Polar core vortex dynamics in disc-trapped homogeneous spin-1 Bose-Einstein condensates

TL;DR

This work investigates polar-core vortices (PCVs) in the easy-plane phase of a ferromagnetic spin-1 Bose-Einstein condensate confined to a two-dimensional disc. It employs a mean-field spin-1 Gross-Pitaevskii framework with linear and quadratic Zeeman terms to analyze the static and dynamic properties of single PCVs, dipoles, and same-sign pairs under realistic experimental parameters, including finite axial magnetization. Key findings show that a single PCV experiences boundary-image forces causing outward radial motion, oppositely charged dipoles typically attract and annihilate with additional edge effects near the boundary, while same-sign PCV pairs repel with dynamics that accelerate with increasing quadratic Zeeman energy; finite axial magnetization induces spiral trajectories well captured by an Archimedes-like spiral model. The results illuminate the rich vortex dynamics of spinor condensates in homogeneous-like disc geometries and point toward future explorations of spinor vortices in other confining geometries for potential atomtronic applications.

Abstract

We study the dynamics of polar core vortices in the easy plane phase of an atomic spin-1 Bose-Einstein condensate confined in a two-dimensional disc potential. A single vortex moves radially outward due to its interaction with background flows that arise from boundary effects. Pairs of opposite sign vortices, which tend to attract, move either radially inward or outward, depending on their strength of attraction relative to boundary effects. Pairs of same sign vortices repel. Spiral vortex dynamics are obtained for same-sign pairs in the presence of a finite axial magnetization. We quantify the dynamics for a range of realistic experimental parameters, finding that the vortex dynamics are accelerated with increasing quadratic Zeeman energy, consistent with existing studies in planar systems.

Figures (8)

• Figure 1: (color online) Ground state phases of Eq. \ref{['eqn:ham_s']} are shown in (a) for (a) antiferromagnetic $g_s>0$ and (b) ferromagnetic $g_s<0$ (b) interactions with $|j\rangle\equiv|m_{\rm F}=j\rangle$. Panel (c) and (d) show examples of the spin densities $|\langle\hat{S}\rangle|/n_0$ (Eq. \ref{['eqn:den_s']}) and $\langle\hat{S}_{\parallel}\rangle/n_0$ (Eq. \ref{['eqn:den_p']}) respectively for fixed values of $p/q_0$. Here $n_0$ defines the mean mass density.
• Figure 2: (color online) Single PCV dynamics. Panels (a) and (b) explore the displacement of a PCV as a function of time, while (c) and (d) show the corresponding lifetime $t_{\rm pcv}$ of a vortex. Example initial states corresponding to (a) are presented in (i) and (ii), showing the phase of the transverse $\langle\hat{S}_{\perp}({\bf r})\rangle$ and axial spin densities $\langle\hat{S}_{\parallel}({\bf r})\rangle$ respectively.
• Figure 3: (color online) PCV pair stationary states. Stationary solutions to Eq. \ref{['eqn:sgpe']} with the initial state Eq. \ref{['eqn:mpcv']} are presented. (a) and (b) show cross-sections of the hyperfine densities $|\psi_{m}({\bf r})|^2$ for $p/q_0=0$. Then panels (c)-(e) explore the polar core vortex densities with fixed $q/q_0=0.25$ for $p/q_0>0$. Panel (f) shows the axial spin densities $\langle\hat{S}_{\parallel}({\bf r})\rangle$ corresponding to the data in (c)-(e). The final two panels, (g) and (h) depict the phase of the transverse $\langle\hat{S}_{\perp}({\bf r})\rangle$ and axial $\langle\hat{S}_{\parallel}({\bf r})\rangle$ spin densities for $(q/q_0,p/q_0)=(0.25,0.1)$.
• Figure 4: (color online) Polar core vortex dipole dynamics. Panel (a) shows the displacement $\Delta r(t)$ of vortex dipoles for different $q/q_0$, with individual (x(t),y(t)) trajectories shown above for three different values of $q/q_0$. Panel (b) depicts the lifetimes $t_{\rm pcv}$ obtained from (a), while (c) compares the numerical hyperfine populations $N_j$ with their analytical counterparts, $|\Psi_{\rm BA}|^2$ and Eq. \ref{['eqn:ab']}. Examples of the transverse $\langle\hat{S}_{\perp}({\bf r})\rangle$ and axial $\langle\hat{S}_{\parallel}({\bf r})\rangle$ spin dynamics, corresponding to the red markers in (a) are shown in panels (i)-(iv).
• Figure 5: (color online) Vortex dipole disc edge dynamics. (a) shows the displacement of PCV dipoles at large initial separations, corresponding trajectories shown per the grey discs. (i) and (ii) present examples of the spin densities ${\rm arg}(\langle\hat{S}_{\perp}({\bf r})\rangle)$ and $\langle\hat{S}_{\parallel}({\bf r})\rangle$ per the label in (a)