The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing, memory elements, reduced noise characteristics in an oscillator or signal amplification. Approaching the quantum regime, concepts have been proposed that enable low backaction measurement techniques or facilitate the visualisation of quantum mechanical effects. Here we study the dynamic response of nanoelectromechanical resonators in the nonlinear regime aiming at a more detailed understanding and an exploitation for switching applications. Whereas most previous investigations concentrated on dynamic phenomena arising at the onset of bistability, we present experiments that yield insight into the non-adiabatic evolution of the system while subjected to strong driving pulses and the subsequent relaxation. Modeling the behaviour quantitatively with a Duffing oscillator, we can control switching between its two stable states at high speeds, exceeding recently demonstrated results by 10,000.
We study nanomechanical resonators with frequency fluctuations due to diffusion of absorbed particles. The diffusion depends on the vibration amplitude through inertial effect. We find that, if the diffusion coefficient is sufficiently large, the resonator response to periodic driving displays bistability. The lifetime of the coexisting vibrational states scales exponentially with the diffusion coefficient. It also displays a characteristic scaling dependence on the distance to bifurcation points.
Nanomechanical resonators, machined out of Silicon-on-Insulator wafers, are operated in the nonlinear regime to investigate higher-order mechanical mixing at radio frequencies, relevant to signal processing and nonlinear dynamics on nanometer scales. Driven by two neighboring frequencies the resonators generate rich power spectra exhibiting a multitude of satellite peaks. This nonlinear response is studied and compared to $n^{th}$-order perturbation theory and nonperturbative numerical calculations.
Dynamic stabilization by simultaneous primary and superharmonic resonances for high order nonlinearity cancellation is demonstrated with an electrostatically-actuated, piezoresistively-transduced nanomechanical resonator. We prove experimentally how the combination of both the third-order nonlinearity cancellation and simultaneous resonances can be used to linearly drive a nanocantilever up to very large amplitudes compared to fundamental limits like pull-in occurrence, opening the way towards resonators with high frequency stability for high-performance sensing or time reference.
We report on a systematic study of nanomechanical dissipation in high-frequency (approximatively 300 MHz) gallium arsenide optomechanical disk resonators, in conditions where clamping and fluidic losses are negligible. Phonon-phonon interactions are shown to contribute with a loss background fading away at cryogenic temperatures (3 K). Atomic layer deposition of alumina at the surface modifies the quality factor of resonators, pointing towards the importance of surface dissipation. The temperature evolution is accurately fitted by two-level systems models, showing that nanomechanical dissipati…
We present measurements on nanomechanical resonators machined from Silicon-on-Insulator substrates. The resonators are designed as freely suspended Au/Si beams of lengths on the order of 1 - 4 um and a thickness of 200 nm. The beams are driven into nonlinear response by an applied modulation at radio frequencies and a magnetic field in plane. The strong hysteresis of the magnetomotive response allows sensitive charge detection by varying the electrostatic potential of a gate electrode.
We describe the measurement and modeling of amplitude noise and phase noise in ultra-high Q nanomechanical resonators made from stoichiometric silicon nitride. With quality factors exceeding 2 million, the resonators' noise performance is studied with high precision. We find that the amplitude noise can be well described by the thermomechanical model, however, the resonators exhibit sizable extra phase noise due to their intrinsic frequency fluctuations. We develop a method to extract the resonator frequency fluctuation of a driven resonator and obtain a noise spectrum with dependence, which c…
We demonstrate how to build a vibrating wire resonator for phonon excitation in liquid helium. The resonator is designed as a nanoscopic mechanically flexible beam machined out of a semiconductor/metal-hybrid. Quenching of the mechanical resonance around 100 MHz by phonon excitation in liquid ^4He at 4.2 K is shown. First measurements operating the nano-resonator in a dilution of ^3He/^4He at 30 mK are presented.
Misfit strain is inevitable in various heterostructures like the graphene/MoS 2 van der Waals heterostructure. Although the misfit strain effect on electronic and other physical properties have been well studied, it is still unclear how will the misfit strain affect the performance of the nanomechanical resonator based on the graphene/MoS 2 heterostructure. By performing molecular dynamics simulations, we disclose a misfit strain-induced decoupling phenomenon between the graphene layer and the MoS 2 layer during the resonant oscillation of the heterostructure. A direct relationship between the…
The damping rates of high quality factor nanomechanical resonators are well beyond intrinsic limits. Here, we explore the underlying microscopic loss mechanisms by investigating the temperature-dependent damping of the fundamental and third harmonic transverse flexural mode of a doubly clamped silicon nitride string. It exhibits characteristic maxima reminiscent of two-level defects typical for amorphous materials. Coupling to those defects relaxes the momentum selection rules, allowing energy transfer from discrete long wavelength resonator modes to the high frequency phonon environment.
We present measurements of the dissipation and frequency shift in nanomechanical gold resonators at temperatures down to 10 mK. The resonators were fabricated as doubly-clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 MHz and 3.87 MHz revealed that from 30 mK to 500 mK the dissipation increases with temperature as $T^{0.5}$, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous…
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 10^6 at frequencies as high as 100 MHz. Temperature dependent studies indicate that the Q-factors obtained at a few K are still limited by the materials loss. The high-Q diamond nanomechanical resonators provide a promising hybrid quantum system for spin-mechanics studies.
We study the transverse oscillatory modes of nanomechanical silicon nitride strings under high tensile stress as a function of geometry and mode index m <= 9. Reproducing all observed resonance frequencies with classical elastic theory we extract the relevant elastic constants. Based on the oscillatory local strain we successfully predict the observed mode-dependent damping with a single frequency independent fit parameter. Our model clarifies the role of tensile stress on damping and hints at the underlying microscopic mechanisms.
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…
We analyze the noise properties of two single electron transistors (SETs) coupled via a shared voltage gate consisting of a nanomechanical resonator. Working in the regime where the resonator can be treated as a classical system, we find that the SETs act on the resonator like two independent heat baths. The coupling to the resonator generates positive correlations in the currents flowing through each of the SETs as well as between the two currents. In the regime where the dynamics of the resonator is dominated by the back-action of the SETs, these positive correlations can lead to parametrica…
We observe transport of electrons through a metallic island on the tip of a nanomechanical pendulum. The resulting tunneling current shows distinct features corresponding to the discrete mechanical eigenfrequencies of the pendulum. We report on measurements covering the temperature range from 300 K down to 4.2 K. We explain the I-V curve, which differs from previous theoretical predictions, with model calculations based on a Master equation approach.
We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically …
We present an integrated scheme for dielectric drive and read-out of high-Q nanomechanical resonators which enables tuning of both the resonance frequency and quality factor with an applied DC voltage. A simple model for altering these quantities is derived, incorporating the resonator's complex electric polarizability and position in an inhomogeneous electric field, which agrees very well with the experimental findings as well as FEM simulations. By comparing two sample geometries we are able to show that careful electrode design can determine the direction of frequency tuning of flexural in-…
The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here we present a classical mechanical model system exhibiting analogous behaviour using two inversely tuneable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.
The dynamics of nanomechanical resonators driven by both low- and high-frequency signals is studied. Considering, as an example, resonators made of a doubly-clamped beam with magnetomotive driving, it is shown that three-frequency resonances arise due to the interaction of the above frequencies. Properties and characteristics of these resonances are determined analytically for linear and nonlinear modes of the resonator excitation. It is shown that in opposite to the conventional two-frequency resonance, the central frequency of these resonances, their linear dynamic range, and the critical va…
I study dephasing of an underdamped nanomechanical resonator subject to random mass loading of small particles. I present a frequency noise model which describes dephasing due to attachment and detachment of particles at random points and particle diffusion along the resonator. This situation is commonly encountered in current mass measurement experiments using NEM resonators. I discuss the conditions which can lead to inhomogeneous broadening and fine structure in the modes absorption spectra. I also show that the spectra of the higher order cumulants of the (complex) vibrational mode amplitu…
The energy dissipation 1/Q (where Q is the quality factor) and resonance frequency characteristics of single-crystal 3C-SiC ultrahigh frequency (UHF) nanomechanical resonators are measured, for a family of UHF resonators with resonance frequencies of 295MHz, 395MHz, 411MHz, 420MHz, 428MHz, and 482MHz. A temperature dependence of dissipation, 1/Q ~ T^(0.3) has been identified in these 3C-SiC devices. Possible mechanisms that contribute to dissipation in typical doubly-clamped beam UHF resonators are analyzed. Device size and dimensional effects on the dissipation are also examined. Clamping los…
Controlling the strain in two-dimensional materials is an interesting avenue to tailor the mechanical properties of nanoelectromechanical systems. Here we demonstrate a technique to fabricate ultrathin tantalum oxide nanomechanical resonators with large stress by laser-oxidation of nano-drumhead resonators made out of tantalum diselenide (TaSe2), a layered 2D material belonging to the metal dichalcogenides. Prior to the study of their mechanical properties with a laser interferometer, we checked the oxidation and crystallinity of the freely-suspended tantalum oxide in a high-resolution electro…
We investigate nonlinear dispersive mode coupling between the flexural in- and out-of-plane modes of two doubly clamped, nanomechanical silicon nitride string resonators. As the amplitude of one mode transitions from the linear response regime into the nonlinear regime, we find a frequency shift of two other modes. The resonators are strongly elastically coupled via a shared clamping point and can be tuned in and out of resonance dielectrically, giving rise to multimode avoided crossings. When the modes start hybridizing, their polarization changes. This affects the nonlinear dispersive coupli…
The electrical response of two-dimensional electron gas to vibrations of a nanomechanical cantilever containing it is studied. Vibrations of perpendicularly oriented cantilevers are experimentally shown to change oppositely the conductivity near their bases. This indicates the piezoelectric nature of electromechanical coupling. A physical model is developed, which quantitatively explains the experiment. It shows that the main origin of the conductivity change is a rapid change in the mechanical stress on the boundary between suspended and non-suspended areas, rather than the stress itself.
We discuss two theoretical proposals for controlling the nonequilibrium steady state of nanomechanical resonators using quantum electronic transport. Specifically?, we analyse two approaches to achieve the ground-state cooling of the mechanical vibration coupled to a quantum dot embedded between (i) spin-polarised contacts or (ii) a normal metal and a superconducting contact. Assuming a suitable coupling between the vibrational modes and the charge or spin of the electrons in the quantum dot, we show that ground-state cooling of the mechanical oscillator is within the state of the art for susp…
We show that the vibrations of a nanomechanical resonator can be cooled to near its quantum ground state by tunnelling injection of electrons from an STM tip. The interplay between two mechanisms for coupling the electronic and mechanical degrees of freedom results in a bias-voltage dependent difference between the probability amplitudes for vibron emission and absorption during tunneling. For a bias voltage just below the Coulomb blockade threshold we find that absorption dominates, which leads to cooling corresponding to an average vibron population of the fundamental bending mode of 0.2.
When a contaminant diffuses on the surface of a nanomechanical resonator, the motions of the two become correlated. Despite being a high-order effect in the resonator-particle coupling, such correlations affect the system dynamics by inducing dissipation of the resonator energy. Here, we consider this diffusion-induced dissipation in the cases of multiple particles adsorbed on carbon nanotube and graphene resonators. By solving the stochastic equations of motion, we simulate the ringdown of the resonator, in order to determine the resonator energy decay rate. We find two different scalings wit…
Thermalization in nonlinear systems is a central concept in statistical mechanics and has been extensively studied theoretically since the seminal work of Fermi, Pasta and Ulam (FPU). Using molecular dynamics and continuum modeling of a ring-down setup, we show that thermalization due to nonlinear mode coupling intrinsically limits the quality factor of nanomechanical graphene drums and turns them into potential test beds for FPU physics. We find the thermalization rate $Γ$ to be independent of radius and scaling as $Γ\sim T^*/ε_{\rm pre}^2$, where $T^*$ and $ε_{\rm pre}$ are effective resonat…
We present nanofabrication and mechanical measurements of single-crystal diamond cantilevers with thickness down to 85 nm, thickness uniformity better than 20 nm, and lateral dimensions up to 240 um. Quality factors exceeding one million are found at room temperature, surpassing those of state-of-the-art single-crystal silicon cantilevers of similar dimensions by roughly an order of magnitude. Force sensitivities of a few hundred zeptonewtons result for the best cantilevers at millikelvin temperatures. Single-crystal diamond could thus directly improve existing force and mass sensors by a simp…
We investigate the nonlinear response of a vibrating suspended nanomechanical beam on external periodic driving. The amplitude of the fundamental transverse mode behaves thereby like a weakly damped quantum particle in a driven anharmonic potential. Upon using a Born-Markovian master equation, we calculate the fundamental mode amplitude for varying driving frequencies. In the nonlinear regime, we observe resonances which are absent in the corresponding classical model. They are shown to be associated with resonant multi-phonon excitations. Furthermore, we identify resonant tunneling in a dynam…
We study the nonequilibrium steady state of a mechanical resonator in the quantum regime realized by a suspended carbon nanotube quantum dot contacted by two ferromagnets. Because of the spin-orbit interaction and/or an external magnetic field gradient, the spin on the dot couples directly to the flexural eigenmodes. Accordingly, the nanomechanical motion induces inelastic spin flips of the tunneling electrons. A spin-polarized current at finite bias voltage causes either heating or active cooling of the mechanical modes. We show that maximal cooling is achieved at resonant transport when the …
Owing to their extraordinary sensitivity to external forces, nanomechanical systems have become important tools for studying a variety of mesoscopic physical systems and realizing hybrid quantum systems. While nanomechanics has been widely applied in solid-state systems, its use in liquid is scantily studied. There it finds unique applications such as biosensing, rheological sensing, and studying fluid dynamics in unexplored regimes. Its use in quantum fluids offers new opportunities in studying fluids at low excitation levels all the way down to the quantum limit and in nano-metric scales rea…
We present results from a study of the nonlinear intermodal coupling between different flexural vibrational modes of a single high-stress, doubly-clamped silicon nitride nanomechanical beam. The measurements were carried out at 100 mK and the beam was actuated using the magnetomotive technique. We observed the nonlinear behavior of the modes individually and also measured the coupling between them by driving the beam at multiple frequencies. We demonstrate that the different modes of the resonator are coupled to each other by the displacement induced tension in the beam, which also leads to th…
Black phosphorus (P), a layered material that can be isolated down to individual 2D crystalline sheets, exhibits highly anisotropic mechanical properties due to its corrugated crystal structure in each atomic layer, which are intriguing for 2D nanomechanical devices. Here we lay the framework for describing the mechanical resonant responses in free-standing black P structures, by using a combination of analytical modeling and numerical simulation. We find that thicker devices (>100nm) operating in the elastic plate regime exhibit pronounced signatures of mechanical anisotropy, and can lead to …
We investigate the mechanical properties of freely suspended nanostrings fabricated from tensile-stressed, crystalline In$_{1-x}$Ga$_{x}$P. The intrinsic strain is a consequence of the epitaxial growth given by the lattice mismatch between the thin film and the substrate which is confirmed by x-ray diffraction measurements. The flexural eigenfrequencies of the nanomechanical string resonators reveal an orientation dependent stress with a maximum value of 650 MPa. The angular dependence is explained by a combination of anisotropic Young's modulus and a change of elastic properties caused by def…
We describe a quantum computational architecture based on integrating nanomechanical resonators with Josephson junction phase qubits, with which we implement single- and multi-qubit operations. The nanomechanical resonator is a GHz-frequency, high-quality-factor dilatational resonator, coupled to the Josephson phase through a piezoelectric interaction. This system is analogous to one or more few-level atoms (the Josephson qubits) in a tunable electromagnetic cavity (the nanomechanical resonator). Our architecture combines the best features of solid-state and cavity-QED approaches, and may make…
The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, cond-mat/0008211, to appear in J. MEMS (2002)] involving a parametrically-excited micromechanical resonator array. Future experiments are suggested that could provide quantitative tests of the the…
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength λ~ a_0 = 1.4 Å, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain ε~ (w/L)^2 due to a deflection w leads to a …
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
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…
We report a circuit cavity optomechanical system in which a nanomechanical resonator is adiabatically embedded inside an optical ring resonator with ultralow transition loss. The nanomechanical device forms part of the top layer of a horizontal silicon slot ring resonator, which enables dispersive coupling to the dielectric substrate via a tapered nanogap. Our measurements show nearly uncompromised optical quality factors (Q) after the release of the mechanical beam.
Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radiofrequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position;back-action effects manifest themselves as an effectiv…
Precise control of tensile stress and intrinsic damping is crucial for the optimal design of nanomechanical systems for sensor applications and quantum optomechanics in particular. In this letter we study the in uence of oxygen plasma on the tensile stress and intrinsic damping of nanomechanical silicon nitride resonators. Oxygen plasma treatments are common steps in micro and nanofabrication. We show that oxygen plasma of only a few minutes oxidizes the silicon nitride surface, creating several nanometer thick silicon dioxide layers with a compressive stress of 1.30(16)GPa. Such oxide layers …
We consider the tension-induced non-linearities of mechanical resonators, and derive the Hamiltonian of the flexural modes up to the fourth order in the position operators. This tension can be controlled by a nearby gate voltage. We focus on systems which allow large deformations $u(x)\gg h$ compared to the thickness $h$ of the resonator and show that in this case the third-order coupling can become non-zero due to the induced dc deformation and offers the possibility to realize equations of motion encountered in optomechanics. The fourth-order coupling is relevant especially for relatively lo…
Nanoscale mechanical resonators are widely utilized to provide high sensitivity force detectors. Here we demonstrate that such high quality factor resonators immersed in superfluid \(^4\mathrm{He}\) can be excited by a modulated flux of phonons. A nanosized heater immersed in superfluid \(^4\mathrm{He}\) acts as a source of ballistic phonons in the liquid -- "phonon wind". When the modulation frequency of the phonon flux matches the resonance frequency of the mechanical resonator, the motion of the latter can be excited. This ballistic thermomechanical effect can potentially open up new types …
We present a scheme of generating large-amplitude Schrödinger cat states and entanglement in a coupled system of nanomechanical resonator and single Cooper pair box (SCPB), without being limited by the magnitude of the coupling. It is shown that the entanglement between the resonator and the SCPB can be detected by a spectroscopic method.
We develop a simple continuum model to analyze the vibrational modes of a nanomechanical multi-element structure. In this model, arrays of sub-micron cantilevers located symmetrically on both sides of the central clamped-clamped nanobeam are replaced by a continuum. In this approach, the punctual shear forces exerted by the cantilevers on the central beam are smoothed out and the equations of motion of the structure become exactly solvable. Our analytical results capture the main features of the vibrational modes observed both numerically and experimentally. Furthermore, using a perturbative a…
We report quantitative experimental measurements of the nonlinear response of a radiofrequency mechanical resonator, with very high quality factor, driven by a large swept-frequency force. We directly measure the noise-free transition dynamics between the two basins of attraction that appear in the nonlinear regime, and find good agreement with those predicted by the one-dimensional Duffing equation of motion. We then measure the response of the transition rates to controlled levels of white noise, and extract the activation energy from each basin. The measurements of the noise-induced transit…
Stochastic resonance with white noise has been well established as a potential signal amplification mechanism in nanomechanical two-state systems. While white noise represents the archetypal stimulus for stochastic resonance, typical operating environments for nanomechanical devices often contain different classes of noise, particularly colored noise with a 1/f spectrum. As a result, improved understanding of the effects of noise color will be helpful in maximizing device performance. Here we report measurements of stochastic resonance in a silicon nanomechanical resonator using 1/f noise and …
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…
We show two effects as a result of considering the second-order correction to the spectrum of a nanomechanical resonator electrostatically coupled to a Cooper-pair box. The spectrum of the Cooper-pair box is modified in a way which depends on the Fock state of the resonator. Similarly, the frequency of the resonator becomes dependent on the state of the Cooper-pair box. We consider whether these frequency shifts could be utilized to prepare the nanomechanical resonator in a Fock state, to perform a quantum non-demolition measurement of the resonator Fock state, and to distinguish the phase sta…
The detection of mechanical vibrations near the quantum limit is a formidable challenge since the displacement becomes vanishingly small when the number of phonon quanta tends towards zero. An interesting setup for on-chip nanomechanical resonators is that of coupling them to electrical microwave cavities for detection and manipulation. Here we show how to achieve a large cavity coupling energy of up to (2 π) 1 MHz/nm for metallic beam resonators at tens of MHz. We used focused ion beam (FIB) cutting to produce uniform slits down to 10 nm, separating patterned resonators from their gate electr…
We analyze the response of a nanomechanical resonator to an external drive when it is also coupled to a single-electron transistor (SET). The interaction between the SET electrons and the mechanical resonator depends on the amplitude of the mechanical motion leading to a strongly non-linear response to the drive which is similar to that of a Duffing oscillator. We show that the average dynamics of the resonator is well-described by a simple effective model which incorporates damping and frequency renormalization terms which are amplitude dependent. We also find that for a certain range of para…
Recent theoretical work has shown that radiation pressure effects can in principle cool a mechanical degree of freedom to its ground state. In this paper, we apply this theory to our realization of an opto-mechanical system in which the motion of mechanical oscillator modulates the resonance frequency of a superconducting microwave circuit. We present experimental data demonstrating the large mechanical quality factors possible with metallic, nanomechanical beams at 20 mK. Further measurements also show damping and cooling effects on the mechanical oscillator due to the microwave radiation fie…
We investigate the effect of mechanical strain on the dynamics of thin $\mathrm{MoS_2}$ nanodrum resonators. Using a piezoelectric crystal, compressive and tensile biaxial strain is induced in initially flat and buckled devices. In the flat device, we observe a remarkable strain-dependence of the resonance line width, while the change in the resonance frequency is relatively small. In the buckled device, the strain-dependence of the damping is less pronounced, and a clear hysteresis is observed. The experiment suggests that geometric imperfections, such as microscopic wrinkles, could play a ro…
We investigate the tensile stress in freely suspended nanomechanical string resonators, and observe a material-independent dependence on the resonator length. We compare strongly stressed sting resonators fabricated from four different material systems based on amorphous silicon nitride, crystalline silicon carbide as well as crystalline indium gallium phosphide. The tensile stress is found to increase by approximately 50% for shorter resonators. We establish a simple elastic model to describe the observed length dependence of the tensile stress. The model accurately describes our experimental…
We report on nanomechanical resonators with very high-quality factors operated as mechanical probes in liquid helium \(^4\mathrm{He}\), with special attention to the superfluid regime down to millikelvin temperatures. Such resonators have been used to map out the full range of damping mechanisms in the liquid on the nanometer scale from \(10\,\mathrm{mK}\) up to \(\sim3\,\mathrm{K}\). The high sensitivity of these doubly-clamped beams to thermal excitations in the superfluid \(^4\mathrm{He}\) makes it possible to drive them using the momentum transfer from phonons generated by a nearby heater.…
We consider a quantum model of a nanomechanical flexing beam resonator interacting with a bath comprising a few damped tunneling two level systems (TLS's). In contrast with a resonator interacting bilinearly with an ohmic free oscillator bath (modeling clamping loss, for example), the mechanical resonator damping is amplitude dependent, while the decoherence of quantum superpositions of mechanical position states depends only weakly on their spatial separation.
