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:cond-mat/0406150 · Physical Review Letters

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

Kenichi Kasamatsu, Makoto Tsubota, Masahito Ueda

Published Dec 16, 2004• 147 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.93.250406

Related papers

VORTICES IN MULTICOMPONENT BOSE–EINSTEIN CONDENSATES

Kenichi Kasamatsu, Makoto Tsubota, Masahito Ueda

We review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.

arXiv:cond-mat/0505546•International Journal of Modern Physics B•Apr 30, 2005•244 citations

Spin textures in rotating two-component Bose-Einstein condensates

Kenichi Kasamatsu, Makoto Tsubota, Masahito Ueda

We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a ``skyrmion'' and a ``meron-pair,'' respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.

arXiv:cond-mat/0411544•Physical Review A•Apr 25, 2005•153 citations

Vortex trimer in three-component Bose-Einstein condensates

Minoru Eto, Muneto Nitta

Vortex trimer is predicted in three-component Bose-Einstein condensates (BEC's) with internal coherent couplings. The molecule is made by three constituent vortices which are bounded by domain walls of the relative phases. We show that the shape and the size of the molecule can be controlled by changing the internal coherent couplings.

arXiv:1201.0343•Physical Review A•May 29, 2012•43 citations

Vortex-pair states in spin-orbit-coupled Bose–Einstein condensates with coherent coupling

Yong-Kai Liu, Hong-Xia Yue, Liang-Liang Xu +1 more

Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.

Frontiers of Physics•Aug 8, 2018•7 citations

Distributed vorticity model for vortex molecule dynamics

Sarthak Choudhury, Joachim Brand

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.

arXiv:2212.07131•Physical Review A•May 19, 2023•0 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
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 review the topic of quantized vortices in multicomponent Bose–Einstein condensates of dilute atomic gases, with an emphasis on the two-component condensates. First, we review the fundamental structure, stability and dynamics of a single vortex state in a slowly rotating two-component condensates. To understand recent experimental results, we use the coupled Gross–Pitaevskii equations and the generalized nonlinear sigma model. An axisymmetric vortex state, which was observed by the JILA group, can be regarded as a topologically trivial skyrmion in the pseudospin representation. The internal, coherent coupling between the two components breaks the axisymmetry of the vortex state, resulting in a stable vortex molecule (a meron pair). We also mention unconventional vortex states and monopole excitations in a spin-1 Bose–Einstein condensate. Next, we discuss a rich variety of vortex states realized in rapidly rotating two-component Bose–Einstein condensates. We introduce a phase diagram with axes of rotation frequency and the intercomponent coupling strength. This phase diagram reveals unconventional vortex states such as a square lattice, a double-core lattice, vortex stripes and vortex sheets, all of which are in an experimentally accessible parameter regime. The coherent coupling leads to an effective attractive interaction between two components, providing not only a promising candidate to tune the intercomponent interaction to study the rich vortex phases but also a new regime to explore vortex states consisting of vortex molecules characterized by anisotropic vorticity. A recent experiment by the JILA group vindicated the formation of a square vortex lattice in this system.
We investigate two kinds of coreless vortices with axisymmetric and nonaxisymmetric configurations in rotating two-component Bose-Einstein condensates. Starting from the Gross-Pitaevskii energy functional in a rotating frame, we derive a nonlinear sigma model generalized to the two-component condensates. In terms of a pseudospin representation, an axisymmetric vortex and a nonaxisymmetric one correspond to spin textures referred to as a ``skyrmion'' and a ``meron-pair,'' respectively. A variational method is used to investigate the dependence of the sizes of the stable spin textures on system parameters, and the optimized variational function is found to reproduce well the numerical solution. In the SU(2) symmetric case, the optimal skyrmion and meron-pair are degenerate and transform to each other by a rotation of the pseudospin. An external rf field that couples coherently the hyperfine states of two components breaks the degeneracy in favor of the meron-pair texture due to an effective transverse pseudomagnetic field. The difference between the intracomponent and intercomponent interactions yields a longitudinal pseudomagnetic field and a ferromagnetic or an antiferromagnetic pseudospin interaction, leading to a meron-pair texture with an anisotropic distribution of vorticity.
Three types of vortex-pair are identified in two-component Bose–Einstein condensates (BEC) of different kinds of spin-orbit coupling. One type holds the two vortices in one component of the twocomponent condensates. Both the other two types hold a vortex in each component of the twocomponent condensates, and exhibit meron-pair textures that have either null or unit topological charge, respectively. The cores of the two vortices are connected by a string of the relative phase jump. These vortex pairs can be generated from a vortex-free wave packet by incorporating different non- Abelian gauge field into the BEC. When a Rabi coupling is introduced, the distance between the two cores is effectively controlled by the Rabi coupling strength and a transition of vortex configurations is observed.
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.
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.