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

Scientific Reports

Spin texture in Bose–Einstein condensates confined in spin-dependent optical lattices

Shu-Song Wang, Suying Zhang

Published Oct 15, 2025• 0 citations
Publisher

Abstract

We investigate the ground state of rotating two-component Bose-Einstein condensates in the combined potential well of one-dimensional spin-dependent optical lattice potential and harmonic potential. The density distribution of the condensate is striped. By defining the generalized momentum operator, we derive the velocity distribution of the condensate. The velocity contours are concentric circles for each stripe, with different centers for different stripes. This velocity distribution corresponds to a specific spin texture structure. In this texture, the azimuthal angle of the magnetic moments varies along the y-direction, while the z-component of the magnetic moments varies along the x-direction. When the lattice period [Formula: see text], the texture is divided into two regions. The magnetic moments reverse in a counterclockwise direction and in a clockwise direction as y increases in regions I and II, respectively. Furthermore, when the lattice period [Formula: see text], the texture is divided into three regions. The magnetic moments reverse in a counterclockwise direction, do not reverse, and reverse in a clockwise direction as y increases in regions I, II, and III, respectively. Accurate manipulation of the texture can be achieved by adjusting the optical lattice periods [Formula: see text] and [Formula: see text], the relative phase φ, and the rotational angular frequency Ω.

DOI
10.1038/s41598-025-20070-1

Related papers

Half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices

Wei Han, Suying Zhang, Jingjing Jin +1 more

We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternately. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of domain walls, with spatially periodic eyebrowlike spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency, and the period of the optical lattices. Under external disturbances, some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession, are observed.

arXiv:1112.5161•Physical Review A•Apr 30, 2012•22 citations

Ground state of spin-2 dipolar rotating Bose–Einstein condensates

Qiang Zhao

We study the ground state of spin-2 dipolar rotating Bose–Einstein condensates in a harmonic potential. As the strength of dipolar interaction enhances, our results show that the vortex number becomes smaller and smaller at a fixed component. In addition, the vortex stripe occurs and its number increases. The components m[Formula: see text]1 or ±2 display the same density and the total density shows layered distribution. Increasing the rotational frequency to a higher value, the vortex number and vortex row number increase. We also plot the dependence of angular momentum Lz as a function of dipole strength c[Formula: see text], showing that Lz decreases with increasing c[Formula: see text].

International Journal of Modern Physics B•Apr 20, 2019•2 citations

Ground-state phases of a rotating spin-orbit–coupled Bose-Einstein condensate in an optical lattice

Ji-Guo Wang, Liang-Liang Xu, Shi-Jie Yang

We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.

Europhysics Letters (EPL)•Oct 1, 2017•6 citations

Spin domain wall in rotating two-component Bose–Einstein condensates

Jingjing Jin, Suying Zhang, Wei Han

We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.

Journal of Physics B Atomic Molecular and Optical Physics•Jul 20, 2011•9 citations

Stable striped state in a rotating two-dimensional spin–orbit coupled spin-1/2 Bose–Einstein condensate

Xuan Xu, Chao Gao, Ji Lin +1 more

Abstract We consider an effective two-dimensional Bose–Einstein condensate with some spin–orbit coupling (SOC) and a rotation term in an external harmonic potential. We find the striped state, and analyze the effects of SOC, the external potential, and the rotation frequency/direction on the profile and the stability of the striped state. Without the rotation term, the two spinor components exhibit striped pattern, and the numbers of stripes in the two components are always an odd–even or an even–odd. With the increase of the SOC strength, the number of stripes in both components increases, while the difference of the striped numbers is always one. After adding the rotation term, the profiles of the spinor components change qualitatively, and the change regulation of the striped numbers differs, while the difference of the striped numbers is still one. In addition, we find that the rotation direction only makes the striped state of the two spinor components exchange each other, though the clockwise and counterclockwise rotation directions are inequivalent with the presence of SOC. Such regulation is different from the previous study. And the rotation frequency gives rise to the transition from the striped state to a mixture of the striped state and vortex state. Furthermore, we prove the stability of these states by the evolution and linear stability analysis.

Communications in Theoretical Physics•May 11, 2022•0 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
We investigate the ground state of rotating two-component Bose-Einstein condensates in the combined potential well of one-dimensional spin-dependent optical lattice potential and harmonic potential. The density distribution of the condensate is striped. By defining the generalized momentum operator, we derive the velocity distribution of the condensate. The velocity contours are concentric circles for each stripe, with different centers for different stripes. This velocity distribution corresponds to a specific spin texture structure. In this texture, the azimuthal angle of the magnetic moments varies along the y-direction, while the z-component of the magnetic moments varies along the x-direction. When the lattice period [Formula: see text], the texture is divided into two regions. The magnetic moments reverse in a counterclockwise direction and in a clockwise direction as y increases in regions I and II, respectively. Furthermore, when the lattice period [Formula: see text], the texture is divided into three regions. The magnetic moments reverse in a counterclockwise direction, do not reverse, and reverse in a clockwise direction as y increases in regions I, II, and III, respectively. Accurate manipulation of the texture can be achieved by adjusting the optical lattice periods [Formula: see text] and [Formula: see text], the relative phase φ, and the rotational angular frequency Ω.
We investigate half-vortex sheets and domain-wall trains of rotating two-component Bose-Einstein condensates in spin-dependent optical lattices. The two-component condensates undergo phase separation in the form of stripes arranged alternately. The vortices of one component are aligned in lines in the low-density regions and filled with the other component, which results in a stable vortex configuration, straight half-vortex sheets. A train of domain walls, with spatially periodic eyebrowlike spin textures embedded on them, are formed at the interfaces of the two components. We reveal that these spatially periodic textures on the domain walls result from the linear gradient of the relative phase, which is induced by the alternating arrangement of the vortex sheets in the two components. An accurate manipulation of the textures can be realized by adjusting the intercomponent interaction strength, the rotating angular frequency, and the period of the optical lattices. Under external disturbances, some interesting phenomena, including collective movement of vortices along the sheets and spin-wave propagation along the domain walls, as well as local spin precession, are observed.
We study the ground state of spin-2 dipolar rotating Bose–Einstein condensates in a harmonic potential. As the strength of dipolar interaction enhances, our results show that the vortex number becomes smaller and smaller at a fixed component. In addition, the vortex stripe occurs and its number increases. The components m[Formula: see text]1 or ±2 display the same density and the total density shows layered distribution. Increasing the rotational frequency to a higher value, the vortex number and vortex row number increase. We also plot the dependence of angular momentum Lz as a function of dipole strength c[Formula: see text], showing that Lz decreases with increasing c[Formula: see text].
We study the ground-state phases of a two-dimensional rotating spin-orbit–coupled Bose-Einstein condensate loaded in a one-dimensional spin-dependent optical lattice. In the absence of rotation, the system undergoes a phase transition from the stripe phase to the supersolid phase gradually for weak spin-orbit coupling strength and directly for strong spin-orbit coupling strength as the depth of the optical lattice increases. With increasing the rotation strength, the stripe phase transforms to the ringlike state, and the domain number of the ringlike state increases when the Bose-Einstein condensate is in the weak depth of the optical lattice. The supersolid phase transforms to the phase with a single domain of a vortex line for small rotation strength, and alternating vortex lines along the x -direction appear for large rotation strength when the Bose-Einstein condensate is in the strong depth of the optical lattice. The spin textures of the ground-state phases are also discussed.
We study rotating two-component Bose–Einstein condensates with equal particle numbers and strong intercomponent repulsion located in a harmonic potential by numerically solving two-dimensional coupled Gross–Pitaevskii equations. The condensates are observed as a dramatic departure, forming a pair of shells located symmetrically in the trap with a small spatial overlap. Projecting the system into a pseudospin space, a spin domain wall is formed at the interface of the two components. The complex and spatial periodic spin texture is formed on the domain-wall region. We discuss the dependence of the spin texture of the domain wall on the angular velocity in detail. The relation among the number of the vortices, the topological charge and the angular momentum, as an extension of Feynman's rule in the two-component Bose–Einstein condensates, is given, based on the spin texture carrying the angular momentum of the condensates.
Abstract We consider an effective two-dimensional Bose–Einstein condensate with some spin–orbit coupling (SOC) and a rotation term in an external harmonic potential. We find the striped state, and analyze the effects of SOC, the external potential, and the rotation frequency/direction on the profile and the stability of the striped state. Without the rotation term, the two spinor components exhibit striped pattern, and the numbers of stripes in the two components are always an odd–even or an even–odd. With the increase of the SOC strength, the number of stripes in both components increases, while the difference of the striped numbers is always one. After adding the rotation term, the profiles of the spinor components change qualitatively, and the change regulation of the striped numbers differs, while the difference of the striped numbers is still one. In addition, we find that the rotation direction only makes the striped state of the two spinor components exchange each other, though the clockwise and counterclockwise rotation directions are inequivalent with the presence of SOC. Such regulation is different from the previous study. And the rotation frequency gives rise to the transition from the striped state to a mixture of the striped state and vortex state. Furthermore, we prove the stability of these states by the evolution and linear stability analysis.
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.