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:1610.09458 · Physical Review A

Spin-orbit-coupled Bose-Einstein condensates held under a toroidal trap

Xiao-Fei Zhang, Masaya Kato, Wei Han, Shougang Zhang, Hiroki Saito

Published Mar 16, 2017• 52 citations
arXivHTMLPDF

Abstract

We study a quasispin-1/2 Bose-Einstein condensate with synthetically generated spin-orbit coupling in a toroidal trap and show that the system has a rich variety of ground states. As the central hole region increases, i.e., the potential changes from harmoniclike to ringlike, the condensate exhibits a variety of structures, such as a modified stripe, an alternately arranged stripe, and countercircling states. In the limit of a quasi-one-dimensional ring, the quantum many-body ground state is obtained, which is found to be the fragmented condensate.

DOI
10.1103/physreva.95.033620

Related papers

Spin-orbit-coupled Bose gases with nonlocal Rydberg interactions held under a toroidal trap

Xiao-Fei Zhang, Lin Wen, Lin-Xue Wang +3 more

We consider a spin-orbit-coupled Bose-Einstein condensate with nonlocal Rydberg interactions confined in a toroidal trap. Our results show that the interplay among nonlocal Rydberg interactions, contact interactions, spin-orbit coupling, and the external toroidal trap can give rise to a rich variety of ground-state phases, such as lump necklace, chiral supersolid, standing- and plane-wave supersolid, and so on. Furthermore, we clarify the different breaking of symmetry induced by system parameters. Finally, the limiting case of a quasi-one-dimensional ring has also been investigated, and our analytical results agree well with the Gross-Pitaevskii numerical simulations. We also give an experimental protocol to observe these states in future experiments.

Physical Review A•Mar 14, 2022•24 citations

Ground state of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in toroidal trap

Ji Li, Bin Liu, Jing Song Bai +2 more

Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.

Acta Physica Sinica•Jan 1, 2020•3 citations

Ground-state phases of the spin-orbit-coupled spin-1 Bose gas in a toroidal trap

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

We consider the spin-1 Bose-Einstein condensates with the isotropic Rashba spin-orbit coupling in a two-dimensional toroidal trap. Three types of striped phases are found in a nonrotational system, i.e., the stripe phase with the periodic density modulation along the azimuthal direction, the stripe phase with the periodic density modulation along both the azimuthal and the radial directions, and the stripe phase with the periodic density modulation along the radial direction. By adding the rotation, the condensates occupy the ${m}_{F}=0$ component for small rotational frequency, while they occupy both the ${m}_{F}=1$ and ${m}_{F}=\ensuremath{-}1$ components for large rotational frequency when both the relative interaction and the spin-orbit coupling are weak. For the stronger relative interaction and spin-orbit coupling, the vortices of the system are elongated along the radial direction and linked one after another. As the rotational frequency further increases, the density evolves from the elongated effect of the vortices into a laminar vortex ring.

Physical Review A•Sep 25, 2017•30 citations

Effect of Anisotropic Spin-Orbit Coupling on the Ground State of Bose–Einstein Condensate in an External Potential*

Wan-Quan He, Ri-Li 日丽 Gao 高, Pei 培 Zhang 张 +3 more

Abstract Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantum-state manipulation and will contribute to the design and exploration of novel quantum devices. Here we consider a quasi-two-dimensional spin-orbit coupled Bose–Einstein condensate confined in an external harmonic potential, with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system. For the cases with spin-orbit coupling solely in x- or y-axis direction, the ground-state structure can develop to the well-known standing wave phase, in which the two components always form an alternative density arrangement. For a two-dimensional anisotropic spin-orbit coupling, the separated lumps first become bend, then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction. Furthermore, the distance between these two rows of stripe structure is also investigated in detail.

Communications in Theoretical Physics•Mar 1, 2015•0 citations

Effect of Anisotropic Spin-Orbit Coupling on the Ground State of Bose-Einstein Condensate in an External Potential

和万全, 高日丽, 张培 +3 more

Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.

理论物理通讯：英文版•Jan 1, 2015•0 citations

Exotic ground states of a spin–orbit-coupled spinor Bose–Einstein condensate trapped by a toroidal potential

Ping Peng, Guan-Qiang Li, Wen‐Li Yang +1 more

Abstract The ground-state properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) in a toroidal trap are investigated. The exotic ground states, such as the necklace state, the persistent flow and even the vortex state, for the three components in the system are induced by adjustable external parameters. It is found that the petal number of the necklace states is increased with increasing the intensity of the spin–orbit coupling (SOC), and the anisotropy of the SOC can be used to control the structure of the ground states. The rotation of the condensate induced by the external field makes the densities of the three components asymmetric and tends to transform the necklace state to the persistent flow. The radius of the toroidal potential is another degree of freedom for manipulating the necklace state. In addition, the transition between the necklace state and the vortex, intermediated by the persistent flow, can be controlled by the ratio of the density-density and spin-exchange interactions. All of above results enrich our knowledge about the properties of the ground states of spin-1 BEC trapped in the toroidal trap.

Laser Physics Letters•Jun 20, 2018•7 citations
We study a quasispin-1/2 Bose-Einstein condensate with synthetically generated spin-orbit coupling in a toroidal trap and show that the system has a rich variety of ground states. As the central hole region increases, i.e., the potential changes from harmoniclike to ringlike, the condensate exhibits a variety of structures, such as a modified stripe, an alternately arranged stripe, and countercircling states. In the limit of a quasi-one-dimensional ring, the quantum many-body ground state is obtained, which is found to be the fragmented condensate.
We consider a spin-orbit-coupled Bose-Einstein condensate with nonlocal Rydberg interactions confined in a toroidal trap. Our results show that the interplay among nonlocal Rydberg interactions, contact interactions, spin-orbit coupling, and the external toroidal trap can give rise to a rich variety of ground-state phases, such as lump necklace, chiral supersolid, standing- and plane-wave supersolid, and so on. Furthermore, we clarify the different breaking of symmetry induced by system parameters. Finally, the limiting case of a quasi-one-dimensional ring has also been investigated, and our analytical results agree well with the Gross-Pitaevskii numerical simulations. We also give an experimental protocol to observe these states in future experiments.
Realization of spinor Bose-Einstein condensate in an optical trap has made it possible to create a variety of topological nontrivial structures, due to the vector character of the order parameter. Recently, artificial spin-orbit coupling in the spinor Bose-Einstein condensate, owing to coupling between the spin and the center-of-mass motion of the atom, provides an unprecedented opportunity to search for novel quantum states. As is well known, the potential well in the Bose-Einstein condensate is adjustable. The toroidal trap is an important model potential because of its simplicity and richness in physics. In particular, the spinor Bose-Einstein condensate under the toroidal trap has brought an ideal platform for studying fascinating properties of a superfluid, such as persistent flow and symmetry-breaking localization. For the case of the spin-orbit-coupled Bose-Einstein condensate, the previous studies of the toroidal trap mainly focused on the two-component or antiferromagnetic case. However, in the presence of a toroidal trap, there remains an open question whether the combined effects of the spin-orbit coupling and rotation can produce previously unknown types of topological excitations in the ferromagnetic Bose-Einstein condensate. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of spin-orbit coupled rotating ferromagnetic Bose-Einstein condensate in the toroidal trap. We concentrate on the effects of the spin-orbit coupling and the rotation on the ground states. The numerical results show that in the presence of a toroidal trap, the ground state structure is displayed as half-skyrmion chain with circular distribution. Adjusting the strength of spin-orbit coupling not only changes the number of half-skyrmion in the system, but also controls the symmetry of half-skyrmion with circular distribution. As the rotation frequency increases, the system undergoes the transitions from the plane wave to the half-skyrmion chain with circular distribution, and eventually developing the half-skyrmion phase of triangular lattice. Next, we examine the effect of spin-independent interaction on spin-orbit coupled rotating spinor Bose-Einstein condensate. As the spin-independent interaction increases, the topological defects in the condensate increase due to the variation of the local magnetic order. We also discuss the influence of well shape on the ground state structure. These topological structures can be detected via the time-of-flight absorption imaging technique. The spin-orbit coupled spinor Bose-Einstein condensate in the toroidal trap is an important quantum platform, which not only opens up a new avenue for exploring the exotic topological structures, but also is crucial for realizing the transitions among different ground states. This work paves the way for futureexploring the topological defects and the corresponding dynamical stability in quantum system subjected to the toroidal trap.
We consider the spin-1 Bose-Einstein condensates with the isotropic Rashba spin-orbit coupling in a two-dimensional toroidal trap. Three types of striped phases are found in a nonrotational system, i.e., the stripe phase with the periodic density modulation along the azimuthal direction, the stripe phase with the periodic density modulation along both the azimuthal and the radial directions, and the stripe phase with the periodic density modulation along the radial direction. By adding the rotation, the condensates occupy the mF=0{m}_{F}=0mF​=0 component for small rotational frequency, while they occupy both the mF=1{m}_{F}=1mF​=1 and ${m}_{F}=\ensuremath{-}1$ components for large rotational frequency when both the relative interaction and the spin-orbit coupling are weak. For the stronger relative interaction and spin-orbit coupling, the vortices of the system are elongated along the radial direction and linked one after another. As the rotational frequency further increases, the density evolves from the elongated effect of the vortices into a laminar vortex ring.
Abstract Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantum-state manipulation and will contribute to the design and exploration of novel quantum devices. Here we consider a quasi-two-dimensional spin-orbit coupled Bose–Einstein condensate confined in an external harmonic potential, with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system. For the cases with spin-orbit coupling solely in x- or y-axis direction, the ground-state structure can develop to the well-known standing wave phase, in which the two components always form an alternative density arrangement. For a two-dimensional anisotropic spin-orbit coupling, the separated lumps first become bend, then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction. Furthermore, the distance between these two rows of stripe structure is also investigated in detail.
Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.
Abstract The ground-state properties of a spin–orbit-coupled spin-1 Bose–Einstein condensate (BEC) in a toroidal trap are investigated. The exotic ground states, such as the necklace state, the persistent flow and even the vortex state, for the three components in the system are induced by adjustable external parameters. It is found that the petal number of the necklace states is increased with increasing the intensity of the spin–orbit coupling (SOC), and the anisotropy of the SOC can be used to control the structure of the ground states. The rotation of the condensate induced by the external field makes the densities of the three components asymmetric and tends to transform the necklace state to the persistent flow. The radius of the toroidal potential is another degree of freedom for manipulating the necklace state. In addition, the transition between the necklace state and the vortex, intermediated by the persistent flow, can be controlled by the ratio of the density-density and spin-exchange interactions. All of above results enrich our knowledge about the properties of the ground states of spin-1 BEC trapped in the toroidal trap.