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arXiv:2506.15389

Microgravity-assisted off-axis spin vortex in a $^{87}$Rb dipolar spinor Bose-Einstein condensate

Hui Tang, Wenxian Zhang

Published Jun 18, 2025• 0 citations
arXivHTMLPDF

Abstract

The generation of the ground state of a spin vortex in a $^{87}$Rb Bose-Einstein condensate with the assistance of an optical plug has been studied. However, gravity is everywhere, and this potential linear dependence on the spatial position will destroy the axisymmetric structure of the system with the optical plug. In this case, the question of whether the spin vortex ground state still exists remains unresolved. The present study aims to explore the impact of microgravity on the formation of the spin vortex state with the assistance of an optical plug. To this end, a simple model has been employed to provide a comprehensive understanding of the phenomenon. The Gross-Pitaevskii equations are solved by setting the optical plug intensity, adjusting the optical plug width, and adjusting the microgravity strength. This process results in the phase diagram for the single-mode state and spin vortex state. Under microgravity situations, we observe an off-axis structure of the spin vortex state. Our calculations offer a reliable approach to generating spin vortex states in a microgravity environment.

DOI
10.48550/arxiv.2506.15389

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Microgravity-assisted off-axis spin vortex in a 87^{87}87Rb dipolar spinor Bose-Einstein condensate
The generation of the ground state of a spin vortex in a 87^{87}87Rb Bose-Einstein condensate with the assistance of an optical plug has been studied. However, gravity is everywhere, and this potential linear dependence on the spatial position will destroy the axisymmetric structure of the system with the optical plug. In this case, the question of whether the spin vortex ground state still exists remains unresolved. The present study aims to explore the impact of microgravity on the formation of the spin vortex state with the assistance of an optical plug. To this end, a simple model has been employed to provide a comprehensive understanding of the phenomenon. The Gross-Pitaevskii equations are solved by setting the optical plug intensity, adjusting the optical plug width, and adjusting the microgravity strength. This process results in the phase diagram for the single-mode state and spin vortex state. Under microgravity situations, we observe an off-axis structure of the spin vortex state. Our calculations offer a reliable approach to generating spin vortex states in a microgravity environment.
Generating a spin vortex in a 87Rb^{87}\mathrm{Rb}87Rb dipolar spinor Bose-Einstein condensate in a controllable way is still experimentally challenging. We propose an experimentally easy and tunable way to produce a spin vortex by varying the potential barrier height and the width of an additionally applied optical plug. A topological phase transition occurs from the trivial single-mode approximation phase to the optical-plug-assisted-vortex one, as the barrier height increases and the width lies in an appropriate range. The optical plug causes radial density variation and thus the spin vortex is favored by significantly lowering the intrinsic magnetic dipolar energy. A type of coreless spin vortex, different from the conventional polar core vortex, is predicted by our numerical results. Our proposal removes a major obstacle to investigating the topological phase transition in a 87Rb^{87}\mathrm{Rb}87Rb dipolar spinor Bose-Einstein condensate.
It has been shown that a vortex in a Bose-Einstein condensate with spin degrees of freedom can be created by manipulating with external magnetic fields. In the previous work [Phys. Rev. A 61, 063610 (2000)] an optical plug along the vortex axis has been introduced to avoid Majorana flips, which take place when the external magnetic field vanishes along the vortex axis while it is created. In the present work, in contrast, we study the same scenario without introducing the optical plug. The magnetic field vanishes only in the center of the vortex at a certain moment of the evolution and hence we expect that the system will lose only a fraction of the atoms by Majorana flips even in the absence of an optical plug. Our conjecture is justified by numerically solving the Gross-Pitaevskii equation, where the full spinor degrees of freedom of the order parameter are properly taken into account. A significant simplification of the experimental realization of the scenario is attained by the omission of the optical plug.
Topological phase imprinting is a well-established technique for deterministic vortex creation in spinor Bose-Einstein condensates of alkali-metal atoms. It was recently shown that counterdiabatic quantum control may accelerate vortex creation in comparison to the standard adiabatic protocol and suppress the atom loss due to nonadiabatic transitions. Here we apply this technique, assisted by an optical plug, for vortex pumping to theoretically show that sequential phase imprinting up to 20 cycles generates a vortex with a very large winding number. Our method significantly increases the fidelity of the pump for rapid pumping compared to the case without the counterdiabatic control, leading to the highest angular momentum per particle reported to date for the vortex pump. Our studies are based on numerical integration of the three-dimensional multicomponent Gross-Pitaevskii equation, which conveniently yields the density profiles, phase profiles, angular momentum, and other physically important quantities of the spin-1 system. Our results motivate the experimental realization of the vortex pump and studies of the rich physics it involves.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
The behavior of a harmonically trapped dipolar Bose-Einstein condensate with its dipole moments rotating at angular frequencies lower than the transverse harmonic trapping frequency is explored in the co-rotating frame. We obtain semi-analytical solutions for the stationary states in the Thomas-Fermi limit of the corresponding dipolar Gross-Pitaevskii equation and utilize linear stability analysis to elucidate a phase diagram for the dynamical stability of these stationary solutions with respect to collective modes. These results are verified via direct numerical simulations of the dipolar Gross-Pitaevskii equation, which demonstrate that dynamical instabilities of the co-rotating stationary solutions lead to the seeding of vortices that eventually relax into a triangular lattice configuration. Our results illustrate that rotation of the dipole polarization represents a new route to vortex formation in dipolar Bose-Einstein condensates.
We study the formation of vortices in a dipolar Bose–Einstein condensate in a synthetic magnetic field by numerically solving the Gross–Pitaevskii equation. The formation process depends on the dipole strength, the rotating frequency, the potential geometry, and the orientation of the dipoles. We make an extensive comparison with vortices created by a rotating trap, especially focusing on the issues of the critical rotating frequency and the vortex number as a function of the rotating frequency. We observe that a higher rotating frequency is needed to generate a large number of vortices and the anisotropic interaction manifests itself as a perceptible difference in the vortex formation. Furthermore, a large dipole strength or aspect ratio also can increase the number of vortices effectively. In particular, we discuss the validity of the Feynman rule.