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Chinese Physics B

Vortex chains induced by anisotropic spin–orbit coupling and magnetic field in spin-2 Bose-Einstein condensates

Hao Zhu, Shougen Yin, Wu-Ming Liu

Published Dec 7, 2021• 2 citations
Publisher

Abstract

We investigate the anisotropic spin–orbit coupled spin-2 Bose–Einstein condensates with Ioffe–Pritchard magnetic field. With nonzero magnetic field, anisotropic spin–orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin–orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.

DOI
10.1088/1674-1056/ac4020

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We investigate the anisotropic spin–orbit coupled spin-2 Bose–Einstein condensates with Ioffe–Pritchard magnetic field. With nonzero magnetic field, anisotropic spin–orbit coupling will introduce several vortices and further generate a vortex chain. Inside the vortex chain, the vortices connect to each other, forming a line along the axis. The physical nature of the vortex chain can be explained by the particle current and the momentum distribution. The vortex number inside the vortex chain can be influenced via varying the magnetic field. Through adjusting the anisotropy of the spin–orbit coupling, the direction of the vortex chain is changed, and the vortex lattice can be triggered. Moreover, accompanied by the variation of the atomic interactions, the density and the momentum distribution of the vortex chain are affected. The realization and the detection of the vortex chain are compatible with current experimental techniques.
We investigate the rotating spin-1 Bose-Einstein condensates with anisotropic spin-orbit coupling by using the damped projected Gross-Pitaevskii equation. The anisotropic spin-orbit coupling can cause some vortices to form the vortex chain, where the vortices link up with each other in a line. The formation of the vortex chain starts from very small rotation frequency and coexists with more remanent vortices with the increasing rotation frequency. By increasing the anisotropy of the spin-orbit coupling, the creation of the vortex chain is enhanced, accompanied by the emergence of several types of vortex chain and other vortex configurations. When the vortices of the ${m}_{F}=\ensuremath{-}1$ and mF=+1{m}_{F}=+1mF​=+1 components are of synchronous phases, such vortex configurations do not cause any topological excitation in the spin texture.
We investigate the combined effects of spin-orbit coupling and rotation on the topological vortical phase transition in F=2F=2F=2 Bose-Einstein condensates. We find that the spin-orbit coupling can precisely manipulate the canonical atom current which is generated in the opposite direction of the gauge atom current and causes both a continuous and a discontinuous canonical angular momentum. We apply the canonical angular momentum and magnetization to reveal the emergence of novel topological excitations, such as the Anderson-Toulouse vortex as well as the vortex--dipole lattice. Especially, strong spin-orbit coupling can induce two perpendicular vortex chains. We also find that both the first-order and the second-order phase transition can be characterized by the canonical angular momentum and the magnetization. Differently from the spin singlet-pairing interaction, the spin-exchange interaction can adjust the canonical angular momentum and control the phase transition well. The topological vortical phase transition in an F=2F=2F=2 cold-atom system is compatible with the current experiment and can be detected by the spin polarization procedure.
Weinvestigate the vortex structures excited by Ioffe–Pritchard magnetic field and Dresselhaus-type spin–orbit coupling in F = 2 ferromagnetic Bose–Einstein condensates. In the weakly interatomic interacting regime, an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero. With the combined effect of spin–orbit coupling and magnetic field, the ground state experiences a transition from polar-core vortex to Mermin–Ho vortex, in which the canonical particle current is anticlockwise. For fixed spin–orbit coupling strengths, the evolution of phase winding, magnetization, and degree of phase separation with magnetic field are studied. Additionally, with further increasing spin–orbit coupling strength, the condensate exhibits symmetrical density domains separated by radial vortex arrays. Our work paves the way to explore exotic topological excitations in high-spin systems.
Abstract The ground-state phases of Rashba spin–orbit (SO)-coupled Bose–Einstein condensates (BECs) in a quadrupole magnetic field are studied. The coupling of quadrupole magnetic field and spin induces local nonzero gauge particle current, accompanied by the generation of equal and opposite canonical particle current, and leads to the spontaneous nucleation of quantized vortices. The condensates exhibit a variety of rich density patterns and vortex arrangements resulting from the competition among quadrupole magnetic field, SO coupling, and interatomic interactions. Novel vortex structures, such as static vortex dipole, three-vortex molecule and the structure of a cross-arranged vortices and anti-vortices surrounded by a density annulus are found in the condensates. These structures greatly enrich the ground-state phases of SO-coupled BECs, and help to understand the superfluid behavior of a BEC and the nonlinear behavior of coherent matter waves.
Two-component Bose-Einstein condensate offers an ideal platform for investigating many intriguing topological defects due to the interplay between intraspecies and interspecies interactions. The recent realization of spin-orbit coupling in two-component Bose-Einstein condensate, owing to coupling between the spin and the centre-of-mass motion of the atom, provides possibly new opportunities to search for novel quantum states. In particular, the gradient magnetic field in the Bose-Einstein condensate has brought a new way to create topologically nontrivial structures including Dirac monopoles and quantum knots. Previous studies of the gradient magnetic field effect in the Bose-Einstein condensate mainly focused on the three-component case. However, it remains unclear how the gradient magnetic field affects the ground state configuration in the rotating two-component Bose-Einstein condensate with spin-orbit coupling. In this work, by using quasi two-dimensional Gross-Pitaevskii equations, we study the ground state structure of a rotating two-component Bose-Einstein condensate with spin-orbit coupling and gradient magnetic field. We concentrate on the effects of the spin-orbit coupling and the gradient magnetic field on the ground state. The numerical results show that increasing the strength of the spin-orbit coupling can induce a phase transition from skyrmion lattice to skyrmion chain in the presence of the gradient magnetic field. Unlike the study of skyrmion in rotating two-component Bose-Einstein condensate with only spin-orbit coupling, the skyrmion chain can occur under the isotropic spin-orbit coupling when the gradient magnetic field is considered. It is worth noting that the skyrmion chain here is arrayed along the diagonal direction. Next we examine the effect of the gradient magnetic field on spin-orbit coupled two-component Bose-Einstein condensate. For the case of weak spin-orbit coupling and the slow rotation, a phase transition from a single plane-wave to half-skyrmion is found through increasing magnetic field gradient strength. For the case of strong spin-orbit coupling and the fast rotation, the nature of the ground state is shown to support the formation of a hidden vortex as the gradient magnetic field is enhanced. These hidden vortices have no visible cores in density distributions but have phase singularities in phase distributions, which are arrayed along the diagonal direction. This result confirms a new method of creating the hidden vortices in the two-component Bose-Einstein condensate. These topological structures can be detected by using the time-of-flight absorption imaging technique. Our results illustrate that the gradient magnetic field not only provides an opportunity to explore the exotic topological structures in spin-orbit coupled spinor Bose-Einstein condensate, but also is crucial for realizing the phase transitions among different ground states. This work paves the way for the future exploring of topological defect and the corresponding dynamical stability in quantum systems subjected to a gradient magnetic field.
Abstract We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ ≥ 1 and is nonlinear with λ < 1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.