupling of such dielectric membranes is rather weak. Here we add a single layer of graphene on SiN micromembranes and compare electromechanical coupling and mechanical properties to bare dielectric membranes and to membranes metallized with an aluminium layer. Th…
We study experimentally and theoretically the phenomenon of persistent response in ultra-strongly driven membrane resonators. This term denotes the development of a vibrating state with nearly constant amplitude over an extreme wide frequency range. We reveal the underlying mechanism of the persistent response state by directly imaging the vibrational state using advanced optical interferometry. We argue that the persistent state is related to the nonlinear interaction between higher order flexural modes and higher-order overtones of the driven mode. Finally, we propose a stability diagram for…
Metamaterials and plasmonics are powerful tools for unconventional manipulation and harnessing of light. Metamaterials can be engineered to possess intriguing properties lacking in natural materials, such as negative refractive index. Plasmonics offers capabilities to confine light in subwavelength dimensions and to enhance light-matter interactions. Recently,graphene-based plasmonics has revealed emerging technological potential as it features large tunability, higher field-confinement and lower loss compared to metal-based plasmonics. Here,we introduce hybrid structures comprising graphene p…
The Dicke effect is examined in an all-optical system of an optical waveguide side coupled to two interacting ring resonators in a liquid crytal environment. The system is shown to exhibit all the signatures of the Dicke effect under an active and reversible control by an applied voltage.
The availability of compact, low-cost magnetic resonance imaging instruments would further broaden the substantial impact of this technology. We report highly sensitive detection of magnetic resonance using low-stress silicon nitride (SiN$_x$) membranes. We use these membranes as low-loss, high-frequency mechanical oscillators and find they are able to mechanically detect spin-dependent forces with high sensitivity enabling ultrasensitive magnetic resonance detection. The high force detection sensitivity stems from their high mechanical quality factor $Q\sim10^6$ combined with the low mass of …
We experimentally demonstrate coupling of an atomically thin, free-standing graphene membrane to an optical cavity. By changing the position of the membrane along the standing-wave field of the cavity we tailor the dissipative coupling between the membrane and the cavity, and we show that the dissipative coupling can outweigh the dispersive coupling. Such a system, for which controlled dissipation prevails dispersion, will prove useful for novel laser-cooling schemes in optomechanics. In addition, we have determined the continuous-wave optical damage threshold of free-standing monolayer graphe…
Quantum backaction disturbs the measurement of the position of a mechanical oscillator by introducing additional fluctuations. In a quantum backaction measurement technique, the backaction can be evaded, although at the cost of losing part of the information. In this work, we carry out such a quantum backaction measurement using a large 0.5 mm diameter silicon nitride membrane oscillator with 707 kHz frequency, via a microwave cavity readout. The measurement shows that quantum backaction noise can be evaded in the quadrature measurement of the motion of a large object.
We propose a method for fast, deterministic resonator reset based on tunable dissipative modes. The dissipator is based on a Josephson junction with relatively low quality factor. When the dissipator is tuned into resonance with a high quality microwave resonator, resonator photons are absorbed by the dissipator at a rate orders of magnitude faster than the resonator relaxation rate. We determine the optimal parameters for realization of the tunable dissipator, and examine application of the dissipator to removing spurious photon population in the qubit readout resonator in circuit quantum ele…
Using optical diffraction, we study the mechanical vibrations of an array of micromechanical resonators. Implementing tunable electrostatic coupling between the suspended, doubly-clamped Au beams leads to the formation of a band of collective vibrational modes within these devices. The evolution of these modes with coupling strength is clearly manifested in the optical diffraction pattern of light transmitted through the array. The experimental results are analyzed using a simple model for one-dimensional phonons. These structures offer unique prospects for spectral analysis of complex mechani…
High quality factor mechanical resonators have shown great promise in developing classical or quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here we combine these two directions of progress in a single platform consisting of coupled Silicon Nitride (SiNx) and graphene mechanical resonators. We show that nonlinear response can be induced on a large area SiNx resonator mode and can be efficiently controlled by coupling it to a gate-tunable, freely suspended graphene mode. The induced nonlinear response of the hybrid modes, as measur…
We study the optomechanical properties of stoichiometric SiN resonators through a combination of spectroscopic and interferometric imaging techniques. At room temperature, we demonstrate ultrahigh quality factors of $5 \times 10^7$ and a $f \times Q$ product of $1 \times 10^{14}$ Hz that, to our knowledge, correspond to the largest values yet reported for mesoscopic flexural resonators. Through a comprehensive study of the limiting dissipation mechanisms as a function of resonator and substrate geometry, we identify radiation loss through the supporting substrate as the dominant loss process. …
We present a system which allows to tune the coupling between a superconducting resonator and a transmission line. This storage resonator is addressed through a second, coupling resonator, which is frequency-tunable and controlled by a magnetic flux applied to a superconducting quantum interference device (SQUID). We experimentally demonstrate that the lifetime of the storage resonator can be tuned by more than three orders of magnitude. A field can be stored for 18 μs when the coupling resonator is tuned off resonance and it can be released in 14 ns when the coupling resonator is tuned on res…
Imaging the vibrations of nanomechanical resonators means measuring their flexural mode shapes from the dependence of their frequency response on in-plane position. Applied to two-dimensional resonators, this technique provides a wealth of information on the mechanical properties of atomically-thin membranes. We present a simple and robust system to image the vibrations of few layer graphene (FLG) resonators at room temperature and in vacuum with an in-plane displacement precision of $\approx0.20$ $μ$m. It consists of a sturdy vacuum enclosure mounted on a three-axis micropositioning stage and…
Dielectric membranes with exceptional mechanical and optical properties present one of the most promising platforms in quantum opto-mechanics. The performance of stressed silicon nitride nanomembranes as mechanical resonators notoriously depends on how their frame is clamped to the sample mount, which in practice usually necessitates delicate, and difficult-to-reproduce mounting solutions. Here, we demonstrate that a phononic bandgap shield integrated in the membrane's silicon frame eliminates this dependence, by suppressing dissipation through phonon tunneling. We dry-etch the membrane's fram…
We investigate the sideband spectra of a driven nonlinear mode with its eigenfrequency being modulated at a low frequency (< 1 kHz). This additional parametric modulation leads to prominent antiresonance lineshapes in the sideband spectra, which can be controlled through the vibration state of the driven mode. We also establish a direct connection between the antiresonance frequency and the squeezing of thermal fluctuation in the system. Our work not only provides a simple and robust method for squeezing characterization but also opens a new possibility toward sideband applications.
The ability to control microwave emission from a spin ensemble is a requirement of several quantum memory protocols. Here, we demonstrate such ability by using a resonator whose frequency can be rapidly tuned with a bias current. We store excitations in an ensemble of rare-earth-ions and suppress on-demand the echo emission (`echo silencing') by two methods: 1) detuning the resonator during the spin rephasing, and 2) subjecting spins to magnetic field gradients generated by the bias current itself. We also show that spin coherence is preserved during silencing.
We have studied microwave response of a high-mobility two-dimensional electron system (2DES) contacted by two side electrodes. Using kinetic inductance of the 2DES and inter-electrode capacitance, we have constructed a subwavelength 2D plasmonic resonator. We have shown that the resonant frequency of this circuit can be controlled by 2D electron density, external magnetic field, or size of the electrodes. This opens up possibilities for using arrays of plasmonic circuits as tunable components in different frequency ranges.
We present a sensitive, tunable radio-frequency resonator designed to detect reactive changes in nanoelectronic devices down to dilution refrigerator temperatures. The resonator incorporates GaAs varicap diodes to allow electrical tuning of the resonant frequency and the coupling to the input line. We find a resonant frequency tuning range of 8.4 MHz at 55 mK that increases to 29 MHz at 1.5 K. To assess the impact on performance of different tuning conditions, we connect a quantum dot in a silicon nanowire field-effect transistor to the resonator, and measure changes in the device capacitance …
We study the mechanical quality factors of bilayer aluminum/silicon-nitride membranes. By coating ultrahigh-Q Si3N4 membranes with a more lossy metal, we can precisely measure the effect of material loss on Q's of tensioned resonator modes over a large range of frequencies. We develop a theoretical model that interprets our results and predicts the damping can be reduced significantly by patterning the metal film. Using such patterning, we fabricate Al-Si3N4 membranes with ultrahigh Q at room temperature. Our work elucidates the role of material loss in the Q of membrane resonators and informs…
We image and characterize the mechanical modes of a 2D drum resonator made of hBN suspended over a high-stress Si$_3$N$_4$ membrane. Our measurements demonstrate hybridization between various modes of the hBN resonator and those of the Si$_3$N$_4$ membrane. The measured resonance frequencies and spatial profiles of the modes are consistent with finite-element simulations based on an idealized geometry. Spectra of the thermal motion reveal that, depending on the degree of hybridization with modes of the heavier and higher-quality-factor Si$_3$N$_4$ membrane, the quality factors and the motional…
We have measured the backaction of a dc superconducting quantum interference device (SQUID) position detector on an integrated 1 MHz flexural resonator. The frequency and quality factor of the micromechanical resonator can be tuned with bias current and applied magnetic flux. The backaction is caused by the Lorentz force due to the change in circulating current when the resonator displaces. The experimental features are reproduced by numerical calculations using the resistively and capacitively shunted junction (RCSJ) model.
We present an experimental study of an optomechanical system formed by a vibrating thin semi-transparent membrane within a high-finesse optical cavity. We show that the coupling between the optical cavity modes and the vibrational modes of the membrane can be tuned by varying the membrane position and orientation. In particular we demonstrate a large quadratic dispersive optomechanical coupling in correspondence with avoided crossings between optical cavity modes weakly coupled by scattering at the membrane surface. The experimental results are well explained by a first order perturbation trea…
We have designed, fabricated and measured high-Q $λ/2$ coplanar waveguide microwave resonators whose resonance frequency is made tunable with magnetic field by inserting a DC-SQUID array (including 1 or 7 SQUIDs) inside. Their tunability range is 30% of the zero field frequency. Their quality factor reaches up to 3$\times10^4$. We present a model based on thermal fluctuations that accounts for the dependance of the quality factor with magnetic field.
We explore the prospects and benefits of combining the techniques of cavity optomechanics with efforts to image spins using magnetic resonance force microscopy (MRFM). In particular, we focus on a common mechanical resonator used in cavity optomechanics -- high-stress stoichiometric silicon nitride (Si$_3$N$_4$) membranes. We present experimental work with a trampoline membrane resonator that has a quality factor above $10^6$ and an order of magnitude lower mass than a comparable standard membrane resonators. Such high-stress resonators are on a trajectory to reach 0.1 $\rm{aN}/\sqrt{\rm{Hz}}$…
Controlling the dynamics of mechanical resonators is central to many quantum science and metrology applications. Optomechanical control of diamond resonators is attractive owing to diamond's excellent physical properties and its ability to host electronic spins that can be coherently coupled to mechanical motion. Using a confocal microscope, we demonstrate tunable amplification and damping of a diamond nanomechanical resonator's motion. Observation of both normal mode cooling from room temperature to 80K, and amplification into self--oscillations with $60\,μ\text{W}$ of optical power is observ…
We have developed capacitively-transduced nanomechanical resonators using sp$^2$-rich diamond-like carbon (DLC) thin films as conducting membranes. The electrically conducting DLC films were grown by physical vapor deposition at a temperature of $500{\,\,}^\circ$C. Characterizing the resonant response, we find a larger than expected frequency tuning that we attribute to the membrane being buckled upwards, away from the bottom electrode. The possibility of using buckled resonators to increase frequency tuning can be of advantage in rf applications such as tunable GHz filters and voltage-control…
The non-linear interaction between two mechanical resonances of the same freely suspended carbon nanotube resonator is studied. We find that in the Coulomb blockade regime, the non-linear modal interaction is dominated by single-electron-tunneling processes, and that the mode-coupling parameter can be tuned with the gate voltage, allowing both mode softening and mode stiffening behavior. This is in striking contrast to tension-induced mode coupling in strings, where the coupling parameter is positive and gives rise to a stiffening of the mode. The strength of the mode coupling in carbon nanotu…
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 modelling 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 ag…
We present a microelectromechanical system, in which a silicon beam is attached to a comb-drive actuator, that is used to tune the tension in the silicon beam, and thus its resonance frequency. By measuring the resonance frequencies of the system, we show that the comb-drive actuator and the silicon beam behave as two strongly coupled resonators. Interestingly, the effective coupling rate (~ 1.5 MHz) is tunable with the comb-drive actuator (+10%) as well as with a side-gate (-10%) placed close to the silicon beam. In contrast, the effective spring constant of the system is insensitive to eithe…
Superconducting microwave circuits show great potential for practical quantum technological applications such as quantum information processing. However, fast and on-demand initialization of the quantum degrees of freedom in these devices remains a challenge. Here, we experimentally implement a tunable heat sink that is potentially suitable for the initialization of superconducting qubits. Our device consists of two coupled resonators. The first resonator has a high quality factor and a fixed frequency whereas the second resonator is designed to have a low quality factor and a tunable resonanc…
We demonstrate coherent tunable coupling between a superconducting phase qubit and a lumped element resonator. The coupling strength is mediated by a flux-biased RF SQUID operated in the non-hysteretic regime. By tuning the applied flux bias to the RF SQUID we change the effective mutual inductance, and thus the coupling energy, between the phase qubit and resonator . We verify the modulation of coupling strength from 0 to $100 MHz$ by observing modulation in the size of the splitting in the phase qubit's spectroscopy, as well as coherently by observing modulation in the vacuum Rabi oscillatio…
We have designed, fabricated, and characterized magnetostatic wave (MSW) resonators on a chip. The resonators are fabricated by patterning single-crystal yttrium iron garnet (YIG) film on a gadolinium gallium garnet (GGG) substrate and excited by loop-inductor transducers. We achieved this technology breakthrough by developing a YIG film etching process and fabricating thick aluminum coplanar waveguide (CPW) inductor loop around each resonator to individually address and excite MSWs. At 4.77 GHz, the 0.68 square mm resonator achieves a quality factor Q > 5000 with a bias field of 987 Oe. We al…
We realize a device allowing for tunable and switchable coupling between two superconducting resonators mediated by an artificial atom. For the latter, we utilize a persistent current flux qubit. We characterize the tunable and switchable coupling in frequency and time domain and find that the coupling between the relevant modes can be varied in a controlled way. Specifically, the coupling can be tuned by adjusting the flux through the qubit loop or by saturating the qubit. Our time domain measurements allow us to find parameter regimes for optimal switch performance with respect to qubit driv…
Microring resonators are critical photonic components used in filtering, sensing and nonlinear applications. To date, the development of high performance microring resonators in LNOI has been limited by the sidewall angle, roughness and etch depth of fabricated rib waveguides. We present large free spectral range microring resonators patterned via electron beam lithography in high-index contrast $Z$-cut LNOI. Our microring resonators achieve an FSR greater than 5 nm for ring radius of 30 $μ$m and a large 3 dB resonance bandwidth. We demonstrate 3 pm/V electro-optic tuning of a 70 $μ$m-radius r…
The harmonic oscillator is one of the most widely used model systems in physics: an indispensable theoretical tool in a variety of fields. It is well known that otherwise linear oscillators can attain novel and nonlinear features through interaction with another dynamical system. We investigate such an interacting system: a superconducting LC-circuit dispersively coupled to a superconducting quantum interference device (SQUID). We find that the SQUID phase behaves as a classical two-level system, whose two states correspond to one linear and one nonlinear regime for the LC-resonator. As a resu…
We investigate theoretically the non-linear dynamics of a coupled nanomechanical oscillator. Under a weak radio frequency excitation, the resonators can be parametrically tuned into a self-sustained oscillatory regime. The transfer of electrons from one contact to the other is then mechanically assisted, generating a rectified current. The direction of the rectified current is, in most unstable regions, determined by the phase shift between the mechanical oscillations and the signal. However, we locate intriguing parametrical regions of uni-directional rectified current, suggesting a practical…
Measuring thermodynamic quantities can be easy or not, depending on the system that is being studied. For a macroscopic object, measuring temperatures can be as simple as measuring how much a column of mercury rises when in contact with the object. At the small scale of quantum electromechanical systems, such simple methods are not available and invariably detection processes disturb the system state. Here we propose a method for measuring the temperature on a suspended semiconductor membrane clamped at both ends. In this method, the membrane is mediating a capacitive coupling between two tran…
The germanium (Ge) hut wire system has strong spin-orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of …
A split-ring resonator is a prototype of meta-atom in metamaterials. Though noble metal-based split-ring resonators have been extensively studied, up to date, there is no experimental demonstration of split-ring resonators made from graphene, an emerging intriguing plasmonic material. Here, we experimentally demonstrate graphene split-ring resonators with deep subwavelength (about one hundredth of the excitation wavelength) magnetic dipole response in the terahertz regime. Meanwhile, the quadrupole and electric dipole are observed,depending on the incident light polarization. All modes can be …
We report spin and intensity coupling of an exciton-polariton condensate to the mechanical vibrations of a circular membrane microcavity. We optically drive the microcavity resonator at the lowest mechanical resonance frequency while creating an optically-trapped spin-polarized polariton condensate in different locations on the microcavity, and observe spin and intensity oscillations of the condensate at the vibration frequency of the resonator. Spin oscillations are induced by vibrational strain driving, whilst the modulation of the optical trap due to the displacement of the membrane causes …
We create a Josephson parametric amplifier from a transmission line resonator whose inner conductor is made from a series SQUID array. By changing the magnetic flux through the SQUID loops, we are able to adjust the circuit's resonance frequency and, consenquently, the center of the amplified band, between 4 and 7.8 GHz. We observe that the amplifier has gains as large as 28 dB and infer that it adds less than twice the input vacuum noise.
