Nanofriction in cold ion traps

ARTICLE Received 10 Nov 2010 | Accepted 7 Feb 2011 | Published 15 Mar 2011 DOI: 10.1038/ncomms1230 Nanofriction in cold ion traps A. Benassi1,2, A. Vanossi1,2 & E. Tosatti1,2,3 Sliding friction between crystal lattices and the physics of cold ion traps are so far nonoverlapping fields. Two sliding lattices may either stick and show static friction or slip with dynamic friction; cold ions are known to form static chains, helices or clusters, depending on the trapping conditions. Here we show, based on simulations, that much could be learnt about friction by sliding, through, for example, an electric field, the trapped ion chains over a corrugated potential. Unlike infinite chains, in which the theoretically predicted Aubry transition to free sliding may take place, trapped chains are always pinned. Yet, a properly defined static friction still vanishes Aubry-like at a symmetric–asymmetric structural transition, found for decreasing corrugation in both straight and zig-zag trapped chains. Dynamic friction is also accessible in ringdown oscillations of the ion trap. Long theorized static and dynamic one-dimensional friction phenomena could thus become accessible in future cold ion tribology. 1 CNR-IOM Democritos National Simulation Center, Via Bonomea 265, I-34136 Trieste, Italy. 2 International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy. 3 International Centre for Theoretical Physics (ICTP), PO Box 586, I-34014 Trieste, Italy. Correspondence and requests for materials should be addressed to E.T. (email: ). NATURE COMMUNICATIONS | 2:236 | DOI: 10.1038/ncomms1230 | www.nature.com/naturecommunications © 2011 Macmillan Publishers Limited. All rights reserved. 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms1230 T he field of sliding friction has been recently revived because of experimental and theoretical advances especially connected with nanosystems, with brand new opportunities to grasp the underlying phenomena of this important and technologically relevant area. Unlike macroscopic friction, in which contact irregularities dominate, the nanoscale offers perfectly defined crystal lattice facets that can mutually slide. One fundamental piece of physics arising in this limit is the possibility of frictionless sliding when two perfect lattices are mutually incommensurate—their periodicities unrelated through any rational number—an idealized situation sometimes referred to as superlubric1. Graphite flakes sliding on graphite were, for example, shown to be pinned by static friction—the finite threshold force Fs necessary to provoke motion— when aligned, but to turn essentially free sliding once a rotation makes them incommensurate2. An additional prediction, rigorously proven for one-dimensional (1D) infinite harmonic chains sliding in a periodic potential (the ‘corrugation’ potential, in frictional language), is that the incommensurate vanishing of static friction will only occur as long as the sliding chain is sufficiently hard compared with the corrugation strength. Instead, when that strength exceeds a critical value, the chain becomes locked, or ‘pinned’, to the corrugation, thus developing static friction despite incommensurability. Unlike most conventional phase transitions, this celebrated Aubry transition3–6 involves no structural order parameter and no breaking of symmetry—just a change of phase space between the two states, the unpinned and the pinned one. The concept of pinned and unpinned states is by now qualitatively established in the sliding of real incommensurate 3D crystal surfaces7. Yet, the onset of static friction in the prototypical 1D chain, in which the Aubry transition is mathematically established, has never been experimentally validated. Even less is known about dynamic friction, about which we have no other insight than generic linear response8 and some data on 3D rare gas overlayers9, both suggesting a quadratic increase with corrugation. Cold atomic ions can form linear chains. Despite their mutual Coulomb repulsion, ions can be corralled inside effective potential traps generated by quadrupolar radio-frequency electrodes10. So far, cold ion chains raised interest in view of promising applications for spectroscopy11–13, frequency standards14,15, study and control of chemical reactions16 and quantum information17–20. We are concerned here with the possibility that they could be of use in the field of friction. In the rest of this work, explicitly simulated gedanken experiments will demonstrate that trapped cold ions may in fact represent an ideal system for future nanotribological studies addressing both static and dynamic friction. In static friction, the celebrated Aubry transition will become experimentally accessible for the first time. In dynamics, the friction rise with increasing corrugation should become measurable, giving new impulse to future theory work. Results Model and symmetry breaking transition. The low-temperature equilibrium geometry of trapped cold ions is determined by the aspect ratio asymmetry of the confining potential, according to the effective hamiltonian21,22 ⎧1 ⎫ N 1 e2 ⎪ ⎪ 2 2 + m[w ⊥ (xi + yi2 ) + w2 zi2 ]⎬ H 0 = ∑ ⎨ mri2 + ∑ 2 2 − r r ⎪⎭ j i ⎪ j ≠i i ⎩ (1) where ri = (xi, yi, zi) is the position of the ith ion, m its mass, e its charge and the three terms represent kinetic energy, Coulomb repulsion and the effective parabolic trapping potential, respectively, with transverse and longitudinal trapping frequencies ω⬜ and ω||. As is known experimentally23 and theoretically24,25, by decreasing the asymmetry aspect ratio R = ω||/ω⬜, the trap potential deforms 2 1D ion chain Trapping potential isosurface Laser-generated periodic potential Linear chain Zig-zag chain Figure 1 | Trapped ion chains over a periodic corrugated potential. (a,b) Sketch of the proposed ion trap configuration in a periodic potential; (c) sketch of the straight and zig-zag chain equilibrium geometries determined by different aspect ratios of the trapping quadrupolar potential. The lateral zig-zag amplitude has been artificially magnified. from spherical to cigar-shaped and the equilibrium ion geometry changes from 3D clusters to helices to chains, initially zig-zag and finally linear and straight along z, as shown in Figure 1c. As many as a hundred ions may be stabilized in a linear configuration, with a few μm ion–ion spacing a0, typical repulsion energy e 2/a0~3.3 K and temperatures below ~1 μK. An interesting observation was made by Garcia-Mata et al.26, that ion chains in an additional incommensurate periodic potential (produced, for example, by suitable laser beams) would, if only the spatial inhomogeneity of the trapping potential could be neglected, resemble precisely the 1D system in which an Aubry transition is expected as a function of corrugation strength. Unfortunately, the trapping potential itself introduces an additional and brutal break of translational invariance, at first sig (...truncated)