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

arXiv:2212.07131 · Physical Review A

Distributed vorticity model for vortex molecule dynamics

Sarthak Choudhury, Joachim Brand

Published May 19, 2023• 0 citations
arXivHTMLPDF

Abstract

We analyze the effect of a hard wall trapping potential on the dynamics of a vortex molecule in a two-component Bose-Einstein condensate with linear coherent coupling. A vortex molecule consists of a vortex of the same charge in each component condensate connected by a domain wall of the relative phase. In a previous paper [S. Choudhury and J. Brand, Phys. Rev. A 106, 043319 (2022)] we described the interaction of a vortex molecule with the boundary using the method of images by separately treating each component vortex as a point vortex, in addition to a Magnus force effect from the surface tension of the domain wall. Here we extend the model by considering a continuous distribution of image vorticity reflecting the effect of the domain wall on the vortex molecule phase structure. In the case of a precessing centered vortex molecule in an isotropic trap, distributing the image vorticity weakens its contribution to the precession frequency. We test the model predictions against numerical simulations of the coupled Gross-Pitaevskii equations in a two-dimensional circular disk and find support for the improved model.

DOI
10.1103/physreva.107.053314

Related papers

Confinement and precession of vortex pairs in coherently coupled Bose-Einstein condensates

Marek Tylutki, Лев П. Питаевский, Alessio Recati +1 more

The dynamic behavior of vortex pairs in two-component coherently (Rabi) coupled Bose-Einstein condensates is investigated in the presence of harmonic trapping. We discuss the role of the surface tension associated with the domain wall connecting two vortices in condensates of atoms occupying different spin states and its effect on the precession of the vortex pair. The results, based on the numerical solution of the Gross-Pitaevskii equations, are compared with the predictions of an analytical macroscopic model and are discussed as a function of the size of the pair, the Rabi coupling, and the intercomponent interaction. We show that the increase of the Rabi coupling results in the disintegration of the domain wall into smaller pieces, connecting vortices of newly created vortex pairs. The resulting scenario is the analog of quark confinement and string breaking in quantum chromodynamics.

arXiv:1601.03695•Physical Review A•Apr 27, 2016•64 citations

Vortex Molecules in Coherently Coupled Two-Component Bose-Einstein Condensates

Kenichi Kasamatsu, Makoto Tsubota, Masahito Ueda

A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and one in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule," which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.

arXiv:cond-mat/0406150•Physical Review Letters•Dec 16, 2004•147 citations

Vortex sheet in rotating two-component Bose-Einstein condensates

Kenichi Kasamatsu, Makoto Tsubota

We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.

arXiv:0812.4075•Physical Review A•Feb 4, 2009•85 citations

Wall-vortex composite solitons in two-component Bose-Einstein condensates

Kenichi Kasamatsu, Hiromitsu Takeuchi, Makoto Tsubota +1 more

We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of the two components is homogeneous, the system can be mapped to the O(3) nonlinear $\ensuremath{\sigma}$ model for the pseudospin representing the two-component order parameter, and the analytical solutions of the composite solitons can be obtained. Based on the analytical solutions, we discuss the detailed structure of the composite solitons in two-component condensates by employing the generalized nonlinear $\ensuremath{\sigma}$ model, where all degrees of freedom of the original Gross-Pitaevskii theory are active. The domain wall pulled by a vortex is logarithmically bent as a membrane pulled by a pin. It bends more flexibly than the domain wall in the $\ensuremath{\sigma}$ model, because the density inhomogeneity results in a reduction of the domain wall tension from that in the $\ensuremath{\sigma}$ model limit. We find, however, that the curvature of the wall bending pulled by a vortex is still greater than that expected from the reduced tension due to only the density inhomogeneity. Finally, we study the composite soliton structure for actual experimental situations with trapped immiscible condensates under rotation, through numerical simulations of the coupled Gross-Pitaevskii equations.

arXiv:1303.7052•Physical Review A•Jul 15, 2013•47 citations

Direct and Reverse Precession of a Massive Vortex in a Binary Bose–Einstein Condensate

V. P. Ruban

The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose–Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross–Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system.

arXiv:2205.14878•Journal of Experimental and Theoretical Physics Letters•Apr 1, 2022•14 citations

Vortex precession dynamics in general radially symmetric potential traps in two-dimensional atomic Bose-Einstein condensates

P. G. Kevrekidis, Wenlong Wang, R. Carretero-González +2 more

We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\ensuremath{\omega}$ on the chemical potential $\ensuremath{\mu}$, this is no longer true for a general potential $V(r)\ensuremath{\propto}{r}^{p}$. Our calculations suggest that for $p>2$, the precession frequency scales with $\ensuremath{\mu}$ as $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\mu}}^{\ensuremath{-}2/p}$. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov--de Gennes) stability analysis by identifying the relevant precession mode dependence on $\ensuremath{\mu}$ but also through direct numerical computations of the vortex evolution in the large-$\ensuremath{\mu}$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.

arXiv:1706.07137•Physical Review A•Oct 13, 2017•11 citations
We analyze the effect of a hard wall trapping potential on the dynamics of a vortex molecule in a two-component Bose-Einstein condensate with linear coherent coupling. A vortex molecule consists of a vortex of the same charge in each component condensate connected by a domain wall of the relative phase. In a previous paper [S. Choudhury and J. Brand, Phys. Rev. A 106, 043319 (2022)] we described the interaction of a vortex molecule with the boundary using the method of images by separately treating each component vortex as a point vortex, in addition to a Magnus force effect from the surface tension of the domain wall. Here we extend the model by considering a continuous distribution of image vorticity reflecting the effect of the domain wall on the vortex molecule phase structure. In the case of a precessing centered vortex molecule in an isotropic trap, distributing the image vorticity weakens its contribution to the precession frequency. We test the model predictions against numerical simulations of the coupled Gross-Pitaevskii equations in a two-dimensional circular disk and find support for the improved model.
The dynamic behavior of vortex pairs in two-component coherently (Rabi) coupled Bose-Einstein condensates is investigated in the presence of harmonic trapping. We discuss the role of the surface tension associated with the domain wall connecting two vortices in condensates of atoms occupying different spin states and its effect on the precession of the vortex pair. The results, based on the numerical solution of the Gross-Pitaevskii equations, are compared with the predictions of an analytical macroscopic model and are discussed as a function of the size of the pair, the Rabi coupling, and the intercomponent interaction. We show that the increase of the Rabi coupling results in the disintegration of the domain wall into smaller pieces, connecting vortices of newly created vortex pairs. The resulting scenario is the analog of quark confinement and string breaking in quantum chromodynamics.
A vortex molecule is predicted in rotating two-component Bose-Einstein condensates whose internal hyperfine states are coupled coherently by an external field. A vortex in one component and one in the other are connected by a domain wall of the relative phase, constituting a "vortex molecule," which features a nonaxisymmetric (pseudo)spin texture with a pair of merons. The binding mechanism of the vortex molecule is discussed based on a generalized nonlinear sigma model and a variational ansatz. The anisotropy of vortex molecules is caused by the difference in the scattering lengths, yielding a distorted vortex-molecule lattice in fast rotating condensates.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
We study composite solitons, consisting of domain walls and vortex lines attaching to the walls in two-component Bose-Einstein condensates. When the total density of the two components is homogeneous, the system can be mapped to the O(3) nonlinear $\ensuremath{\sigma}$ model for the pseudospin representing the two-component order parameter, and the analytical solutions of the composite solitons can be obtained. Based on the analytical solutions, we discuss the detailed structure of the composite solitons in two-component condensates by employing the generalized nonlinear $\ensuremath{\sigma}$ model, where all degrees of freedom of the original Gross-Pitaevskii theory are active. The domain wall pulled by a vortex is logarithmically bent as a membrane pulled by a pin. It bends more flexibly than the domain wall in the $\ensuremath{\sigma}$ model, because the density inhomogeneity results in a reduction of the domain wall tension from that in the $\ensuremath{\sigma}$ model limit. We find, however, that the curvature of the wall bending pulled by a vortex is still greater than that expected from the reduced tension due to only the density inhomogeneity. Finally, we study the composite soliton structure for actual experimental situations with trapped immiscible condensates under rotation, through numerical simulations of the coupled Gross-Pitaevskii equations.
The dynamics of a filled massive vortex is studied numerically and analytically using a two-dimensional model of a two-component Bose–Einstein condensate trapped in a harmonic trap. This condensate exhibits phase separation. In the framework of the coupled Gross–Pitaevskii equations, it is demonstrated that, in a certain range of parameters of the nonlinear interaction, the precession of a sufficiently massive vortex around the center is strongly slowed down and even reverses its direction with a further increase in the mass. An approximate ordinary differential equation is derived that makes it possible to explain this behavior of the system.
We consider the motion of individual two-dimensional vortices in general radially symmetric potentials in Bose-Einstein condensates. We find that although in the special case of the parabolic trap there is a logarithmic correction in the dependence of the precession frequency $\ensuremath{\omega}$ on the chemical potential $\ensuremath{\mu}$, this is no longer true for a general potential $V(r)\ensuremath{\propto}{r}^{p}$. Our calculations suggest that for p>2p>2p>2, the precession frequency scales with $\ensuremath{\mu}$ as $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\mu}}^{\ensuremath{-}2/p}$. This theoretical prediction is corroborated by numerical computations, not only at the level of spectral (Bogolyubov--de Gennes) stability analysis by identifying the relevant precession mode dependence on $\ensuremath{\mu}$ but also through direct numerical computations of the vortex evolution in the large-$\ensuremath{\mu}$, so-called Thomas-Fermi, limit. Additionally, the dependence of the precession frequency on the distance to the trap center of an initially displaced vortex is examined, and the corresponding predictions are tested against numerical results.