Dynamics of topological defects in ion Coulomb crystals

Partner, Heather L.; Nigmatullin, Ramil; Burgermeister, T.; Pyka, Karsten; Keller, Jonas; Retzker, Alex; Plenio, Martin B.

doi:10.1088/1367-2630/15/10/103013

Cited by 40 publications

(44 citation statements)

References 37 publications

(82 reference statements)

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“…In order to avoid long-range interactions between defects, one could exploit the properties of the more localized odd kinks. Calculations of the Peierls-Nabarro potential of the different types of kinks will allow identification of optimum ion numbers, trap parameters to reduce losses and enable stable trapping of multiple kinks 28,29 . Experimental limitations in the system size can be overcome by using, for example, cryogenic ion traps that allow storage of large Coulomb crystals with long lifetimes 30 .…”

Section: Discussionmentioning

confidence: 99%

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

et al. 2013

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Section: Discussionmentioning

confidence: 99%

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

et al. 2013

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“…This 'trapping' of kinks at the crystal center is the result of the PN potential being modified from a (modulated) periodic potential to a global trapping potential [3]. The PN potential is studied using a constrained energy minimization approach in [49].…”

Section: Formation Of the Peierls-nabarro Potentialmentioning

confidence: 99%

Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals

et al. 2013

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We study discrete solitons (kinks) accessible in the state-of-theart trapped ion experiments, considering zigzag crystals and quasi-threedimensional configurations, both theoretically and experimentally. We first extend the theoretical understanding of different phenomena predicted and recently experimentally observed in the structure and dynamics of these topological excitations. Employing tools from topological degree theory, we analyze bifurcations of crystal configurations in dependence on the trapping parameters, and investigate the formation of kink configurations and the transformations of kinks between different structures. This allows us to accurately define and calculate the effective potential experienced by solitons within the Wigner crystal, and study how this (so-called Peierls-Nabarro) potential gets modified to a non-periodic globally trapping potential in certain parameter regimes. The kinks' rest mass (energy) and spectrum of modes are computed and the dynamics of linear and nonlinear kink oscillations are analyzed. We also present novel, experimentally observed, configurations of kinks incorporating a large-mass defect realized by an embedded molecular ion, and of pairs of interacting kinks stable for long times, offering the perspective for exploring and exploiting complex collective nonlinear excitations, controllable on the quantum level.

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“…Apart from the equilibrium studies of the rich structural phase diagram, there is an increasing interest in investigating the nonlinear and nonequilibrium dynamical phenomena by exploiting the various ion crystal structural transitions in a precisely controlled experimental setting. Some examples of the studies of the nonlinear dynamics of ion crystals include the simulation of linear and nonlinear Klein-Gordon fields on a lattice [11], the study of nucleation of topological defects [12][13][14], dynamics of discrete solitons [15,16], dry friction [17][18][19][20], as as well as proposals to realize models related to energy transport [18,21] and synchronization [22]. Even though all of the above experiments and proposals are classical, the high degree of isolation of the ion crystals from the surrounding environment implies also the possibility to enter the regime where quantum mechanical effects must be accounted for to describe critical phenomena [11,[23][24][25] and where the quantum motion can be utilized for quantum information processing using trapped ions [26,27].…”

Section: Introductionmentioning

confidence: 99%

Formation of helical ion chains

et al. 2016

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We study the nonequilibrium dynamics of the linear to zigzag structural phase transition exhibited by an ion chain confined in a trap with periodic boundary conditions. The transition is driven by reducing the transverse confinement at a finite quench rate, which can be accurately controlled. This results in the formation of zigzag domains oriented along different transverse planes. The twists between different domains can be stabilized by the topology of the trap and under laser cooling the system has a chance to relax to a helical chain with nonzero winding number. Molecular dynamics simulations are used to obtain a large sample of possible trajectories for different quench rates. The scaling of the average winding number with different quench rates is compared to the prediction of the Kibble-Zurek theory, and a good quantitative agreement is found.

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Dynamics of topological defects in ion Coulomb crystals

Cited by 40 publications

References 37 publications

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

Structure, dynamics and bifurcations of discrete solitons in trapped ion crystals

Formation of helical ion chains

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