Penetration of a vortex dipole across an interface of Bose-Einstein condensates

The dynamics of a vortex dipole in a quasi-two-dimensional two-component Bose-Einstein condensate is investigated. A vortex dipole is shown to penetrate the interface between the two components when the incident velocity is sufficiently large. A vortex dipole can also disappear or disintegrate at the interface, depending on its velocity and the interaction parameters.

Figure 1

Dynamics of normalized density profiles $|{\psi }_j{|}^2/n_0$ and phase profiles $\arg {\psi }_j$ for $g_{11}=g_{22}$ and $\Delta =g_{12}/g_{11}-1={10}^{-3}$. The velocity of the incident vortex dipole is $v_{\mathrm{in}}=0.31v_{\mathrm{s}}$, where $v_{\mathrm{s}}$ is the sound velocity. The direction of the vortex dipole propagation is indicated by the arrows in the left panels, and the circulations of vortices are indicated by the arrows in the right panels. The time is normalized as $\tilde{t}=t{v}_{\mathrm{s}}/\xi$, where $\xi$ is the healing length. The origin of time $\tilde{t}=0$ is taken arbitrarily. The field of view of each panel is $120\xi \times 30\xi$.

Figure 2

Dynamics of normalized density profiles $|{\psi }_j{|}^2/n_0$ and phase profiles $\arg {\psi }_j$ for $\Delta =0.05$ and $v_{\mathrm{in}}=0.12v_{\mathrm{s}}$. The direction of the vortex dipole propagation is indicated by the arrows in the left panels, and the circulations of vortices are indicated by the arrows in the right panels. The field of view of each panel is $120\xi \times 30\xi$.

Figure 3

Dynamics of normalized density profile $|{\psi }_1{|}^2/n_0$ of component 1 for (a) $\Delta =0.05$ and $v_{\mathrm{in}}=0.088v_{\mathrm{s}}$ and (b) $\Delta =0.2$ and $v_{\mathrm{in}}=0.039v_{\mathrm{s}}$. The field of view of each panel is $60\xi \times 160\xi$.

Figure 4

Dependence of the dynamics of a vortex dipole on $\Delta$ and $v_{\mathrm{in}}$. The region of “Penetration (empty core)” corresponds to the penetration dynamics of a vortex dipole as shown in Fig. 1. In the region of “Penetration (occupied core)” the cores of a vortex dipole after the penetration are occupied by component 1, as in Fig. 2. The regions of “Interface disturbance” and “Disintegration” correspond to the dynamics shown in Figs. 3a and 3b, respectively. The circles indicate the parameters used in Figs. 1, 2, 3.

Figure 5

Incident velocity $v_{\mathrm{in}}$ of a vortex dipole versus outgoing velocity $v_{\mathrm{out}}$ after the penetration across the interface for $\Delta =0.01$ (circles), $0.05$ (squares), and $0.1$ (triangles). The line indicates $v_{\mathrm{in}}=v_{\mathrm{out}}$.

Figure 6

(a),(b) Snapshots and (c),(d) stroboscopic images of the normalized density profiles $|{\psi }_j{|}^2$ for $\Delta =0.05$, $v=0.13v_{\mathrm{s}}$, and the incident angle ${\tan }^{-1}0.4$. In (c) and (d), the images from $\tilde{t}=360$ to $\tilde{t}=1200$ are superimposed at time intervals of $\Delta \tilde{t}=40$. The images in the dashed circles in (a) and (b) correspond to those in (c) and (d), respectively. The direction of vortex dipole propagation is indicated by the arrows. The field of view of each panel is $50\xi \times 120\xi$ in (a) and (b) and $120\xi \times 80\xi$ in (c) and (d).

Figure 7

Snapshots of the density profiles $|{\psi }_j{|}^2$ of the dynamics for $T=1.0$ ms. The inset magnifies the phase profile $\arg {\psi }_2$ in the dashed square. The arrows in the inset indicate the directions of circulation. The unit of density is $8.4\times {10}^{11}$ ${\mathrm{cm}}^{-2}$. The field of view of each panel is $54.3\times 54.3$ $\mu {\mathrm{m}}^2$.

Figure 8

Snapshots of the density profiles $|{\psi }_j{|}^2$ of the dynamics for $T=1.4$ ms. The white arrows indicate the directions of propagation. The insets magnify the phase profile $\arg {\psi }_2$ in the dashed squares. The arrows in the insets indicate the directions of circulation. The unit of density is $8.4\times {10}^{11}$ ${\mathrm{cm}}^{-2}$. The field of view of each panel is $54.3\times 54.3$ $\mu {\mathrm{m}}^2$.

Figure 9

Snapshots of the density profiles $|{\psi }_j{|}^2$ of the dynamics for $T=2.4$ ms. The white arrow indicates the direction of propagation. The inset magnifies the phase profile $\arg {\psi }_2$ in the dashed square. The arrows in the insets indicate the directions of circulation. The unit of density is $8.4\times {10}^{11}$ ${\mathrm{cm}}^{-2}$. The field of view of each panel is $54.3\times 54.3$ $\mu {\mathrm{m}}^2$.