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

Abstract

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.

Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

“…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 .…”

Formation of helical ion chains

“…This type of structural defects is often referred to as Z 2 kinks or solitons, since they arise as a result of phase transitions that break reflectional Z 2 symmetry. Kinks in two dimensional Coulomb crystals were studied theoretically and experimentally as discrete soliton model systems [16,37,45], as possible qubit candidates for quantum information processing [27] and in the context of KZ mechanism [12][13][14]30].…”

“…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].…”

Structural transitions of nearly second order in classical dipolar gases

“…[12]. In the Coulomb case, indeed, the inhomogeneous configurations are excitations [34], and the linear-zigzag transition is continuous [12]. Our numerical results clearly indicate that the structural transition for dipolar gases (and, in general, for α > 2) deviates from the behavior predicted from the Landau theory for second-order phase transitions.…”