© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:2407.20977 · New Journal of Physics

2D Skyrmion topological charge of spin textures with arbitrary boundary conditions: a two-component spinorial BEC as a case study

Saúl Sánchez-Reséndiz, Eleazar Neri, Saul Gonzalez-Hernandez, Vı́ctor Romero-Rochı́n

Published Sep 27, 2024• 1 citation

Abstract

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

DOI: 10.1088/1367-2630/ad80ba

Related papers

Skyrmions with arbitrary topological charges in spinor Bose–Einstein condensates

R Zamora-Zamora, Vı́ctor Romero-Rochı́n

Abstract Topological Skyrmion defects with arbitrary topological charges are shown to appear in spinor F = 1 Bose–Einstein condensates, under the presence of external gauge or magnetic fields with cylindrical symmetry. We show that, depending on the magnetic field boundary conditions, the spin texture, at the planes perpendicular to the cylindrical axis, can be forced to show Skyrmions with topological charge zero, half-integer, or any desired arbitrary value between − 1 / 2 and 1/2. Our findings are obtained by numerically solving the corresponding fully coupled Gross–Pitaevskii equations without any symmetry assumptions and by analyzing the Skyrmion topological charge. We study, both, polar 23 Na and ferromagnetic 87 Rb condensates.

arXiv:1703.03795•Journal of Physics B Atomic Molecular and Optical Physics•Dec 20, 2017•11 citations

Stable double-pair skyrmion in an antiferromagneticF= 1 Bose–Einstein condensate

Yong-Kai Liu, Shi-Jie Yang

The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.

New Journal of Physics•Jun 28, 2017•5 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

Observation of Topologically Stable 2D Skyrmions in an Antiferromagnetic Spinor Bose-Einstein Condensate

Jae-yoon Choi, Woo Jin Kwon, Yong-il Shin

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.

arXiv:1110.3858•Physical Review Letters•Jan 19, 2012•182 citations

The ground states and spin textures of rotating two-component Bose–Einstein condensates in an annular trap

Jingjing Jin, Suying Zhang, Wei Han +1 more

We investigate the ground states and spin textures of rotating two-component Bose–Einstein condensates (BECs) confined in an annular potential. For the two-component miscible BECs, we analytically give the critical angular velocity of each component with the Thomas–Fermi approximation (TFA), at which the density profile changes from a disc shape into an annulus shape, forming a giant vortex. We present a phase diagram showing three kinds of density profiles of the ground states that are two disc shaped, one disc and another annulus shaped, and two annulus shaped. For the two-component immiscible BECs with particle number grave imbalance, we also discuss their ground states using the TFA, and three kinds of symmetrical structures of the density profiles are classified analytically. The spin textures of the two-component immiscible BECs have been studied and we find three kinds of symmetrical structures of the spin textures in the annular trap. One of these textures is an annular skyrmion which has been observed in harmonic potentials. Both of the other spin textures contain a new structure composed of concentric double-annulus skyrmion whose topological charge is the sum of the ones of two annular skyrmions, and the topological charge of each annular skyrmion is equal to the absolute value of the difference between the quantum numbers of circulation of two components inside this annular skyrmion. We also prove that these new textures are robust by investigating the dynamical behaviours of the system under external disturbances.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 13, 2013•7 citations

Imprinting Skyrmion spin textures in spinor Bose–Einstein condensates

Jae-yoon Choi, Woo Jin Kwon, Moonjoo Lee +3 more

We investigate an experimental method for imprinting Skyrmion spin textures in a spinor Bose–Einstein condensate by rapidly moving the zero-field center of a three-dimensional (3D) quadrupole magnetic field through the condensate. Various excitations such as 2D Skyrmions and coreless vortices were created in spin-1 sodium condensates, initially prepared in a uniform polar or ferromagnetic phase. The spin textures were characterized with the spatial distribution of the spin tilt angle, which is found to be in good quantitative agreement with the local description of single spins under the field rotation. We demonstrate the creation of a highly charged Skyrmion in a trapped condensate by applying the imprinting process multiple times.

New Journal of Physics•May 9, 2012•51 citations

Abstract We derive the most general expression for the Skyrmion topological charge for a two-dimensional spin texture, valid for any type of boundary conditions or for any arbitrary spatial region within the texture. It reduces to the usual one for the appropriate boundary conditions. The general expression resembles the Gauss-Bonet theorem for the Euler-Poincaré characteristic of a 2D surface, but it has definite differences, responsible for the assignment of the proper signs of the Skyrmion charges. Additionally, we show that the charge of a single Skyrmion is the product of the value of the normal component of the spin texture at the singularity times the Index or winding number of the transverse texture, a generalization of a Poincaré theorem. We illustrate our general results analyzing in detail a two-component spinor Bose–Einstein condensate (BEC) in 2D in the presence of an external magnetic field, via the Gross-Pitaevskii equation. The condensate spin textures present Skyrmions singularities at the spatial locations where the transverse magnetic field vanishes. We show that the ensuing superfluid vortices and Skyrmions have the same value for their corresponding topological charges, in turn due to the structure of the magnetic field.

Abstract Topological Skyrmion defects with arbitrary topological charges are shown to appear in spinor F = 1 Bose–Einstein condensates, under the presence of external gauge or magnetic fields with cylindrical symmetry. We show that, depending on the magnetic field boundary conditions, the spin texture, at the planes perpendicular to the cylindrical axis, can be forced to show Skyrmions with topological charge zero, half-integer, or any desired arbitrary value between − 1 / 2 and 1/2. Our findings are obtained by numerically solving the corresponding fully coupled Gross–Pitaevskii equations without any symmetry assumptions and by analyzing the Skyrmion topological charge. We study, both, polar 23 Na and ferromagnetic 87 Rb condensates.

The recent experimental realization of spin-orbit coupling (SOC) in spin-1 ultracold atoms opens up an interesting avenue for exploring new quantum states and novel quantum phenomena in large-spin systems. Two types of two-dimensional double-pair vortices that are connected by a domain-wall can be accommodated in the antiferromagnetic spin-1 Bose–Einstein condensate (BEC). One type, named a 2D double-pair skyrmion, which differs from the conventional 2D skyrmion in the F = 1 polar BEC, hosts a pair of vortices and displays a meron-pair texture with a unit topological charge. The other type has a meron-pair texture but with null topological charge. These two types of double-pair vortices can be naturally generated from a vortex-free Gaussian wave packet by incorporating a non-Abelian gauge field into the spinor condensate.

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.

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to dynamically deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.

We investigate the ground states and spin textures of rotating two-component Bose–Einstein condensates (BECs) confined in an annular potential. For the two-component miscible BECs, we analytically give the critical angular velocity of each component with the Thomas–Fermi approximation (TFA), at which the density profile changes from a disc shape into an annulus shape, forming a giant vortex. We present a phase diagram showing three kinds of density profiles of the ground states that are two disc shaped, one disc and another annulus shaped, and two annulus shaped. For the two-component immiscible BECs with particle number grave imbalance, we also discuss their ground states using the TFA, and three kinds of symmetrical structures of the density profiles are classified analytically. The spin textures of the two-component immiscible BECs have been studied and we find three kinds of symmetrical structures of the spin textures in the annular trap. One of these textures is an annular skyrmion which has been observed in harmonic potentials. Both of the other spin textures contain a new structure composed of concentric double-annulus skyrmion whose topological charge is the sum of the ones of two annular skyrmions, and the topological charge of each annular skyrmion is equal to the absolute value of the difference between the quantum numbers of circulation of two components inside this annular skyrmion. We also prove that these new textures are robust by investigating the dynamical behaviours of the system under external disturbances.

We investigate an experimental method for imprinting Skyrmion spin textures in a spinor Bose–Einstein condensate by rapidly moving the zero-field center of a three-dimensional (3D) quadrupole magnetic field through the condensate. Various excitations such as 2D Skyrmions and coreless vortices were created in spin-1 sodium condensates, initially prepared in a uniform polar or ferromagnetic phase. The spin textures were characterized with the spatial distribution of the spin tilt angle, which is found to be in good quantitative agreement with the local description of single spins under the field rotation. We demonstrate the creation of a highly charged Skyrmion in a trapped condensate by applying the imprinting process multiple times.