Velocity tuning of friction with two trapped atoms

Journal name:
Nature Physics
Year published:
Published online

Our ability to control friction remains modest, as our understanding of the underlying microscopic processes is incomplete1, 2, 3. Atomic force experiments4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 have provided a wealth of results on the dependence of nanofriction on structure5, 6, velocity7, 8, 9, 10 and temperature11, 12, 13, but limitations in the dynamic range, time resolution, and control at the single-atom level have hampered a description from first principles3. Here, using an ion-crystal system with single-atom, single-substrate-site spatial and single-slip temporal resolution15, 16, we measure the friction force over nearly five orders of magnitude in velocity, and contiguously observe four distinct regimes, while controlling temperature and dissipation. We elucidate the interplay between thermal and structural lubricity for two coupled atoms, and provide a simple explanation in terms of the Peierls–Nabarro potential17. This extensive control at the atomic scale enables fundamental studies of the interaction of many-atom surfaces, possibly into the quantum regime.

At a glance


  1. Friction interface with trapped atomic ions in an optical lattice.
    Figure 1: Friction interface with trapped atomic ions in an optical lattice.

    a,b, Model of the friction interface; one Yb+ ion of mass m = 2.9 × 10−25kg (or two coupled ions separated by a distance d ≈ 5μm) is confined in a Paul trap27 with a spring constant K = mω02 (ω0/2π = 363kHz), whose equilibrium point is translated at a constant velocity v by applying a time-varying electric field. An optical standing wave, detuned by ~12GHz from the atomic 2S1/2 right arrow 2P1/2 transition, creates a sinusoidal potential of periodicity a = 185nm and depth Ul/h ≈ 20MHz along the radiofrequency nodal line of the Paul trap16. The ion is kept at a temperature T ≈ 40μK by means of continuous laser cooling with a dissipation rate constant γ = τc−1 ≈ 104s−1. c,d, Temperature dependence of stick–slip friction. At low temperature or high velocity, the ion (red solid circle) sticks in its initial well, corresponding to a rise in its scattered fluorescence (1–2, dark blue open circles) until it slips to the next well, and the added energy is dissipated through laser cooling (3, dark blue open circles). The ion fluorescence is highest when the slip occurs. At high temperature or low velocity, the ion thermalizes over the energy barrier (1–2), and so smoothly transitions to the next well without frictional dissipation (3). If the trap translation direction is reversed, maximum hysteresis is observed in the low-temperature or high-velocity regime (dark open symbols). A reduced hysteresis is present for an intermediate temperature or velocity regime (light filled symbols). The friction force F is measured by means of the separation 2F between the slips in the hysteresis loop. Error bars are statistical and represent one standard deviation.

  2. Velocity dependence of stick-slip friction for one atom.
    Figure 2: Velocity dependence of stick–slip friction for one atom.

    The transport time a/v should be compared to two timescales: the thermal hopping time between two lattice wells, given by τth = τ0exp(UB/kBT) for a maximum barrier height UB (where kB is the Boltzmann constant and τ0(τc, ω0, ωl) is the hopping attempt time23, 24); and the recooling time after a slip τc. a, Here τth ≈ 10ms and τc ≈ 100μs. Four regimes of friction are observed. The friction force is normalized by its zero-temperature maximum value for η = 2.2, Fη=2.2 ≈ 0.36πUl/a. Here Ul/h = 9.5MHz and kBT/Ul = 0.15(4). The solid orange line shows the expected result , where vth  ~ 1mms−1, from an analytical model in the thermal activation regime3, 23, 24. Similarly in the velocity weakening regime, we model the friction as (orange dotted line), where kBT/Ul = 0.3 and vc = a/τc ~ 2mms−1 (Supplementary Information). The Langevin simulation (dashed green line) is in good agreement with the data over all four velocity regimes for parameters η = 2.2, kBT/Ul = 0.15, τc = 100μs. b, At a larger lattice depth Ul/h = 20MHz, where η = 4.6, increasing the temperature from kBT/Ul = 0.04(1) (blue squares) to kBT/Ul = 0.17(1) (red diamonds) reduces the friction in the thermal activation region 10−5ms−1 v 10−3ms−1 while leaving the friction plateau in the region 10−3ms−1 v 10−2ms−1 almost unaffected. Here, τc ≈ 50μs. The friction force is normalized by its zero-temperature maximum value for η = 4.6, Fη=4.6 ≈ 0.61πUl/a. Solid lines show the expected results from the analytical thermal activation model. Data from a, normalized to Fη=4.6 is shown as open black circles. Langevin simulations (inset, solid lines) are in good agreement with the data for parameters η = 4.6, kBT/Ul = 0.05 (blue), kBT/Ul = 0.13 (red), τc = 50μs. Error bars are statistical and represent one standard deviation.

  3. Thermolubricity for a single atom.
    Figure 3: Thermolubricity for a single atom.

    In the thermal drift regime τth less double a/v, the friction force is proportional to exp(Ul/kBT), whereas it depends only weakly on temperature in the friction plateau regime23 τth double greater than a/v. We vary temperature from kBT/Ul = 0.06 to kBT/Ul = 0.4, and show the friction force on a logarithmic scale against 1/T. We fit data to the model F/Fη=4.6 = fexp(cUl/kBT), where f is a free parameter, and c represents the fitted sensitivity to temperature and is close to unity in the thermal drift regime. For a high velocity (v ≈ 1mms−1) corresponding to the friction plateau regime (green), friction is almost constant for Ul/kBT ≥ 5, and the fit to the model in this temperature range (dashed green line) gives c = 0.016—that is, a very weak temperature dependence. For a low velocity (v ≈ 40μms−1) close to the regime of thermal drift (orange), the friction force is sensitive to temperature, and the fit to the model (red dashed line) gives c = 0.17. Experimental parameters are η = 4.6, Ul/h = 20MHz and τc ≈ 50μs. Error bars are statistical and represent one standard deviation.

  4. Structural and thermal lubricity of two atoms.
    Figure 4: Structural and thermal lubricity of two atoms.

    ac, Velocity dependence of the friction force for two ions, for η = 4.6. a, In the matched case (red circles), where the ion spacing is an integer multiple of the lattice period a, for kBT/Ul = 0.055(10) the data agree with one ion at approximately the same temperature (blue squares), and reach a maximal value near Fη=4.6. Langevin simulations (solid lines) are in good agreement with data for η = 4.6, kBT/Ul = 0.05. b, In the matched case (red diamonds) for a temperature of kBT/Ul = 0.15(2), the maximal friction is ~0.7Fη=4.6. By comparison, the friction for the mismatched case (green circles), where the two ions at their unperturbed position experience opposite forces by the optical lattice, at the same temperature of kBT/Ul = 0.15(3), reaches a maximum of ~0.15Fη=4.6. Finite-temperature Langevin simulations (solid lines) are in good agreement with data for η = 4.6, kBT/Ul = 0.15. c, The ratio of friction forces in the matched and mismatched cases (black circles, 3-point running average) is unity in the low-velocity thermal drift regime, and constant in the high-velocity friction plateau regime, where its value ~4.8 is mostly due to structural lubricity, in good agreement with Langevin simulations (solid gold line). Although barely visible in the data, the peak in the simulations is due to structurally induced thermolubricity: a window of velocities for which the structural friction reduction is enhanced by thermal activation over a reduced energy barrier . d,e, Energy potential landscape for two interacting atoms. In the mismatched case (e), the energy barrier between the wells is reduced by a factor of ~3.7 and the ions pass the barrier one at a time (inset), compared to the matched case UB (d) where the ions pass the barrier simultaneously (inset). At fixed T for a single ion in the friction plateau regime, this barrier reduction would lead to a thermal friction reduction of ~1.4, as can be inferred from the green data in Fig. 3. The expected total reduction of 3.7 × 1.4 = 5.2 is in good agreement with the observed reduction of ~4.8. Error bars are statistical and represent one standard deviation.


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Author information

  1. These authors contributed equally to this work.

    • Dorian Gangloff &
    • Alexei Bylinskii


  1. Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Dorian Gangloff,
    • Alexei Bylinskii,
    • Ian Counts &
    • Vladan Vuletić
  2. Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea

    • Wonho Jhe


D.G., A.B. and V.V. designed the experiments. D.G., A.B. and I.C. collected and analysed data. All authors discussed the results and contributed to the manuscript preparation.

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