Micro- and nanoscale mechanical resonators have recently emerged as ubiquitous devices for use in advanced technological applications, for example in mobile communications and inertial sensors, and as novel tools for fundamental scientific endeavors. Their performance is in many cases limited by the deleterious effects of mechanical damping. Here, we report a significant advancement towards understanding and controlling support-induced losses in generic mechanical resonators. We begin by introducing an efficient numerical solver, based on the "phonon-tunneling" approach, capable of predicting the design-limited damping of high-quality mechanical resonators. Further, through careful device engineering, we isolate support-induced losses and perform the first rigorous experimental test of the strong geometric dependence of this loss mechanism. Our results are in excellent agreement with theory, demonstrating the predictive power of our approach. In combination with recent progress on complementary dissipation mechanisms, our phonon-tunneling solver represents a major step towards accurate prediction of the mechanical quality factor.
Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage-bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper-pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tu…
Carbon nanotubes (CNTs) are nonlinear high-Q resonators with strong coupling to single-electron tunneling. We begin by describing several methods to detect the flexural motion of a CNT resonator. Next, we illustrate how single-electron tunneling in quantum dot CNT resonators leads to sharp dips in the mechanical resonance frequency and significant damping. We discuss four different contributions to the nonlinear oscillation of a CNT resonator: beam-like mechanical nonlinearity, nonlinearity due to gate-induced mechanical tension, electrostatic nonlinearity, and nonlinearity due to single-elect…
Tunneling two level systems affect damping, noise and decoherence in a wide range of devices, including nanoelectromechanical resonators, optomechanical systems, and qubits. Theoretically this interaction is usually described within the tunneling state model. The dimensions of such devices are often small compared to the relevant phonon wavelengths at low temperatures, and extensions of the theoretical description to reduced dimensions have been proposed, but lack conclusive experimental verification. We have measured the intrinsic damping and the frequency shift in magnetomotively driven alum…
We solve Schrödinger equation describing a tunneling macrospin coupled to a torsional oscillator. Energy spectrum is studied for various quantum regimes. Magnetic susceptibility and noise spectrum are computed. We show that entanglement of the spin with mechanical modes of a subnanometer oscillator results in the decoherence of spin tunneling. For larger oscillators the presence of a tunneling spin can be detected through splitting of the mechanical mode at the resonance. Our results apply to experiments with magnetic molecules coupled to nanoresonators.
State of the art nanomechanical resonators present quality factors Q ~ 10^3 - 10^5, which are much lower than those that can be naively extrapolated from the behavior of micromechanical resonators. We analyze the dissipation mechanism that arises in nanomechanical beam-structures due to the tunneling of mesoscopic phonons between the beam and its supports (known as clamping losses). We derive the environmental force spectral density that determines the quantum Brownian motion of a given resonance. Our treatment is valid for low frequencies and provides the leading contribution in the aspect ra…
We focus on a recently experimentally realized scenario of normal-metal-insulator-superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tun…
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 present a design for a tunneling-current-assisted scanning near-field microwave microscope. For stable operation at cryogenic temperatures, making a small and rigid microwave probe is important. Our coaxial resonator probe has a length of approxomately 30 mm and can fit inside the 2-inch bore of a superconducting magnet. The probe design includes an insulating joint, which separates DC and microwave signals without degrading the quality factor. By applying the SMM to the imaging of an electrically inhomogeneous superconductor, we obtain the spatial distribution of the microwave response wit…
By first lithographically fabricating contact electrodes and then as last step growing carbon nanotubes with chemical vapour deposition across the ready-made chip, many potential contamination mechanisms for nanotube devices can be avoided. Combining this with pre-defined trenches on the chip, such that the nanotubes are freely suspended above the substrate, enables the formation of highly regular electronic systems. We show that, in addition, such suspended ultra-clean nanotubes provide excellent high-frequency and low-dissipation mechanical resonators. The motion detection mechanism of our e…
In this theoretical work, we study a double quantum dot interacting strongly with a microcavity, while undergoing resonant tunneling. Effects of interdot tunneling on the light-matter hybridized states are determined, and tunability of their brightness degrees and associated dipole moments is demonstrated. These results predict dipolariton generation in artificial molecules coupled to optical resonators, and provide a promising scenario for control of emission efficiency and coherence times of exciton polaritons.
We show that a properly dc-biased Josephson junction in series with two microwave resonators of different frequencies emits photon pairs in the resonators. By measuring auto- and inter-correlations of the power leaking out of the resonators, we demonstrate two-mode amplitude squeezing below the classical limit. This non-classical microwave light emission is found to be in quantitative agreement with our theoretical predictions, up to an emission rate of 2 billion photon pairs per second.
We use a Born-Markov approximated master equation approach to study the symmetrized-in-frequency current noise spectrum and the oscillator steady state of a nanoelectromechanical system where a nanoscale resonator is coupled linearly via its momentum to a quantum point contact (QPC). Our current noise spectra exhibit clear signatures of the quantum correlations between the QPC current and the back-action force on the oscillator at a value of the relative tunneling phase (η= -π/2) where such correlations are expected to be maximized. We also show that the steady state of the oscillator obeys a …
Superconducting resonators enable fast characterization and readout of mesoscopic quantum devices. Finding ways to perform measurements of interest on such devices using resonators only is therefore of great practical relevance. We report the experimental investigation of an InAs nanowire multi-quantum dot device by probing GHz resonators connected to the device. First, we demonstrate accurate extraction of the DC conductance from measurements of the high-frequency admittance. Because our technique does not rely on DC calibration, it could potentially obviate the need for DC measurements in se…
Dispersive sensing is a powerful technique that enables scalable and high-fidelity readout of solid-state quantum bits. In particular, gate-based dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zero-energy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majorana-zero-mode host system faithfully on short time scales. Here, we demonstrate rapid single-shot detection of a coherent single-electron tunneling amplitude be…
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.
We numerically investigate the decay of initial quantum Fock states and their superpositions for a mechanical resonator mode coupled to an environment comprising interacting, damped tunneling two level system (TLS) defects. The cases of one, three, and six near resonant, interacting TLS's are considered in turn and it is found that the resonator displays Ohmic bath like decay behavior with as few as three TLS's.
Nanoscale resonators that oscillate at high frequencies are useful in many measurement applications. We studied a high-quality mechanical resonator made from a suspended carbon nanotube driven into motion by applying a periodic radio frequency potential using a nearby antenna. Single-electron charge fluctuations created periodic modulations of the mechanical resonance frequency. A quality factor exceeding 10^5 allows the detection of a shift in resonance frequency caused by the addition of a single-electron charge on the nanotube. Additional evidence for the strong coupling of mechanical motio…
We explore the photonic (bright) side of dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated to the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted rad…
Single-electron tunneling processes through a double quantum dot can induce a lasing state in an electromagnetic resonator which is coupled coherently to the dot system. Here we study the noise properties of the transport current in the lasing regime, i.e., both the zero-frequency shot noise as well as the noise spectrum. The former shows a remarkable super-Poissonian behavior when the system approaches the lasing transition, but sub-Poissonian behavior deep in the lasing state. The noise spectrum contains information about the coherent dynamics of the coupled dot-resonator system. It shows pr…
Using low-temperature high-magnetic-field scanning tunneling microscopy and spectroscopy (STM/STS), we systematically study a graphene quantum dot (GQD) defined by a circular graphene p-p junction. Inside the GQD, we observe a series of quasi-bound states arising from whispering-gallery-mode (WGM) confinement of the circular junction and directly visualize these quasi-bound states down to atomic dimensions. By applying a strong magnetic field, a large jump in energy of the quasi-bound states, which is about one-half the energy spacing between the quasi-bound states, is observed. Such a behavio…
Negative differential conductance (NDC), characterized by the decreasing current with increasing voltage, has attracted continuous attention for its various novel applications. The NDC typically exists in a certain range of bias voltages for a selected system and controlling the regions of NDC in curves of current versus voltage (I-V) is experimentally challenging. Here, we demonstrate an unusual magnetic-field-controlled NDC in graphene npn junction resonators. The magnetic field not only can switch on and off the NDC, but also can continuously tune the regions of the NDC in the I-V curves. I…
We have used nanoelectromechanical resonators to probe superfluid $^4$He at different temperature regimes, spanning over four orders of magnitude in damping. These regimes are characterized by the mechanisms which provide the dominant contributions to damping and the shift of the resonance frequency: tunneling two level systems at the lowest temperatures, ballistic phonons and rotons at few hundred mK, and laminar drag in the two-fluid regime below the superfluid transition temperature as well as in the normal fluid. Immersing the nanoelectromechanical resonators in fluid increases their effec…
We study the Landau-Zener dynamics of a tunneling spin coupled to a torsional resonator. For strong spin-phonon coupling, when the oscillator frequency is large compared to the tunnel splitting, the system exhibits multiple Landau-Zener transitions. Entanglement of spin and mechanical angular momentum results in abrupt changes of oscillator dynamics which coincide in time with spin transitions. We show that a large number of spins on a single oscillator coupled only through the in-phase phonon field behaves as a single large spin, greatly enhancing the spin-phonon coupling. We compare purely q…
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…
The interplay of the tunneling transfer of charges and the emission and absorption of light can be investigated in a set-up, where a voltage-biased Josephson junction is placed in series to a microwave cavity. Here, we concentrate on the emission process and show that due to the inherent nonlinearity of the Josephson junction tunneling Cooper-pairs can create a variety of non-classical states of light. Depending on experimental parameters and tuning the device can be described by effective Hamiltonians, indicating specific photon creation mechanisms which lead to strongly bunched or anti-bunch…
Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the…
We study electron mechanical coupling in a suspended carbon nanotube (CNT) quantum dot device. Electron spin couples to the flexural vibration mode due to spin-orbit coupling in the electron tunneling processes. In the weak coupling limit, i.e. electron-vibration coupling is much smaller than the electron energy scale, the damping and resonant frequency shift of the CNT resonator can be obtained by calculating the dynamical spin susceptibility. We find that strong spin-flip scattering processes in Kondo regime significantly affect the mechanical motion of the carbon nanotube: Kondo effect indu…
A suspended, doubly clamped single wall carbon nanotube is characterized at cryogenic temperatures. We observe specific switching effects in dc-current spectroscopy of the embedded quantum dot. These have been identified previously as nano-electromechanical self-excitation of the system, where positive feedback from single electron tunneling drives mechanical motion. A magnetic field suppresses this effect, by providing an additional damping mechanism. This is modeled by eddy current damping, and confirmed by measuring the resonance quality factor of the rf-driven nano-electromechanical resona…
We theoretically address the quantum dynamics of a nanomechanical resonator coupled to the macrospin of a magnetic nanoparticle by both instanton and perturbative approaches. We demonstrate suppression of the tunneling between opposite magnetizations by nanomechanical interference. By approximating the macrospin as a two-level system, we describe magnetopolaritons and their destruction by interference. The predictions can be verified experimentally by a molecular magnet attached to a nanomechanical bridge.
Dissipation of micro- and nano-scale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequencies--usually, for smaller, micron-scale structures--a novel mechanism of phonon pumping of two-level defects gives rise to weakly temperature-dependent internal friction, $Q^{-1}$, concomitant to the effects observed in recent experiments. Due to their size, comparable to or shorter than the emitted phonon wavelength, these structures suffer from superradiance-enhanced dissipation by the collective relaxat…
Temperature is a fundamental parameter in the study of physical phenomena. At the nanoscale, local temperature differences can be harnessed to design novel thermal nanoelectronic devices or test quantum thermodynamical concepts. Determining temperature locally is hence of particular relevance. Here, we present a primary electron thermometer that allows probing the local temperature of a single electron reservoir in single-electron devices. The thermometer is based on cyclic electron tunneling between a system with discrete energy levels and a single electron reservoir. When driven at a finite …
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 …
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…
We demonstrate mechanical modulations of the exciton lifetime by using vibrational strain of a gallium arsenide (GaAs) resonator. The strain-induced modulations have anisotropic dependences on the crystal orientation, which reveals the origin of these modulations to be the piezoelectric effect. Numerical analyses based on the tunneling model clarify that the mechanical strain modulates the internal electric field and spatially separates the electrons and holes, leading to non-radiative exciton decomposition. This carrier separation also generates an optomechanical back-action force from the ph…
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 …
Carbon nanotubes (CNTs) have attracted much attention for use in nanomechanical devices because of their exceptional properties, such as large resonant frequencies, low mass, and high quality factors. Here, we report the first experimental realization of parametric strong coupling between two mechanical modes on a single CNT nanomechanical resonator, by applying an extra microwave pump. This parametric pump method can be used to couple mechanical modes with arbitrary frequency differences. The properties of the mechanical resonator are detected by single-electron tunneling at low temperature, …
We study the cooling of a mechanical resonator (MR) that is capacitively coupled to a double quantum dot (DQD). The MR is cooled by the dynamical backaction induced by the capacitive coupling between the DQD and the MR. The DQD is excited by a microwave field and afterwards a tunneling event results in the decay of the excited state of the DQD. An important advantage of this system is that both the energy level splitting and the decay rate of the DQD can be well tuned by varying the gate voltage. We find that the steady average occupancy, below unity, of the MR can be achieved by changing both…
We have observed the transversal vibration mode of suspended carbon nanotubes at millikelvin temperatures by measuring the single-electron tunneling current. The suspended nanotubes are actuated contact-free by the radio frequency electric field of a nearby antenna; the mechanical resonance is detected in the time-averaged current through the nanotube. Sharp, gate-tuneable resonances due to the bending mode of the nanotube are observed, combining resonance frequencies of up to ν_0 = 350 MHz with quality factors above Q = 10^5, much higher than previously reported results on suspended carbon na…
In this report, we present nanoelectromechanical resonators fabricated with thin exfoliated crystals of a high-T$_c$ cuprate superconductor Bi$_2$Sr$_2$Ca$_1$Cu$_2$O$_{8+δ}$. The mechanical readout is performed by capacitively coupling their motion to a coplanar waveguide microwave cavity fabricated with a superconducting alloy of molybdenum-rhenium. We demonstrate mechanical frequency tunability with external dc-bias voltage, and quality factors up to 36600. Our spectroscopic and time-domain measurements show that mechanical dissipation in these systems is limited by the contact resistance ar…
We report kelvin to millikelvin-temperature measurements of dissipation and frequency shift in megahertz-range resonators fabricated from ultra-nanocrystalline diamond. Frequency shift $δf/f_0$ and dissipation $Q^{-1}$ demonstrate temperature dependence in the millikelvin range similar to that predicted by the glass model of tunneling two level systems. The logarithmic temperature dependence of $δf/ f_0$ is in good agreement with such models, which include phonon relaxation and phonon resonant absorption. Dissipation shows a weak power law, $Q^{-1}\propto T^{1/3}$, followed by saturation at lo…
We study a voltage biased InAs double quantum dot (DQD) that is coupled to a superconducting transmission line resonator. Inelastic tunneling in the DQD is mediated by electron phonon coupling and coupling to the cavity mode. We show that electronic transport through the DQD leads to photon emission from the cavity at a rate of 10 MHz. With a small cavity drive field, we observe a gain of up to 15 in the cavity transmission. Our results are analyzed in the context of existing theoretical models and suggest that it may be necessary to account for inelastic tunneling processes that proceed via s…
We study dissipation in Pd nano-mechanical resonators at low temperatures in the linear response regime. Metallic resonators have shown characteristic features of dissipation due to tunneling two level systems (TLS). This system offers a unique tunability of the dissipation scenario by adsorbing hydrogen ($H_2$) which induces a compressive stress. The intrinsic stress is expected to alter TLS behaviour. We find a sub-linear power law $\sim T^{0.4}$ in dissipation. As seen in TLS dissipation scenarios we find a logarithmic increase of frequency characteristic from the lowest temperatures till a…
Superconducting quantum circuits are potential candidates to realize a large-scale quantum computer. The envisioned large density of integrated components, however, requires a proper thermal management and control of dissipation. To this end, it is advantageous to utilize tunable dissipation channels and to exploit the optimized heat flow at exceptional points (EPs). Here, we experimentally realize an EP in a superconducting microwave circuit consisting of two resonators. The EP is a singularity point of the Hamiltonian, and corresponds to the most efficient heat transfer between the resonator…
We propose an approach to cool a mechanical resonator (MR) via quantum interference in a triple quantum dot (TQD) capacitively coupled to the MR. The TQD connected to three electrodes is an electronic analog of a three-level atom in $Λ$ configuration. The electrons can tunnel from the left electrode into one of the two dots with lower-energy states, but can only tunnel out from the higher-energy state at the third dot to the right electrode. When the two lower-energy states are tuned to be degenerate, an electron in the TQD can be trapped in a superposition of the degenerate states called the …
Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping mani…
We derive fluctuation-dissipation relations for a tunnel junction driven by a high impedance microwave resonator, displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical forces hold, provided the effect of the circuit's quantum fluctuations is incorporated into a modified non-linear $I(V)$ curve. We also demonstrate that all quantities measured under a coherent time dependent bias can be reconstructed from their dc counterpart with a photo-assisted tunneling relation. We confirm these predictions by implementing the circuit and measuring…
We present a combined scanning force and tunneling microscope working in a dilution refrigerator that is optimized for the study of individual electronic nano-devices. This apparatus is equipped with commercial piezo-electric positioners enabling the displacement of a sample below the probe over several hundred microns at very low temperature, without excessive heating. Atomic force microscopy based on a tuning fork resonator probe is used for cryogenic precise alignment of the tip with an individual device. We demonstrate the local tunneling spectroscopy of a hybrid Josephson junction as a fu…
Damping-dependent thermalization of neighboring nanomechanical resonators below 1 mK
Swiss Federal Institute of Technology Lausanne (EPFL)（洛桑联邦理工学院）；EDWATEC SA（EDWATEC公司）；Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、内耳研究所）
