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Title: Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates

Abstract

Here in the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing the evolution of a vortex ring and not only consider its spectrum of linearized excitations, but also explore the full nonlinear dynamical evolution of the ring as a vortical filament. The theory predicts that the ring is stable for 1 ≤ λ ≤ 2, where λ = ωzr is the ratio of the trapping frequencies along the z and r axes, i.e., for spherical to slightly oblate condensates. We compare this prediction with direct numerical simulations of the full three-dimensional Gross-Pitaevskii equation (GPE) capturing the linearization spectrum of the ring for different values of the chemical potential and as a function of the anisotropy parameter λ . We identify this result as being only asymptotically valid as the chemical potential μ → ∞, revealing how the stability interval narrows and, in particular, its upper bound decreases for finite μ. Finally, we compare at the dynamical level the results of the GPE with the ones effectively capturing the ring dynamics, revealing the unstable evolutionmore » for different values of λ, as well as the good agreement between the two.« less

Authors:
 [1];  [2];  [3]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Royal Inst. of Technology, Stockholm (Sweden). Dept. of Theoretical Physics
  3. Univ. of Massachusetts, Amherst, MA (United States). of Dept. of Mathematics and Statistics
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1492669
Alternate Identifier(s):
OSTI ID: 1473996
Report Number(s):
LA-UR-18-26982
Journal ID: ISSN 2469-9926; PLRAAN
Grant/Contract Number:  
89233218CNA000001; AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Atomic; Nuclear and Particle Physics

Citation Formats

Ticknor, Christopher, Wang, Wenlong, and Kevrekidis, P. G. Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates. United States: N. p., 2018. Web. doi:10.1103/PhysRevA.98.033609.
Ticknor, Christopher, Wang, Wenlong, & Kevrekidis, P. G. Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates. United States. doi:10.1103/PhysRevA.98.033609.
Ticknor, Christopher, Wang, Wenlong, and Kevrekidis, P. G. Wed . "Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates". United States. doi:10.1103/PhysRevA.98.033609. https://www.osti.gov/servlets/purl/1492669.
@article{osti_1492669,
title = {Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates},
author = {Ticknor, Christopher and Wang, Wenlong and Kevrekidis, P. G.},
abstractNote = {Here in the present work, motivated by numerous recent experimental developments we revisit the dynamics of a single vortex ring in anisotropic harmonic traps. At the theoretical level, we start from a general Lagrangian dynamically capturing the evolution of a vortex ring and not only consider its spectrum of linearized excitations, but also explore the full nonlinear dynamical evolution of the ring as a vortical filament. The theory predicts that the ring is stable for 1 ≤ λ ≤ 2, where λ = ωz /ωr is the ratio of the trapping frequencies along the z and r axes, i.e., for spherical to slightly oblate condensates. We compare this prediction with direct numerical simulations of the full three-dimensional Gross-Pitaevskii equation (GPE) capturing the linearization spectrum of the ring for different values of the chemical potential and as a function of the anisotropy parameter λ . We identify this result as being only asymptotically valid as the chemical potential μ → ∞, revealing how the stability interval narrows and, in particular, its upper bound decreases for finite μ. Finally, we compare at the dynamical level the results of the GPE with the ones effectively capturing the ring dynamics, revealing the unstable evolution for different values of λ, as well as the good agreement between the two.},
doi = {10.1103/PhysRevA.98.033609},
journal = {Physical Review A},
number = 3,
volume = 98,
place = {United States},
year = {2018},
month = {9}
}

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