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Title: Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates

Abstract

Here, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortex-ring states. We systematically capture these as stationary states of the system and quantify their BdG spectra numerically. We found that although the vortex ring may be unstable when bifurcating, its instabilities weaken and may even eventually disappear for sufficiently large chemical potentials and suitable trap settings. For instance, we demonstrate the stability of the vortex ring for an isotropic trap in the large-chemical-potential regime.

Authors:
 [1];  [2]; ORCiD logo [1];  [3];  [4]; ORCiD logo [1];  [5]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Massachusetts, Amherst, MA (United States). Dept. of Physics
  3. San Diego State Univ., CA (United States). Computational Sciences Research Center, Dept. of Mathematics and Statistics
  4. Univ. of Athens (Greece). Dept. of Physics
  5. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States). 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); National Science Foundation (NSF)
OSTI Identifier:
1414082
Alternate Identifier(s):
OSTI ID: 1222505
Report Number(s):
LA-UR-15-25870
Journal ID: ISSN 1050-2947; PLRAAN; TRN: US1800617
Grant/Contract Number:  
AC52-06NA25396; DMR-208046; DMS-1312856; DMS-1309035
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 92; Journal Issue: 4; Journal ID: ISSN 1050-2947
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Atomic and Nuclear Physics

Citation Formats

Bisset, R. N., Wang, Wenlong, Ticknor, C., Carretero-González, R., Frantzeskakis, D. J., Collins, L. A., and Kevrekidis, P. G. Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates. United States: N. p., 2015. Web. doi:10.1103/PhysRevA.92.043601.
Bisset, R. N., Wang, Wenlong, Ticknor, C., Carretero-González, R., Frantzeskakis, D. J., Collins, L. A., & Kevrekidis, P. G. Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates. United States. doi:10.1103/PhysRevA.92.043601.
Bisset, R. N., Wang, Wenlong, Ticknor, C., Carretero-González, R., Frantzeskakis, D. J., Collins, L. A., and Kevrekidis, P. G. Thu . "Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates". United States. doi:10.1103/PhysRevA.92.043601. https://www.osti.gov/servlets/purl/1414082.
@article{osti_1414082,
title = {Bifurcation and stability of single and multiple vortex rings in three-dimensional Bose-Einstein condensates},
author = {Bisset, R. N. and Wang, Wenlong and Ticknor, C. and Carretero-González, R. and Frantzeskakis, D. J. and Collins, L. A. and Kevrekidis, P. G.},
abstractNote = {Here, we investigate how single- and multi-vortex-ring states can emerge from a planar dark soliton in three-dimensional (3D) Bose-Einstein condensates (confined in isotropic or anisotropic traps) through bifurcations. We characterize such bifurcations quantitatively using a Galerkin-type approach and find good qualitative and quantitative agreement with our Bogoliubov–de Gennes (BdG) analysis. We also systematically characterize the BdG spectrum of the dark solitons, using perturbation theory, and obtain a quantitative match with our 3D BdG numerical calculations. We then turn our attention to the emergence of single- and multi-vortex-ring states. We systematically capture these as stationary states of the system and quantify their BdG spectra numerically. We found that although the vortex ring may be unstable when bifurcating, its instabilities weaken and may even eventually disappear for sufficiently large chemical potentials and suitable trap settings. For instance, we demonstrate the stability of the vortex ring for an isotropic trap in the large-chemical-potential regime.},
doi = {10.1103/PhysRevA.92.043601},
journal = {Physical Review. A},
number = 4,
volume = 92,
place = {United States},
year = {2015},
month = {10}
}

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