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

TL;DR

This paper investigates the structure, dynamics, and bifurcations of discrete solitons in trapped ion crystals, combining theoretical analysis and experimental observations to understand their behavior and potential for quantum control.

Contribution

It extends theoretical understanding of topological excitations in ion crystals and introduces new experimental configurations involving defects and interacting kinks.

Findings

Analysis of bifurcations in crystal configurations

Observation of kink configurations with embedded defects

Calculation of kink spectra and dynamics

Abstract

We study discrete solitons (kinks) accessible in state-of-the-art trapped ion experiments, considering zigzag crystals and quasi-3D 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 nonperiodic 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.