Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2108.07635 · Physical Review Research

Quantum nanofriction in trapped ion chains with a topological defect

Lars Timm, L. -A. Rüffert, Hendrik Weimer, Luis Santos, T. E. Mehlstäubler

Published Nov 29, 2021• 10 citations
arXivHTMLPDF

Abstract

Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.

DOI
10.1103/physrevresearch.3.043141

Related papers

Kinks and nanofriction: Structural phases in few-atom chains

Dorian A. Gangloff, Alexei Bylinskii, Vladan Vuletić

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.

arXiv:1910.07088•Physical Review Research•Mar 30, 2020•15 citations

Trapping of Topological-Structural Defects in Coulomb Crystals

Manuel Mielenz, J. Brox, S. Kahra +5 more

We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.

arXiv:1211.6867•Physical Review Letters•Mar 28, 2013•110 citations

Nanofriction in Cavity Quantum Electrodynamics

Thomás Fogarty, Cecilia Cormick, Haggai Landa +3 more

The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions' phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-the-art setups of cavity quantum electrodynamics.

arXiv:1504.00275•Physical Review Letters•Dec 1, 2015•26 citations

Deterministic engineering of topological defects in two-dimensional single-species ion Coulomb crystals

L. -A. Rüffert, Hemanth Kalathur, Tanja E. Mehlstäubler

We propose and numerically demonstrate a deterministic protocol for preparing and tailoring topological defects in two-dimensional single-species Coulomb crystals confined in radio-frequency traps. In conventional finite-rate quenches through the linear-to-zigzag transition, defects form stochastically from independently chosen broken-symmetry domains, and the quench rate controls the resulting domain structure. We instead use an initial three-dimensional helix structure and planarize it into a deterministic defected state. We demonstrate that the number and approximate axial positions of kinks are encoded by the projected nodes of the initial helix. We find that selected helices can remain on metastable finite-winding branches during planarization and yield reproducible single- or multi-kink states, even in the adiabatic limit. Using the quench rate as an additional control parameter substantially enlarges the set of precursor helices that result in defected states, as a fast planarization can prevent reordering during the quench and freeze in the pre-existing domain pattern. After planarization, the survival and mutual interaction of the defects are governed by their effective Peierls--Nabarro potential landscape. By numerically isolating the interaction energy for the two defect types, we find that the interaction of extended kinks is attractive over the investigated parameter range, while odd kinks exhibit a short-range repulsive barrier tunable by the anisotropy of the trapping potential $α$. Finally, we introduce an experimentally motivated post-selection scheme in which $α$ is used to selectively destabilize, annihilate, or convert targeted defects. Our results provide a route to deterministic single- and multi-kink preparation in single-species Coulomb crystals, enabling controlled studies of defect interactions, transport, and nanofriction.

arXiv:2609.10425•Sep 9, 2026•0 citations

Injection and nucleation of topological defects in the quench dynamics of the Frenkel-Kontorova model

Oksana Chelpanova, Shane P. Kelly, Giovanna Morigi +2 more

Abstract Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments.

arXiv:2210.14904•Europhysics Letters (EPL)•Jun 28, 2023•8 citations

Quantum structural phase transition in chains of interacting atoms

Efrat Shimshoni, Giovanna Morigi, Shmuel Fishman

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 $T$. We focus in particular on a trapped-ion system and estimate the implied limitations on $T$ and on the interparticle distance. We conclude that the experimental observation of the quantum critical behavior is, in principle, accessible.

arXiv:1012.4332•Physical Review A•Mar 14, 2011•37 citations
Trapped ion systems constitute a well controllable scenario for the study and emulation of nanofriction, and in particular of Frenkel-Kontorova-like models. This is in particular the case when a topological defect is created in a zigzag ion Coulomb crystal, which results in an Aubry transition from free sliding to pinned phase as a function of the trap aspect ratio. We explore the quantum effects of the Aubry transition by means of an effective simplified model, in which the defect is treated like a single quantum particle that experiences an effective Peierls-Nabarro potential and a position-dependent mass. We demonstrate the relevance of quantum tunneling in a finite range of aspect ratios close the critical point, showing that the quantum effects may be observed in the kink dynamics for sufficiently low temperatures. Finally, we discuss the requirements to reveal quantum effects at the Aubry transition in future experiments on trapped ions.
We study experimentally and theoretically structural defects which are formed during the transition from a laser cooled cloud to a Coulomb crystal, consisting of tens of ions in a linear radio frequency trap. We demonstrate the creation of predicted topological defects ("kinks") in purely two-dimensional crystals and also find kinks which show novel dynamical features in a regime of parameters not considered before. The kinks are always observed at the center of the trap, showing a large nonlinear localized excitation, and the probability of their occurrence saturates at ∼0.5. Simulations reveal a strong anharmonicity of the kink's internal mode of vibration, due to the kink's extension into three dimensions. As a consequence, the periodic Peierls-Nabarro potential experienced by a discrete kink becomes a globally confining potential, capable of trapping one cooled defect at the center of the crystal.
The dynamics of cold trapped ions in a high-finesse resonator results from the interplay between the long-range Coulomb repulsion and the cavity-induced interactions. The latter are due to multiple scatterings of laser photons inside the cavity and become relevant when the laser pump is sufficiently strong to overcome photon decay. We study the stationary states of ions coupled with a mode of a standing-wave cavity as a function of the cavity and laser parameters, when the typical length scales of the two self-organizing processes, Coulomb crystallization and photon-mediated interactions, are incommensurate. The dynamics are frustrated and in specific limiting cases can be cast in terms of the Frenkel-Kontorova model, which reproduces features of friction in one dimension. We numerically recover the sliding and pinned phases. For strong cavity nonlinearities, they are in general separated by bistable regions where superlubric and stick-slip dynamics coexist. The cavity, moreover, acts as a thermal reservoir and can cool the chain vibrations to temperatures controlled by the cavity parameters and by the ions' phase. These features are imprinted in the radiation emitted by the cavity, which is readily measurable in state-of-the-art setups of cavity quantum electrodynamics.
We propose and numerically demonstrate a deterministic protocol for preparing and tailoring topological defects in two-dimensional single-species Coulomb crystals confined in radio-frequency traps. In conventional finite-rate quenches through the linear-to-zigzag transition, defects form stochastically from independently chosen broken-symmetry domains, and the quench rate controls the resulting domain structure. We instead use an initial three-dimensional helix structure and planarize it into a deterministic defected state. We demonstrate that the number and approximate axial positions of kinks are encoded by the projected nodes of the initial helix. We find that selected helices can remain on metastable finite-winding branches during planarization and yield reproducible single- or multi-kink states, even in the adiabatic limit. Using the quench rate as an additional control parameter substantially enlarges the set of precursor helices that result in defected states, as a fast planarization can prevent reordering during the quench and freeze in the pre-existing domain pattern. After planarization, the survival and mutual interaction of the defects are governed by their effective Peierls--Nabarro potential landscape. By numerically isolating the interaction energy for the two defect types, we find that the interaction of extended kinks is attractive over the investigated parameter range, while odd kinks exhibit a short-range repulsive barrier tunable by the anisotropy of the trapping potential ααα. Finally, we introduce an experimentally motivated post-selection scheme in which ααα is used to selectively destabilize, annihilate, or convert targeted defects. Our results provide a route to deterministic single- and multi-kink preparation in single-species Coulomb crystals, enabling controlled studies of defect interactions, transport, and nanofriction.
Abstract Topological defects have strong impact on both elastic and inelastic properties of materials. In this article, we investigate the possibility to controllably inject topological defects in quantum simulators of solid state lattice structures. We investigate the quench dynamics of a Frenkel-Kontorova chain, which is used to model discommensurations of particles in cold atoms and trapped ionic crystals. The interplay between an external periodic potential and the inter-particle interaction makes lattice discommensurations, the topological defects of the model, energetically favorable and can tune a commensurate-incommensurate structural transition. Our key finding is that a quench from the commensurate to incommensurate phase causes a controllable injection of topological defects at periodic time intervals. We employ this mechanism to generate quantum states which are a superposition of lattice structures with and without topological defects. We conclude by presenting concrete perspectives for the observation and control of topological defects in trapped ion experiments.
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.