Creating vortices in dipolar spinor condensates via rapid adiabatic passage

We propose to create vortices in spin-1 condensates via magnetic dipole-dipole interaction. Starting with a polarized condensate prepared under large axial magnetic field, we show that by gradually inverting the field, population transfer among different spin states can be realized in a controlled manner. Under optimal condition, we generate a doubly quantized vortex state containing nearly all atoms in the condensate. The resulting vortex state is a direct manifestation of the dipole-dipole interaction and spin textures in spinor condensates. We also point out that the whole process can be qualitatively described by a simple three-level rapid adiabatic passage model.

Figure 1

Schematic plot of the magnetic field dependence of the ground-state structure in an oblate trap.

Figure 2

(Color online) Typical dynamic behaviors in an oblate trap $\left(\lambda =6\right)$. (a) The time dependence of reduced atom number $n_1$ for various control parameters $\left(N,B_0,v_B\right)$. (b) The integrated densities ${\overline{\rho }}_1\left(x,y\right)$ and phases (insets) of wave function ${\psi }_1\left(x,y,0\right)$ for $\left(N,B_0\right)=\left(2\times {10}^6,-40\right)$ with various $v_B$’s. (c) Same as (b) except for $N={10}^7$, $B_0=-100\mu \text{G}$, and $v_B=0.5$.

Figure 3

(Color online) Time dependence of relative population (a) $n_1$ and integrated density (b) ${\overline{\rho }}_1$ in various trapping potentials for $B_0=-60\mu \text{G}$ and $v_B=0.5$. Insets in (b) show the phases of wave function ${\psi }_1\left(x,y,0\right)$.

Figure 4

(Color online) (a) Eigenenergies of $H_{\text{LZT}}$ as a function of axial field $b$. (b) Population dynamics of the LZT model with $b_x=1$, $b_0=-10$, and $v_b=1.5$. (c) Reduced atom numbers $n_{\alpha }$ and total energy per atom $\mathcal{E}$ versus magnetic field in an oblate trap $\left(\lambda =6\right)$, obtained from the full numerical simulation of Eq. (1). Other parameters are $B_0=-40\mu \text{G}$ and $v_B=0.25$.

Figure 5

(Color online) The $\theta$ dependence of ${\ell }_1$ (red triangles) and $n_1$ (blue squares) at time ${\omega }_{0}t=600$. Other parameters are $\lambda =6$, $B_0=-40\mu \text{G}$, and $v_B=0.15$. Inset shows the integrated density ${\overline{\rho }}_1$ at ${\omega }_{0}t=600$ for $\theta =3°$.