Half-Quantum Vortex Molecules in a Binary Dipolar Bose Gas

We study the ground state phases of a rotating two-component, or binary, Bose-Einstein condensate, wherein one component possesses a large permanent magnetic dipole moment. A variety of nontrivial phases emerge in this system, including a half-quantum vortex (HQV) chain phase and a HQV molecule phase, where HQVs bind at short distances. We attribute these phases to the development of a minimum in the HQV interaction potential, which emerges without coherent coupling or attractive interactions between the components. Thus, we show that the presence of dipolar interactions in this system provides a unique mechanism for the formation of HQV molecules and results in a rich ground state phase diagram.

Figure 1

Emergent HQV phases of the rotating binary dipolar BEC for $N\tilde{g}=10^4$, $\mathrm{\Delta }=0.3$, $\mathrm{\Omega }=0.5{\omega }_{\rho }$, and $\lambda =10$. (a)–(c) Densities of the nondipolar component, $n_2(\mathit{\rho })$, and (d)–(f) locations of (1,0) (red squares) and (0,1) (blue circles) HQVs for (a),(d) ${\tilde{g}}_d/\tilde{g}=0$, (b),(e) ${\tilde{g}}_d/\tilde{g}=0.65$, and (c),(f) ${\tilde{g}}_d/\tilde{g}=1.25$. For clarity, we show HQVs only within a radius of $25l_z$ from the origin, marked by the black dashed line.

Figure 2

Phase diagram of the balanced binary BEC with a trap aspect ratio $\lambda =10$, a rotation frequency $\mathrm{\Omega }=0.5{\omega }_{\rho }$, and $N\tilde{g}=10^4$. See the text for a discussion of phases.

Figure 3

Adiabatic interaction potentials $U_{(1,1)}(R)$ [as defined in Eq. (6)] of a (1,1) HQV system for various DDI strengths in component 1. The interaction parameters are $n_0\tilde{g}=2$ and $n_0{\tilde{g}}_{12}=1.8$. Notice that as $n_0{\tilde{g}}_d$ is increased, a short-range minimum emerges in $U_{(1,1)}(R)$.

Figure 4

(a)–(c) Density profiles $n_1(x,y=0)$ (blue lines) and $n_2(x,y=0)$ (red lines) for a homogeneous ($\lambda =\infty$) binary BEC with interaction parameters $n_0\tilde{g}=2$, $n_0{\tilde{g}}_{12}=1.8$, and (a) $n_0{\tilde{g}}_d=0$ (b),(c) $n_0{\tilde{g}}_d=2.8$. In (a),(b), we show a (1,0) HQV at ${\mathit{\rho }}_{(1,0)}=0$. Notice that the presence of dipolar interactions results in the emergence of a standing longitudinal spin wave near the HQV center. In (c) we show a (1,1) HQV system with $R=2.5$, corresponding to the minimum of $U_{(1,1)}(R)$ for these parameters. (d) The spin-wave quasiparticle spectrum for the system in (b),(c), but with no HQVs.