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:1006.5839 · Progress of Theoretical Physics Supplement

Topological Excitations in Spinor Bose-Einstein Condensates

Yuki Kawaguchi, Michikazu Kobayashi, Muneto Nitta, Masahito Ueda

Published Oct 1, 2010• 26 citations
arXivHTMLPDF

Abstract

A rich variety of order parameter manifolds of multicomponent Bose-Einstein condensates (BECs) admit various kinds of topological excitations, such as fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss two topological excitations in spinor BECs: non-Abelian vortices and knots. Unlike conventional vortices, non-Abelian vortices neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. We discuss the collision dynamics of non-Abelian vortices in the cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is a unique topological object characterized by a linking number or a Hopf invariant [π3 (S2) = Z], can be created using a conventional quadrupole magnetic field in a cold atomic system.

DOI
10.1143/ptps.186.455

Related papers

Physics of non-Abelian vortices in Bose-Einstein condensates

Michikazu Kobayashi

A wide order-parameter manifolds of Bose-Einstein condensates (BECs) with spin degrees of freedom enables various kinds of topological defects which never appear in conventional scalar BECs. In this paper, we focus on the characteristic example of them; non-Abelian vortices and their dynamics in the cyclic phase of a spin-2 BEC. Non-Abelian vortices shows the unique effect in their collision dynamics, i.e. unlike Abelian vortices, they do neither reconnect themselves nor pass through each other but create a rung vortex between them.

Journal of Physics Conference Series•May 1, 2011•4 citations

Creation and dynamics of topological structures in Bose–Einstein condensates

Tuomas Ollikainen

Topology provides deep conceptual links between the various branches of physics. Bose–Einstein condensates with spin degrees of freedom are among the most accessible quantum systems available for studying topological structures. A wide range of topological defects and textures available in condensates, such as vortices, monopoles, knots, and skyrmions, are analogous to those predicted in electromagnetism, high-energy physics, and cosmology. In this dissertation, we numerically and experimentally investigate novel creation methods for topological structures and study their dynamical properties. Specifically, we experimentally observe the evolution of an isolated monopole into a Dirac monopole in the presence of a quadrupole magnetic field. The Dirac monopole appears in the synthetic magnetic field of the condensate and is accompanied by spontaneously emerging nodal lines. We observe the decay of a quantum knot into a polar-core spin vortex in the presence of a uniform magnetic field. Furthermore, we observe that a decaying coreless-vortex state gives rise to a pair of singular SO(3) vortices. Many of the studied creation methods for topological structures in the condensate rely on adiabatic control of the external magnetic field. The counterdiabatic protocol offers a way to speed up the otherwise slow magnetic field driving required for adiabatic dynamics with a correcting magnetic field. Using this method, we numerically implement a scheme for fast vortex pumping which leads to the vortex with highest angular momentum reported to date in Bose–Einstein condensates with experimentally feasible methods. We further use the counterdiabatic protocol in a novel way to create quantum knots in the condensate. Another focal point of this dissertation is the study on different types of skyrmions in spinor condensates. Our simulations of two-dimensional skyrmions are in a quantitative agreement with an experiment carried out elsewhere, explaining the experimentally observed instabilities. We numerically analyze the exotic spin-2 skyrmions available in the cyclic and biaxial nematic phases. Importantly, we present the first experimental observations of Shankar skyrmions in spin-1 condensates and analyze their synthetic electromagnetic properties. This dissertation addresses an extensive amount of topological structures available in the condensate, but many different structures await future studies. In addition, the precise computational characterization of the elementary excitations of monopoles, knots, and skyrmions is of great interest. The results of this dissertation form a sturdy basis for future experimental studies on the dynamics of topological structures in spinor condensates.; Topologia tarjoaa syvallisia kasitteellisia yhteyksia fysiikan eri haarojen valilla. Bosen–Einsteinin kondensaatit spin-vapausasteilla ovat yksia monipuolisimmista systeemeista topologisten rakenteiden tutkimukseen. Laaja kirjo kondensaatissa esiintyvia topologisia rakenteita, kuten kvanttipyorteet, monopolit, solmut ja skyrmionit, ovat…

•Jan 1, 2019•0 citations

Collision Dynamics and Rung Formation of non-Abelian Vortices

Michikazu Kobayashi, Yuki Kawaguchi, Muneto Nitta +1 more

We investigate the collision dynamics of two non-Abelian vortices and find that, unlike Abelian vortices, they neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. Our predictions are verified using the model of the cyclic phase of a spin-2 spinor Bose-Einstein condensate.

arXiv:0810.5441•Physical Review Letters•Sep 8, 2009•98 citations

Topological objects in two-component Bose-Einstein condensates

Y. M. Cho, Hyojoong Khim, Pengming Zhang

We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the $U(1)$ gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-$\frac{1}{2}$ condensate of $^{87}\mathrm{Rb}$ atoms.

arXiv:cond-mat/0510618•Physical Review A•Dec 2, 2005•18 citations

Bimeron in a ferromagnetic spin-1 Bose–Einstein condensate

Yong-Kai Liu, Ning Yue, Jian-Jun Zhang +1 more

The spin degrees of freedom in multicomponent Bose–Einstein condensates allow for various types of topological excitations, such as skyrmions and knots. Systems with high spins offer a broader range of internal symmetries. For instance, in spin-1 Bose–Einstein condensates, one can observe not only the two-dimensional (2D) skyrmion spin texture but also the bimeron spin texture. However, it remains challenging to experimentally create or stabilize a bimeron and identify the conditions that facilitate its formation. In this context, our research predicts a novel form of topological structure known as the domain wall bimeron in ferromagnetic spin-1 Bose–Einstein condensates by manipulating the magnetic field. Unlike conventional 2D skyrmions, this unique bimeron exhibits a non-axisymmetric spin texture and features complex off-axis vortices whose cores are connected by domain walls. This work significantly contributes to the study of 2D topological excitations in quantum matter with high spins.

Results in Physics•Dec 14, 2023•5 citations

Explicit expressions for the topological defects of spinor Bose–Einstein condensates

H Mäkelä

In this paper we first derive a general method which enables one to create expressions for vortices and monopoles. By using this method we construct several order-parameters describing the vortices and monopoles of Bose–Einstein condensates with hyperfine spin F = 1 and F = 2. We concentrate on defects which are topologically stable in the absence of an external magnetic field. In particular we show that in a ferromagnetic condensate there can be a vortex which does produce any superfluid flow. We also point out that the order-parameter space of the cyclic phase of F = 2 condensate consists of two disconnected sets. Finally we examine the effect of an external magnetic field on the vortices of a ferromagnetic F = 1 condensate and discuss the experimental preparation of a vortex in this system.

arXiv:cond-mat/0510750•Journal of Physics A Mathematical and General•May 23, 2006•30 citations
A rich variety of order parameter manifolds of multicomponent Bose-Einstein condensates (BECs) admit various kinds of topological excitations, such as fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss two topological excitations in spinor BECs: non-Abelian vortices and knots. Unlike conventional vortices, non-Abelian vortices neither reconnect themselves nor pass through each other, but create a rung between them in a topologically stable manner. We discuss the collision dynamics of non-Abelian vortices in the cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is a unique topological object characterized by a linking number or a Hopf invariant [π3 (S2) = Z], can be created using a conventional quadrupole magnetic field in a cold atomic system.
A wide order-parameter manifolds of Bose-Einstein condensates (BECs) with spin degrees of freedom enables various kinds of topological defects which never appear in conventional scalar BECs. In this paper, we focus on the characteristic example of them; non-Abelian vortices and their dynamics in the cyclic phase of a spin-2 BEC. Non-Abelian vortices shows the unique effect in their collision dynamics, i.e. unlike Abelian vortices, they do neither reconnect themselves nor pass through each other but create a rung vortex between them.
Topology provides deep conceptual links between the various branches of physics. Bose–Einstein condensates with spin degrees of freedom are among the most accessible quantum systems available for studying topological structures. A wide range of topological defects and textures available in condensates, such as vortices, monopoles, knots, and skyrmions, are analogous to those predicted in electromagnetism, high-energy physics, and cosmology. In this dissertation, we numerically and experimentally investigate novel creation methods for topological structures and study their dynamical properties. Specifically, we experimentally observe the evolution of an isolated monopole into a Dirac monopole in the presence of a quadrupole magnetic field. The Dirac monopole appears in the synthetic magnetic field of the condensate and is accompanied by spontaneously emerging nodal lines. We observe the decay of a quantum knot into a polar-core spin vortex in the presence of a uniform magnetic field. Furthermore, we observe that a decaying coreless-vortex state gives rise to a pair of singular SO(3) vortices. Many of the studied creation methods for topological structures in the condensate rely on adiabatic control of the external magnetic field. The counterdiabatic protocol offers a way to speed up the otherwise slow magnetic field driving required for adiabatic dynamics with a correcting magnetic field. Using this method, we numerically implement a scheme for fast vortex pumping which leads to the vortex with highest angular momentum reported to date in Bose–Einstein condensates with experimentally feasible methods. We further use the counterdiabatic protocol in a novel way to create quantum knots in the condensate. Another focal point of this dissertation is the study on different types of skyrmions in spinor condensates. Our simulations of two-dimensional skyrmions are in a quantitative agreement with an experiment carried out elsewhere, explaining the experimentally observed instabilities. We numerically analyze the exotic spin-2 skyrmions available in the cyclic and biaxial nematic phases. Importantly, we present the first experimental observations of Shankar skyrmions in spin-1 condensates and analyze their synthetic electromagnetic properties. This dissertation addresses an extensive amount of topological structures available in the condensate, but many different structures await future studies. In addition, the precise computational characterization of the elementary excitations of monopoles, knots, and skyrmions is of great interest. The results of this dissertation form a sturdy basis for future experimental studies on the dynamics of topological structures in spinor condensates.; Topologia tarjoaa syvallisia kasitteellisia yhteyksia fysiikan eri haarojen valilla. Bosen–Einsteinin kondensaatit spin-vapausasteilla ovat yksia monipuolisimmista systeemeista topologisten rakenteiden tutkimukseen. Laaja kirjo kondensaatissa esiintyvia topologisia rakenteita, kuten kvanttipyorteet, monopolit, solmut ja skyrmionit, ovat…
We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the U(1)U(1)U(1) gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-12\frac{1}{2}21​ condensate of 87Rb^{87}\mathrm{Rb}87Rb atoms.
The spin degrees of freedom in multicomponent Bose–Einstein condensates allow for various types of topological excitations, such as skyrmions and knots. Systems with high spins offer a broader range of internal symmetries. For instance, in spin-1 Bose–Einstein condensates, one can observe not only the two-dimensional (2D) skyrmion spin texture but also the bimeron spin texture. However, it remains challenging to experimentally create or stabilize a bimeron and identify the conditions that facilitate its formation. In this context, our research predicts a novel form of topological structure known as the domain wall bimeron in ferromagnetic spin-1 Bose–Einstein condensates by manipulating the magnetic field. Unlike conventional 2D skyrmions, this unique bimeron exhibits a non-axisymmetric spin texture and features complex off-axis vortices whose cores are connected by domain walls. This work significantly contributes to the study of 2D topological excitations in quantum matter with high spins.
In this paper we first derive a general method which enables one to create expressions for vortices and monopoles. By using this method we construct several order-parameters describing the vortices and monopoles of Bose–Einstein condensates with hyperfine spin F = 1 and F = 2. We concentrate on defects which are topologically stable in the absence of an external magnetic field. In particular we show that in a ferromagnetic condensate there can be a vortex which does produce any superfluid flow. We also point out that the order-parameter space of the cyclic phase of F = 2 condensate consists of two disconnected sets. Finally we examine the effect of an external magnetic field on the vortices of a ferromagnetic F = 1 condensate and discuss the experimental preparation of a vortex in this system.