Energetic Stability of Coreless Vortices in Spin-1 Bose-Einstein Condensates with Conserved Magnetization

We show that conservation of longitudinal magnetization in a spinor condensate provides a stabilizing mechanism for a coreless vortex phase-imprinted on a polar condensate. The stable vortex can form a composite topological defect with distinct small- and large-distance topology: the inner ferromagnetic coreless vortex continuously deforms toward an outer singular, singly quantized polar vortex. A similar mechanism can also stabilize a nonsingular nematic texture in the polar phase. A weak magnetization is shown to destabilize a coreless vortex in the ferromagnetic phase.

Figure 1

Top left: Spin profile $⟨\widehat{\mathbf{F}}⟩$ (arrows, whose length together with the color gradient give $|⟨\widehat{\mathbf{F}}⟩|$) of the energetically stable coreless vortex in the polar regime, interpolating between FM and polar phases and displaying the characteristic fountain texture inside the core of a singular polar vortex. Top right: The corresponding continuously varying superfluid velocity $\mathbf{v}$ and its magnitude (arrows), and circulation density $\mathcal{V}=\rho \mathbf{v}·\widehat{\mathit{\phi }}$ (color gradient) [18]. Bottom: Energetically stable NCV, with fountain texture in $\widehat{\mathbf{d}}$ (left, cylinders) together with $\mathcal{V}$ (color gradient), and corresponding $⟨\widehat{\mathbf{F}}⟩$ (right, arrows and color gradient). Conservation of magnetization forces the BEC into the FM phase away from the vortex line.

Figure 2

Stability of the coreless vortex in the polar (left) and FM (right) interaction regimes: (filled square) stable coreless vortex; (empty square) stable effective two-component coreless vortex; instability towards (upward triangle) a half-quantum vortex, (circle) pair of half-quantum vortices (polar regime) or singular vortex (FM regime), (plus) vortex-free state; (cross) nucleation of additional vortices.