Multipartite Entanglement in a Microwave Frequency Comb.

Significant progress has been made with multipartite entanglement of discrete qubits, but continuous variable systems may provide a more scalable path toward entanglement of large ensembles. We demonstrate multipartite entanglement in a microwave frequency comb generated by a Josephson parametric amplifier subject to a bichromatic pump. We find 64 correlated modes in the transmission line using a multifrequency digital signal processing platform. Full inseparability is verified in a subset of seven modes. Our method can be expanded to generate even more entangled modes in the near future.

Probing nano-scale viscoelastic response in air and in liquid with dynamic atomic force microscopy.

We perform a comparative study of dynamic force measurements using an Atomic Force Microscope (AFM) on the same soft polymer blend samples in both air and liquid environments. Our quantitative analysis starts with calibration of the same cantilever in both environments. Intermodulation AFM (ImAFM) is used to measure dynamic force quadratures on the same sample. We validate the accuracy of the reconstructed dynamic force quadratures by numerical simulation of a realistic model of the cantilever in liquid. In spite of the very low quality factor of this resonance, we find excellent agreement between experiment and simulation. A recently developed moving surface model explains the measured force quadrature curves on the soft polymer, in both air and liquid.

From force curves to surface nanomechanical properties.

Surface science, which spans the fields of chemistry, physics, biology and materials science, requires information to be obtained on the local properties and property variations across a surface. This has resulted in the development of different scanning probe methods that allow the measurement of local chemical composition and local electrical and mechanical properties. These techniques have led to rapid advancement in fundamental science with applications in areas such as composite materials, corrosion protection and wear resistance. In this perspective article, we focussed on the branch of scanning probe methods that allows the determination of surface nanomechanical properties. We discussed some different AFM-based modes that were used for these measurements and provided illustrative examples of the type of information that could be obtained. We also discussed some of the difficulties encountered during such studies.

Local Charge Injection and Extraction on Surface-Modified Al2O3 Nanoparticles in LDPE.

We use a recently developed scanning probe technique to image with high spatial resolution the injection and extraction of charge around individual surface-modified aluminum oxide nanoparticles embedded in a low-density polyethylene (LDPE) matrix. We find that the experimental results are consistent with a simple band structure model where localized electronic states are available in the band gap (trap states) in the vicinity of the nanoparticles. This work offers experimental support to a previously proposed mechanism for enhanced insulating properties of nanocomposite LDPE and provides a powerful experimental tool to further investigate such properties.

Probing viscoelastic response of soft material surfaces at the nanoscale.

We study the interaction between an AFM tip and a soft viscoelastic surface. Using a multifrequency method we measure the amplitude-dependence of the cantilever dynamic force quadratures, which clearly show the effect of finite relaxation time of the viscoelastic surface. A model is introduced which treats the tip and surface as a two-body dynamic problem with a nonlinear interaction depending on their separation. We find good agreement between simulations of this model and experimental data on polymer blend samples for a variety of materials and measurement conditions.

Determining surface properties with bimodal and multimodal AFM.

Conventional dynamic atomic force microscopy (AFM) can be extended to bimodal and multimodal AFM in which the cantilever is simultaneously excited at two or more resonance frequencies. Such excitation schemes result in one additional amplitude and phase images for each driven resonance, and potentially convey more information about the surface under investigation. Here we present a theoretical basis for using this information to approximate the parameters of a tip-surface interaction model. The theory is verified by simulations with added noise corresponding to room-temperature measurements.

Design, fabrication, and characterization of kinetic-inductive force sensors for scanning probe applications.

We describe a transducer for low-temperature atomic force microscopy based on electromechanical coupling due to a strain-dependent kinetic inductance of a superconducting nanowire. The force sensor is a bending triangular plate (cantilever) whose deflection is measured via a shift in the resonant frequency of a high-Q superconducting microwave resonator at 4.5 GHz. We present design simulations including mechanical finite-element modeling of surface strain and electromagnetic simulations of meandering nanowires with large kinetic inductance. We discuss a lumped-element model of the force sensor and describe the role of an additional shunt inductance for tuning the coupling to the transmission line used to measure the microwave resonance. A detailed description of our fabrication is presented, including information about the process parameters used for each layer. We also discuss the fabrication of sharp tips on the cantilever using focused electron beam-induced deposition of platinum. Finally, we present measurements that characterize the spread of mechanical resonant frequency, the temperature dependence of the microwave resonance, and the sensor's operation as an electromechanical transducer of force.

The role of nonlinear dynamics in quantitative atomic force microscopy.

Various methods of force measurement with the atomic force microscope are compared for their ability to accurately determine the tip-surface force from analysis of the nonlinear cantilever motion. It is explained how intermodulation, or the frequency mixing of multiple drive tones by the nonlinear tip-surface force, can be used to concentrate the nonlinear motion in a narrow band of frequency near the cantilever's fundamental resonance, where accuracy and sensitivity of force measurement are greatest. Two different methods for reconstructing tip-surface forces from intermodulation spectra are explained. The reconstruction of both conservative and dissipative tip-surface interactions from intermodulation spectra are demonstrated on simulated data.

Measurement and control of a superconducting quantum processor with a fully integrated radio-frequency system on a chip.

We describe a digital microwave platform called Presto, designed for measurement and control of multiple quantum bits (qubits) and based on the third-generation radio-frequency system on a chip. Presto uses direct digital synthesis to create signals up to 9 GHz on 16 synchronous output ports, while synchronously analyzing responses on 16 input ports. Presto has 16 DC-bias outputs, four inputs and four outputs for digital triggers or markers, and two continuous-wave outputs for synthesizing frequencies up to 15 GHz. Scaling to a large number of qubits is enabled through deterministic synchronization of multiple Presto units. A Python application programming interface configures a firmware for synthesis and analysis of pulses, coordinated by an event sequencer. The analysis integrates template matching (matched filtering) and low-latency (184-254 ns) feedback to enable a wide range of multi-qubit experiments. We demonstrate Presto's capabilities with experiments on a sample consisting of two superconducting qubits connected via a flux-tunable coupler. We show single-shot readout and active reset of a single qubit; randomized benchmarking of single-qubit gates showing 99.972% fidelity, limited by the coherence time of the qubit; and calibration of a two-qubit iSWAP gate.

Intermodulation spectroscopy as an alternative to pump-probe for the measurement of fast dynamics at the nanometer scale.

We present an alternative approach to pump-probe spectroscopy for measuring fast charge dynamics with an atomic force microscope (AFM). Our approach is based on coherent multifrequency lock-in measurement of the intermodulation between a mechanical drive and an optical or electrical excitation. In response to the excitation, the charge dynamics of the sample is reconstructed by fitting a theoretical model to the measured frequency spectrum of the electrostatic force near resonance of the AFM cantilever. We discuss the time resolution, which in theory is limited only by the measurement time, but in practice is of order 1 ns for standard cantilevers and imaging speeds. We verify the method with simulations and demonstrate it with a control experiment, achieving a time resolution of 30 ns in ambient conditions, limited by thermal noise.

Calibrating torsional eigenmodes of micro-cantilevers for dynamic measurement of frictional forces.

Non-invasive thermal noise calibration of both torsional and flexural eigenmodes is performed on numerous cantilevers of 10 different types. We show that for all tipless and short-tipped cantilevers, the ratio of torsional to flexural mode stiffness is given by the ratio of their resonant frequency times a constant, unique to that cantilever type. By determining this constant, we enable a calibration of the torsional eigenmode, starting from a calibration of the flexural eigenmode. Our results are well motivated from beam theory, and we verify them with finite element simulation.

Image reversal for direct electron beam patterning of protein coated surfaces.

Electron beam lithography (EBL) is used to create surfaces with protein patterns, which are characterized by immunofluorescence and atomic force microscopies. Both negative and positive image processes are realized by electron beam irradiation of proteins absorbed on a silicon surface, where image reversal is achieved by selectively binding a second species of protein to the electron beam exposed areas on the first protein layer. Biofunctionality at the cellular level was established by culturing cortical cells on patterned lines of fibronectin adsorbed on a bovine serum albumin background for 7 days in culture.

Electron beam patterning of fibronectin nanodots that support focal adhesion formation.

Nanodots of fibronectin which have radii as small as 100 nm and are biofunctional at the cellular level, can be rapidly fabricated in arbitrary spatial patterns using a technique based on electron beam exposure of a protein monolayer with subsequent backfilling of a second protein species.

Spatial and temporal distribution of phase slips in Josephson junction chains.

The Josephson effect, tunnelling of a supercurrent through a thin insulator layer between two superconducting islands, is a phenomena characterized by a spatially distributed phase of the superconducting condensate. In recent years, there has been a growing focus on Josephson junction devices particularly for the applications of quantum metrology and superconducting qubits. In this study, we report the development of Josephson junction circuit formed by serially connecting many Superconducting Quantum Interference Devices, SQUIDs. We present experimental measurements as well as numerical simulations of a phase-slip center, a SQUID with weaker junctions, embedded in a Josephson junction chain. The DC transport properties of the chain are the result of phase slips which we simulate using a classical model that includes linear external damping, terminating impedance, as well as internal nonlinear quasiparticle damping. We find good agreement between the simulated and the experimental current voltage characteristics. The simulations allow us to examine the spatial and temporal distribution of phase-slip events occurring across the chains and also the existence of travelling voltage pulses which reflect at the chain edges.

Substrate effects in poly(ethylene glycol) self-assembled monolayers on granular and flame-annealed gold.

Poly(ethylene glycol) (PEG) self-assembled monolayers (SAMs) are surface coatings that efficiently prevent nonspecific adhesion of biomolecules to surfaces. Here, we report on SAM formation of the PEG thiol CH3O(CH2CH2O)17NHCO(CH2)2SH (PEG(17)) on three types of Au films: thermally evaporated granular Au and two types of Au films from hydrogen flame annealing of granular Au, Au(111), and Au silicide. The different Au surfaces clearly affects the morphology and mechanical properties of the PEG(17) SAM, which is shown by AFM topographs and force distance curves. The two types of SAMs found on flame-annealed Au were denoted "soft" and "hard" due to their difference in stiffness and resistance to scratching by the AFM probe. With the aim of nanometer scale patterning of the PEG(17), the SAMs were exposed by low energy (1 kV) electron beam lithography (EBL). Two distinctly different types of behaviour were observed on the different types of SAM; the soft PEG(17) SAM was destroyed in a self-developing process while material deposition was dominant for the hard PEG(17) SAM.

Imaging high-speed friction at the nanometer scale.

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales. Understanding its microscopic origin requires methods for measuring force on nanometer-scale asperities sliding at velocities reaching centimetres per second. Despite enormous advances in experimental technique, this combination of small length scale and high velocity remain elusive. We present a technique for rapidly measuring the frictional forces on a single asperity over a velocity range from zero to several centimetres per second. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to smooth sliding friction. We explain measurements on graphite using a modified Prandtl-Tomlinson model, including the damped elastic deformation of the asperity. With its improved force sensitivity and small sliding amplitude, our method enables rapid and detailed surface mapping of the velocity dependence of frictional forces with less than 10 nm spatial resolution.

A virtual instrument to standardise the calibration of atomic force microscope cantilevers.

Atomic force microscope (AFM) users often calibrate the spring constants of cantilevers using functionality built into individual instruments. This calibration is performed without reference to a global standard, hindering the robust comparison of force measurements reported by different laboratories. Here, we describe a virtual instrument (an internet-based initiative) whereby users from all laboratories can instantly and quantitatively compare their calibration measurements to those of others-standardising AFM force measurements-and simultaneously enabling non-invasive calibration of AFM cantilevers of any geometry. This global calibration initiative requires no additional instrumentation or data processing on the part of the user. It utilises a single website where users upload currently available data. A proof-of-principle demonstration of this initiative is presented using measured data from five independent laboratories across three countries, which also allows for an assessment of current calibration.

Improving image contrast and material discrimination with nonlinear response in bimodal atomic force microscopy.

Atomic force microscopy has recently been extented to bimodal operation, where increased image contrast is achieved through excitation and measurement of two cantilever eigenmodes. This enhanced material contrast is advantageous in analysis of complex heterogeneous materials with phase separation on the micro or nanometre scale. Here we show that much greater image contrast results from analysis of nonlinear response to the bimodal drive, at harmonics and mixing frequencies. The amplitude and phase of up to 17 frequencies are simultaneously measured in a single scan. Using a machine-learning algorithm we demonstrate almost threefold improvement in the ability to separate material components of a polymer blend when including this nonlinear response. Beyond the statistical analysis performed here, analysis of nonlinear response could be used to obtain quantitative material properties at high speeds and with enhanced resolution.

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip-surface interactions.

We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a single-point force measurement by using a multimodal drive and its accuracy is independent of the unknown physical amplitude of a higher eigenmode.