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Tuning friction atom-by-atom in an ion-crystal simulator

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Science  05 Jun 2015:
Vol. 348, Issue 6239, pp. 1115-1118
DOI: 10.1126/science.1261422
  • Fig. 1 Ion-crystal simulator of stick-slip friction.

    (A) Synthetic nanofriction interface between a Coulomb crystal of 174Yb+ ions and an optical lattice, with single-ion-resolving microscope. The typical ion spacing is 6 μm, and the lattice period is a = 185 nm. In the bottom illustration of the corrugated potential, the lattice period and the corrugation are strongly exaggerated. (B) Stick-slip results from bistability, illustrated here for a single ion. We linearly ramp a shear force, causing the ion to jump between the minima, and we extract its position from its fluorescence, proportional to the lattice potential energy: (no. 1) ion initialized in the left site; (no. 2) the applied force pushes the ion up the lattice potential, eventually causing the slip; (no. 3) immediately after the slip, the ion is optically recooled and localizes to the right site; (no. 4), (no. 5), and (no. 6), the force ramp reverses and the ion sticks at the right site before slipping back to the left. Slips are identified by maxima in the ion’s fluorescence.

  • Fig. 2 Measured stick-slip hysteresis cycle of a single ion.

    (A) Fluorescence versus applied force during the forward transport (green squares) and reverse transport (red circles), showing hysteresis that is used to measure the maximum static friction force Embedded Image. The stages of the stick-slip process (no. 1) to (no. 6) correspond to the illustrations in Fig. 1B. The bold data points indicate the ion’s position before a slip, and only those data are used to reconstruct the force-displacement curve. (B) The force-displacement hysteresis loop encloses an area equal to twice the dissipated energy per slip Embedded Image. The unit Embedded Image of the applied force corresponds to Embedded Image; here, Embedded Image. (C) The static friction force disappears for corrugations Embedded Image and increases linearly with corrugation for Embedded Image, in excellent agreement with the Prandtl-Tomlinson model with no free parameters (red solid line). In (A), error bars indicate 1 SD, and for (B) and (C), statistical error bars are smaller than the symbols. The data in (A) and (B) were measured at Embedded Image.

  • Fig. 3 Changing friction in a 3-ion crystal from maximal to nearly frictionless (superlubric) by structural mismatch.

    In the matched case (top), the ions stick and slip synchronously during transport (the observed photon detection rate for each ion, expressed in color, is maximum when the given ion slips over a potential barrier). The large hysteresis corresponds to large friction, shown here for the middle ion. In the mismatched case (bottom), the different ions slide over lattice barriers one at a time, and the friction and hysteresis nearly vanish.

  • Fig. 4 The dependence of friction on object-substrate structural matching for different crystal sizes.

    Measured maximum static friction force Embedded Image for N = 2, 3, and 6 ions (red squares, green circles, and blue diamonds, respectively), averaged over the ions and normalized to Embedded Image as measured for a single trapped ion. Error bars represent 1 SD. Simulations for N = 2, 3, and 6 are shown for Embedded Image (red, green, and blue dashed lines, respectively) and finite q-dependent temperature (red, green, and blue solid lines). Simulation parameters are chosen to match known experimental parameters: the measured temperature Embedded Image (corresponding to 48 μK); the optical-lattice depth Embedded Image (equivalent to Embedded Image); the driving velocity Embedded Image; and the recooling rate constant from laser cooling Embedded Image. Only the q = 0 temperature is fitted, yielding Embedded Image (corresponding to 144 μK) for all the values of N shown [see (28)].

Supplementary Materials

  • Tuning friction atom-by-atom in an ion-crystal simulator

    Alexei Bylinskii, Dorian Gangloff, Vladan Vuletić

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