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arXiv:0807.2194 · The European Physical Journal B

Internal structure of a quantum soliton and classical excitations due to trap opening

Yvan Castin

Published Oct 30, 2008• 26 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2008-00407-3

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We propose to realize quantized discrete kinks with cold trapped ions. We show that long-lived solitonlike configurations are manifested as deformations of the zigzag structure in the linear Paul trap, and are topologically protected in a circular trap with an odd number of ions. We study the quantum-mechanical time evolution of a high-frequency, gap separated internal mode of a static kink and find long coherence times when the system is cooled to the Doppler limit. The spectral properties of the internal modes make them ideally suited for manipulation using current technology. This suggests that ion traps can be used to test quantum-mechanical effects with solitons and explore ideas for the utilization of the solitonic internal modes as carriers of quantum information.
We study, analytically and numerically, the dynamics of a matter-wave soliton formed by a Bose-Einstein condensate with an attractive interatomic interaction confined in a one-dimensional harmonic trap and subjected to a flashing weak periodic potential. Within the framework of the Gross-Pitaevski equation, we show that efficient energy transfer to the soliton occurs within two distinct frequency regimes: (a) on resonance with the trapping frequency and (b) on resonance with the internal mode of the soliton. We find that the former regime is well described within the soliton-as-particle approximation, while the latter relies on the extended nature of the localized state and involves strong excitations of the width coupled to translational motion.
By quenching the interatomic interactions, we investigate the nonequilibrium dynamics of two-dimensional Bose–Einstein condensates in boxlike traps with power-law potential boundaries. We show that ring dark solitons can be excited during the quench dynamics for both concave and convex potentials. The quench’s modulation strength and the steepness of the boundary are two major factors influencing the system’s evolution. In terms of the number of ring dark solitons excited in the condensate, five dynamic regimes have been identified. The condensate undergoes damped radius oscillation in the absence of ring dark soliton excitations. When it comes to the appearance of ring dark solitons, their decay produces interesting structures. The excitation patterns for the concave potential show a nested structure of vortex-antivortex pairs. The dynamic excitation patterns for the convex potential, on the other hand, show richer structures with multiple transport behaviors.