Imaging high-speed friction at the nanometer scale

Friction is a complicated phenomenon involving nonlinear dynamics at different length and time scales[1, 2]. The microscopic origin of friction is poorly understood, due in part to a lack of methods for measuring the force on a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4] Despite enormous advance in experimental techniques[5], this combination of small length scale and high velocity remained illusive. Here we present a technique for rapidly measuring the frictional forces on a single asperity (an AFM tip) over a velocity range from zero to several cm/s. At each image pixel we obtain the velocity dependence of both conservative and dissipative forces, revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We explain measurements on graphite using a modified Prandtl-Tomlinson model that takes into account the damped elastic deformation of the asperity. With its greatly improved force sensitivity and very small sliding amplitude, our method enables rapid and detailed surface mapping of the full velocity-dependence of frictional forces with less than 10~nm spatial resolution.Comment: 7 pages, 4 figure

Intermodulation electrostatic force microscopy for imaging surface photo-voltage

We demonstrate an alternative to Kelvin Probe Force Microscopy for imaging surface potential. The open-loop, single-pass technique applies a low-frequency AC voltage to the atomic force microscopy tip while driving the cantilever near its resonance frequency. Frequency mixing due to the nonlinear capacitance gives intermodulation products of the two drive frequencies near the cantilever resonance, where they are measured with high signal to noise ratio. Analysis of this intermodulation response allows for quantitative reconstruction of the contact potential difference. We derive the theory of the method, validate it with numerical simulation and a control experiment, and we demonstrate its utility for fast imaging of the surface photo-voltage on an organic photo-voltaic material.Comment: 4 pages, 3 figures, peer-reviewed, preprin

Seeking the Local Convergence Depth. The Abell Cluster Dipole Flow to 200 Mpc/h

We have obtained new Tully-Fisher (TF) peculiar velocity measurements for 52 Abell galaxy clusters distributed throughout the sky between ~ 50 and 200 Mpc/h.The measurements are based on I band photometry and optical rotation curves for a sample of 522 spiral galaxies, from which an accurate TF template relation has been constructed. Individual cluster TF relations are referred to the template to compute cluster peculiar motions. The reflex motion of the Local Group of galaxies is measured with respect to the reference frame defined by our cluster sample and the distant portion of the Giovanelli et al. (1998) cluster set. We find the Local Group motion in this frame to be 565+/-113 km/s in the direction (l,b)=(267,26)+/-10 when peculiar velocities are weighted according to their errors. After optimizing the dipole calculation to sample equal volumes equally, the vector is 509+/-195 km/s towards (255,33)+/-22. Both solutions agree, to within 1-sigma or better, with the Local Group motion as inferred from the cosmic microwave background (CMB) dipole. Thus, the cluster sample as a whole moves slowly in the CMB reference frame, its bulk flow being at most 200 km/s.Comment: 11 pages, uses AAS LaTeX; to appear in the Astrophysical Journal Letter

Characterization and benchmarking of a phase-sensitive two-qubit gate using direct digital synthesis

We implement an iSWAP gate with two transmon qubits using a flux-tunable coupler. Precise control of the relative phase of the qubit-control pulses and the parametric-coupler drive is achieved with a multi-channel instrument called Presto using direct digital synthesis (DDS), a promising technique for scaling up quantum systems. We describe the process of tuning and benchmarking the iSWAP gate, where the relative phase of the pulses is controlled via software. We perform the iSWAP gate in 290 ns, validate it with quantum-state tomography, and measure 2\% error with interleaved randomized benchmarking

On modeling and measuring viscoelasticity with dynamic Atomic Force Microscopy

The interaction between a rapidly oscillating atomic force microscope tip and a soft material surface is described using both elastic and viscous forces with a moving surface model. We derive the simplest form of this model, motivating it as a way to capture the impact dynamics of the tip and sample with an interaction consisting of two components: interfacial or surface force, and bulk or volumetric force. Analytic solutions to the piece-wise linear model identify characteristic time constants, providing a physical explanation of the hysteresis observed in the measured dynamic force quadrature curves. Numerical simulation is used to fit the model to experimental data and excellent agreement is found with a variety of different samples. The model parameters form a dimensionless impact-rheology factor, giving a quantitative physical number to characterize a viscoelastic surface that does not depend on the tip shape or cantilever frequency.Comment: 13 pages, 7 figure

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

Peculiar Velocities of Clusters in Cold Dark Matter Models

Recently, peculiar velocity measurements became available for a new sample of galaxy clusters, hereafter the SCI sample. From an accurately calibrated Tully-Fisher relation for spiral galaxies, we compute the rms peculiar velocity, Vrms, and compare it with the linear theory predictions of COBE-normalized low-density and open cold dark matter models (ΛCDM and OCDM, respectively). Confidence levels for model rejection are estimated using a Monte Carlo procedure in order to generate a large ensemble of artificial data sets for each model. Following Zaroubi et al., we express our results in terms of constraints on the (Ω0, npr, h) parameter space. Such constraints turn into σ8Ω00.6 = 0.50−0.14+0.25 at the 90% confidence level, thus in agreement with results from cluster abundance. We show that our constraints are also consistent with those implied by the shape of the galaxy power spectrum within a rather wide range for the values of the model parameters. Finally, we point out that our findings disagree at about the 3 σ level with respect to those by Zaroubi et al., based on the Mark III catalog, which tend to prefer larger Ω0 values within the CDM class of models

Correlation Analysis of SFI Peculiar Velocities

We present results of a statistical analysis of the SFI catalog of peculiar velocities, a recently completed survey of spiral field galaxies with I-band Tully-Fisher distances. The velocity field statistic utilized is the velocity correlation function, ψ1(r), originally introduced by Górski et al. The analysis is performed in redshift space so as to circumvent potential ambiguities connected with inhomogeneous Malmquist bias corrections. The results from the SFI sample are compared with linear-theory predictions for a class of cosmological models. We generate a large set of mock samples, extracted from N-body simulations, which are used to assess the reliability of our analysis and to estimate the associated uncertainties. We assume a class of cold dark matter–like power spectrum models, specified by σ8, the rms fluctuation amplitude within a sphere of 8 h-1 Mpc radius, and by the shape parameter, Γ. Defining η8 = σ8Ω, we find that the measured ψ1(r) implies a degenerate constraint in the (η8, Γ)-plane, with η8 = 0.3 ± 0.1(Γ/0.2)0.5 at the 2 σ level for the inverse Tully-Fisher (ITF) calibration presented in this paper. We investigate how much this constraint changes as we account for uncertainties in the analysis method and uncertainties in the distance indicator, and we consider alternative ITF calibrations. We find that both changing the error-weighting scheme and selecting galaxies according to different limiting line widths has a negligible effect. On the contrary, the model constraints are quite sensitive to the ITF calibration. The other ITF calibrations, by Giovanelli et al. and da Costa et al. both yield, for Γ = 0.2, a best-fit value of η8 0.6