Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

Stable three-dimensional vortex solitons in Bose–Einstein condensates with nonlocal dipole–dipole interaction

Volodymyr M. Lashkin, A. I. Yakimenko, Yu. Zaliznyak

Published Mar 1, 2009• 10 citations
Publisher

Abstract

We present spatially localized three-dimensional vortex solitons in Bose–Einstein condensates with local short-range and nonlocal dipole–dipole interactions. By means of a linear stability analysis, we investigate the stability of these structures and show that singly quantized vortices are stable provided that the chemical potential is positive and the number of atoms is below some critical value. The results are confirmed by direct numerical simulations of the Gross–Pitaevskii equation.

DOI
10.1088/0031-8949/79/03/035305

Related papers

Stable three-dimensional spatially modulated vortex solitons in Bose-Einstein condensates

Volodymyr M. Lashkin

We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show that the 3D azimuthon solutions exist as a continuous family parametrized by the angular velocity (or, equivalently, the modulational depth). By a linear stability analysis we show that 3D azimuthons with a sufficiently large phase modulational depth can be stable. The results are confirmed by direct numerical simulations of the Gross-Pitaevskii equation.

arXiv:0808.3468•Physical Review A•Sep 4, 2008•22 citations

Two-dimensional nonlocal vortices, multipole solitons, and rotating multisolitons in dipolar Bose-Einstein condensates

Volodymyr M. Lashkin

We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.

arXiv:nlin/0612055•Physical Review A•Apr 11, 2007•68 citations

Discrete vortex solitons in dipolar Bose–Einstein condensates

Goran Gligorić, Aleksandra Maluckov, Milutin Stepić +2 more

We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 16, 2010•23 citations

Hydrodynamics of vortices and solitons in a dipolar Bose-Einstein condensate

Subramaniyan Sabari, Bishwajyoti Dey

By solving the two-dimensional, nonlocal Gross-Pitaevskii equation numerically, we study the hydrodynamics of quantized vortices in a dipolar Bose-Einstein condensate excited by an oscillating potential. We calculate the critical velocity for the vortex nucleation in the presence and absence of dipole-dipole interaction. Above a critical velocity, the oscillating potential nucleates the vortex pairs, whose impulses alternatively change their direction synchronously with the oscillation of the Gaussian potential. We study the dynamics of the vortices and also the formation of the dark solitons which have not been previously reported in a dipolar Bose-Einstein condensate.

AIP conference proceedings•Jan 1, 2017•1 citation

Three-dimensional vortex structures in a rotating dipolar Bose–Einstein condensate

Ramavarmaraja Kishor Kumar, Thangarasu Sriraman, Henrique Fabrelli +2 more

Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.

arXiv:1506.08184•Journal of Physics B Atomic Molecular and Optical Physics•Jul 5, 2016•21 citations

Vortex dynamics of a three-dimensional dipolar Bose–Einstein condensate

Yuan-Sheng Wang

By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices.

Canadian Journal of Physics•Aug 28, 2023•0 citations
We present spatially localized three-dimensional vortex solitons in Bose–Einstein condensates with local short-range and nonlocal dipole–dipole interactions. By means of a linear stability analysis, we investigate the stability of these structures and show that singly quantized vortices are stable provided that the chemical potential is positive and the number of atoms is below some critical value. The results are confirmed by direct numerical simulations of the Gross–Pitaevskii equation.
We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show that the 3D azimuthon solutions exist as a continuous family parametrized by the angular velocity (or, equivalently, the modulational depth). By a linear stability analysis we show that 3D azimuthons with a sufficiently large phase modulational depth can be stable. The results are confirmed by direct numerical simulations of the Gross-Pitaevskii equation.
We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.
We analyse the existence, stability and dynamics of localized discrete modes with intrinsic vorticity S = 1 and S = 2 in the disc-shaped dipolar Bose-Einstein condensate loaded into a deep two-dimensional optical lattice. The condensate, which features the interplay of local contact and nonlocal dipole-dipole (DD) interactions between atoms, is modelled by the 2D discrete Gross-Pitaevskii equation which includes the long-range DD term. Various species of discrete vortex solitons, which are known in the model of the condensate with local interactions, are found to exist in the presence of the DD interaction too. In locally self-attractive condensates, the isotropic DD repulsion, which corresponds to the orientation of atomic dipoles perpendicular to the confinement plane, helps to extend the region of the vortex stability, while in the case of anisotropic DD interactions, corresponding to the in-plane orientation of the dipoles, vortices are unstable. In the former case, those vortices which are unstable may evolve into robust ring-shaped breathers. The attractive isotropic DD interaction can create localized vortices in the condensate with the local self-repulsion, but they all are unstable, evolving into single-peak asymmetric structures.
By solving the two-dimensional, nonlocal Gross-Pitaevskii equation numerically, we study the hydrodynamics of quantized vortices in a dipolar Bose-Einstein condensate excited by an oscillating potential. We calculate the critical velocity for the vortex nucleation in the presence and absence of dipole-dipole interaction. Above a critical velocity, the oscillating potential nucleates the vortex pairs, whose impulses alternatively change their direction synchronously with the oscillation of the Gaussian potential. We study the dynamics of the vortices and also the formation of the dark solitons which have not been previously reported in a dipolar Bose-Einstein condensate.
Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.
By numerically solving the Gross–Pitaevskii equation with phenomenological dissipation term, we study the vortex formation properties of a three-dimensional dipolar Bose–Einstein condensate of 164Dy atoms. We studied the influence of the contact interaction between atoms on the formation mechanism of vortices. We also study how the dipole orientation affects the vortex formation properties and the number of vortices. We find that enhancing the interaction of short-range repulsion interaction or dipolar repulsion interaction can shorten the time to form a stable vortex structure and increase the number of vortices.