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arXiv:1910.07088 · Physical Review Research

Kinks and nanofriction: Structural phases in few-atom chains

Dorian A. Gangloff, Alexei Bylinskii, Vladan Vuletić

Published Mar 30, 2020• 15 citations
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Abstract

This paper reports the observation of a structural phase transition of a crystal of trapped ions in an optical lattice as captured by the appearance of a kink defect. The authors observe the stick-slip dynamics of the chain atom by atom and find that a critical degree of incommensurability is required for kinks to form.
DOI
10.1103/physrevresearch.2.013380

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The transition between the linear phase and zigzag phase in an ion trap is widely used to study the mechanism of the second-order continuous phase transition. For a linear ion chain, during the quenching across the critical point, kinks are formed. The relation between the density of kinks and quenching rate can be described by the Kibble-Zurek mechanism. In this work, we consider a one-dimensional trapped-ion chain with the motion on the phase-transition plane. Using the interacting Langevin equation, we show that when one ion is kicked out from the chain, the off-axis action caused by this ion will propagate to others one by one with a defined velocity. This velocity will be the same as the sound velocity in some extreme cases but has obviously different meaning. In the presence of finite temperature, which is modeled using a many-body stochastic Langevin equation to unveil a microscopic mechanism for kink formations in this model, we find that the kink can be formed when the diffusion radius is larger than the mean displacement of the ions along the radial direction. This criterion provides an alternative mode for the formation of kinks in realistic experiments. The predictions based on this mechanism can be qualitatively consistent with those from the Kibble-Zurek mechanism in homogeneous structures; however, the microscopic details, such as kink formation and kink disappearance can be seen much clearer in our simplified model.
We show that a chain of trapped ions embedded in microtraps generated by an optical lattice can be used to study oscillator models related to dry friction and energy transport. Numerical calculations with realistic experimental parameters demonstrate that both static and dynamic properties of the ion chain change significantly as the optical lattice power is varied. Finally, we lay out an experimental scheme to use the spin degree of freedom to probe the phase space structure and quantum critical behavior of the ion chain.
A quasi-one-dimensional system of trapped, repulsively interacting atoms (e.g., an ion chain) exhibits a structural phase transition from a linear chain to a zigzag structure, tuned by reducing the transverse trap potential or increasing the particle density. Since it is a one-dimensional transition, it takes place at zero temperature and therefore quantum fluctuations dominate. In Fishman et al. [Phys. Rev. B 77, 064111 (2008)] it was shown that the system close to the linear-zigzag instability is described by a ${\ensuremath{\phi}}^{4}$ model. We propose a mapping of the ${\ensuremath{\phi}}^{4}$ field theory to the well-known Ising chain in a transverse field, which exhibits a quantum critical point. Based on this mapping, we estimate the quantum critical point in terms of the system parameters. This estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs and which has a finite, measurable deviation from the critical point evaluated within the classical theory. A measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures TTT. We focus in particular on a trapped-ion system and estimate the implied limitations on TTT and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is, in principle, accessible.
A string of trapped ions at zero temperature exhibits a structural phase transition to a zigzag structure, tuned by reducing the transverse trap potential or the interparticle distance. The transition is driven by transverse, short wavelength vibrational modes. We argue that this is a quantum phase transition, which can be experimentally realized and probed. Indeed, by means of a mapping to the Ising model in a transverse field, we estimate the quantum critical point in terms of the system parameters, and find a finite, measurable deviation from the critical point predicted by the classical theory. A measurement procedure is suggested which can probe the effects of quantum fluctuations at criticality. These results can be extended to describe the transverse instability of ultracold polar molecules in a one-dimensional optical lattice.
The electronic and motional degrees of freedom of trapped ions can be controlled and coherently coupled on the level of individual quanta.Assembling complex quantum systems ion by ion while keeping this unique level of control remains a challenging task.For many applications, linear chains of ions in conventional traps are ideally suited to address this problem.However, driven motion due to the magnetic or radio-frequency electric trapping fields sometimes limits the performance in one dimension and severely affects the extension to higher-dimensional systems.Here, we report on the trapping of multiple barium ions in a single-beam optical dipole trap without radio-frequency or additional magnetic fields.We study the persistence of order in ensembles of up to six ions within the optical trap, measure their temperature, and conclude that the ions form a linear chain, commonly called a one-dimensional Coulomb crystal.As a proof-of-concept demonstration, we access the collective motion and perform spectrometry of the normal modes in the optical trap.Our system provides a platform that is free of driven motion and combines advantages of optical trapping, such as state-dependent confinement and nanoscale potentials, with the desirable properties of crystals of trapped ions, such as long-range interactions featuring collective motion.Starting with small numbers of ions, it has been proposed that these properties would allow the experimental study of many-body physics and the onset of structural quantum phase transitions between one-and two-dimensional crystals.
The vibrations of a chain of trapped ions can be considered, under suitable experimental conditions, as an ensemble of interacting phonons, whose quantum dynamics is governed by a Bose-Hubbard Hamiltonian. In this work we study the quantum phases which appear in this system, and show that thermodynamical properties, such as critical parameters and critical exponents, can be measured in experiments with a limited number of ions. In addition to that, interacting phonons in trapped ions offer us the possibility to access regimes which are difficult to study with ultracold bosons in optical lattices, such as models with attractive or site-dependent phonon-phonon interactions.