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

Journal of Physics Conference Series

Textures of Spin-Orbit CoupledF= 2 Spinor Bose Einstein Condensates

Takuto Kawakami, Takeshi Mizushima, K. Machida

Published Dec 17, 2012• 0 citations
Publisher

Abstract

Motivated by recent studies of Bose Einstein condensates (BECs) under synthetic gauge fields, we study the textures of F = 2 BECs with a Rashba like spin-orbit coupling (SOC). By analyzing the SOC term, we demonstrate that the SOC favors a helical modulation of order parameters (OPs). In addition, we find the stable textures obtained by the numerical minimization of the Gross-Pitaevskii energy functional and interpret them as a one- or two-dimensional helical modulation. In the parameter region where the polar OP is favored, the emergence of the skyrmion of the uniaxial polar OP and its energetics relative to one-dimensional helical modulation of biaxial polar OP are discussed in details. Through the comparison of the lattice texture in the cyclic favored parameter region and uniaxial polar skyrmion, we show the instability of the lattice of the uniaxial polar skyrmion.

DOI
10.1088/1742-6596/400/1/012028

Related papers

Textures of F=2 spinor Bose-Einstein condensates with spin-orbit coupling

Takuto Kawakami, Takeshi Mizushima, Kazushige Machida

We study the textures of $F=2$ spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) due to the SOC. In particular, the cyclic OP consists of two-dimensional lattice textures, such as the hexagonal lattice and the $\frac{1}{3}$ vortex lattice, commonly understandable as the two-dimensional network of the helical modulations.

arXiv:1104.4179•Physical Review A•Jul 25, 2011•102 citations

Vortex states and spin textures of rotating spin–orbit-coupled Bose–Einstein condensates in a toroidal trap

Huan Wang, Linghua Wen, Hui Yang +2 more

Abstract We consider the ground-state properties of Rashba spin–orbit-coupled pseudo-spin-1/2 Bose–Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin–orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, SOC, and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically. In particular, for a fixed rotation frequency above the critical value, the increasing isotropic SOC favors a visible vortex necklace in each component which is accompanied by a hidden giant vortex plus a (several) hidden vortex necklace(s) in the central region. In the case of one-dimensional anisotropic SOC, large SOC strength results in the generation of hidden linear vortex string and the transition from initial component separation (component mixing) to component mixing (component separation). Furthermore, the peculiar spin textures including skyrmion lattice, skyrmion pair and skyrmion string are revealed in this system.

arXiv:1703.01411•Journal of Physics B Atomic Molecular and Optical Physics•Jun 22, 2017•38 citations

Characterized helical modulation of three-dimensional Skyrmions in the spin-orbit coupled condensate

Hao Tian Jiang, Chong Yu, Shu-Wei Song +3 more

For the Bose–Einstein condensate in the non-Abelian gauge field, the atomic wavefunction obtains helical modulation, which would lead to nontrivial objects, such as three-dimensional Skyrmion. The spin–orbit coupled condensate is usually capable of supporting Skyrmion ground states, which can be well understood through the wavefunction modulation vector concept. In the present manuscript, the modulation vector is characterized both analytically and numerically with respect to the spin–orbit coupling strength. For the SU(2) symmetric condensate, the modulation vector of the wavefunction is linearly proportional to the spin–orbit coupling strength. In the presence of spin-dependent interaction, the modulus of the modulation vector is predicted to increase or decrease according to the sign of the interaction parameter, resulting in a shrunken or expanded Skyrmion. However, the Skyrmion is unstable for a certain area of the parameter space of the spin–orbit coupling and spin-dependent interaction. The condensate favors a single Skyrmion state or the Skyrmion lattice state according to the strength of the spin–orbit coupling.

International Journal of Modern Physics B•Jul 30, 2020•0 citations

Spin-orbit coupling induced polarization textures in trapped Fermi gases

M. Iskin

We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.

•Apr 4, 2013•0 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

Antiferromagnetic Order in a Spin-Orbit Coupled Bose-Einstein Condensate

Zhongbo Yan, Shaolong Wan

Spin-orbit coupling related new physics and quantum magnetism are two branches of great interest both in condensed matter physics and in cold atomic physics. With the introduction of a Rashba-like SOC into a Bose-Einstein condensate (BEC) loaded in a two-dimensional bipartite optical square lattice, we find that the ground state of the BEC always favors a coherent condensate than a fragmented condensate and always exhibits very large degeneracy, and most importantly, an antiferromagnetic order of quantum nature emerges when parameters satisfy certain condition. This provides an ideal platform to study the interplay of antiferromagnetic phase and superfluid phase.

arXiv:1411.3216•Nov 12, 2014•0 citations
Motivated by recent studies of Bose Einstein condensates (BECs) under synthetic gauge fields, we study the textures of F = 2 BECs with a Rashba like spin-orbit coupling (SOC). By analyzing the SOC term, we demonstrate that the SOC favors a helical modulation of order parameters (OPs). In addition, we find the stable textures obtained by the numerical minimization of the Gross-Pitaevskii energy functional and interpret them as a one- or two-dimensional helical modulation. In the parameter region where the polar OP is favored, the emergence of the skyrmion of the uniaxial polar OP and its energetics relative to one-dimensional helical modulation of biaxial polar OP are discussed in details. Through the comparison of the lattice texture in the cyclic favored parameter region and uniaxial polar skyrmion, we show the instability of the lattice of the uniaxial polar skyrmion.
We study the textures of F=2F=2F=2 spinor Bose-Einstein condensates (BECs) with spin-orbit coupling (SOC) induced by a synthetic non-Abelian gauge field. On the basis of the analysis of the SOC energy and the numerical calculation of the Gross-Pitaevskii equation, we demonstrate that the textures originate from the helical modulation of the order parameter (OP) due to the SOC. In particular, the cyclic OP consists of two-dimensional lattice textures, such as the hexagonal lattice and the 13\frac{1}{3}31​ vortex lattice, commonly understandable as the two-dimensional network of the helical modulations.
Abstract We consider the ground-state properties of Rashba spin–orbit-coupled pseudo-spin-1/2 Bose–Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin–orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, SOC, and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically. In particular, for a fixed rotation frequency above the critical value, the increasing isotropic SOC favors a visible vortex necklace in each component which is accompanied by a hidden giant vortex plus a (several) hidden vortex necklace(s) in the central region. In the case of one-dimensional anisotropic SOC, large SOC strength results in the generation of hidden linear vortex string and the transition from initial component separation (component mixing) to component mixing (component separation). Furthermore, the peculiar spin textures including skyrmion lattice, skyrmion pair and skyrmion string are revealed in this system.
For the Bose–Einstein condensate in the non-Abelian gauge field, the atomic wavefunction obtains helical modulation, which would lead to nontrivial objects, such as three-dimensional Skyrmion. The spin–orbit coupled condensate is usually capable of supporting Skyrmion ground states, which can be well understood through the wavefunction modulation vector concept. In the present manuscript, the modulation vector is characterized both analytically and numerically with respect to the spin–orbit coupling strength. For the SU(2) symmetric condensate, the modulation vector of the wavefunction is linearly proportional to the spin–orbit coupling strength. In the presence of spin-dependent interaction, the modulus of the modulation vector is predicted to increase or decrease according to the sign of the interaction parameter, resulting in a shrunken or expanded Skyrmion. However, the Skyrmion is unstable for a certain area of the parameter space of the spin–orbit coupling and spin-dependent interaction. The condensate favors a single Skyrmion state or the Skyrmion lattice state according to the strength of the spin–orbit coupling.
We use the Bogoliubov-de Gennes (BdG) theory to study the interplay between the Zeeman field, spin-orbit coupling (SOC) and resultant skyrmion-like polarization textures in harmonically trapped two-dimensional Fermi gases. Our primary finding is that, in sharp contrast to the no-SOC case where only an easy-axis polarization is possible beyond a threshold Zeeman field (depending on the interaction strength), any non-zero combination of the Zeeman field and Rashba SOC induces not only an easy-axis polarization everywhere in the system but also a spatially-modulated transverse one near the edges. Our secondary finding is that the ground states of Rashba spin-orbit coupled systems are revealed to have stronger Fulde-Ferrell type non-uniform superfluid characters (i.e. phase modulations) but not a Larkin-Ovchinnikov one (i.e. amplitude modulations) under the in-plane Zeeman field, for which the phases of the superfluid order parameters modulate near the edges and most prominently along the transverse direction. The effects of the interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the intricate polarization textures and superfluid order parameter are also discussed.
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.
Spin-orbit coupling related new physics and quantum magnetism are two branches of great interest both in condensed matter physics and in cold atomic physics. With the introduction of a Rashba-like SOC into a Bose-Einstein condensate (BEC) loaded in a two-dimensional bipartite optical square lattice, we find that the ground state of the BEC always favors a coherent condensate than a fragmented condensate and always exhibits very large degeneracy, and most importantly, an antiferromagnetic order of quantum nature emerges when parameters satisfy certain condition. This provides an ideal platform to study the interplay of antiferromagnetic phase and superfluid phase.