Vortex dynamics in anisotropic traps

We investigate the dynamics of linear vortex lattices in anisotropic traps in two dimensions and show that the interplay between the rotation and the anisotropy leads to a rich but highly regular dynamics.

Figure 1

The ground-state density for a condensate of $N={10}^5$ Rb atoms in a trap with $\lambda =2.5$ and ${\omega }_x=10\times 2\pi \hspace{0.5em}\mathrm{Hz}$ (upper panel) and the oscillatory trajectories of the vortices along the $x$ axis as a function of time (lower panel). The center vortex can be seen to remain stationary, while the other four vortices periodically oscillate away from their initial position. The dashed lines in the density plot indicate the range of movement in the $y$ direction for each of the vortices (see Fig. 2).

Figure 2

The position of the vortices in the $y$ direction, which corresponds to the situation shown in Fig. 1. The top row shows the leftmost vortex, and the bottom row shows the rightmost one.

Figure 3

The ground-state density for $\lambda =3.5$ (upper panel and the position of the vortices along the $x$ axis (lower panel). All system parameters are the same as in the $\lambda =2.5$ case, and all observations made apply here as well with reduced amplitude. In the $y$ direction, the movement is on the order of $1\times {10}^{-7}\hspace{0.5em}\mathrm{m}$ (not shown).

Figure 4

Density of the cloud at $t=0.0072\hspace{0.5em}\mathrm{s}$ (upper panel) and $t=0.0108\hspace{0.5em}\mathrm{s}$ (lower panel). The full white line indicates the tilted axis of the vortex crystal, and the broken white line indicates the horizontal starting position. The oscillation of amplitude of the background cloud is too small to be visible in this plot.

Figure 5

Dynamical evolution of the density and phase for a trap of aspect ratio $\lambda =2.5$ for which the rotation has been switched off. Panel (a) shows the initial linear crystal at $t=0\hspace{0.5em}\mathrm{s}$, and the subsequent panels show the times (b) $t=0.03\hspace{0.5em}\mathrm{s},$ (c) $t=0.06\hspace{0.5em}\mathrm{s}$, and (d) $t=0.1\hspace{0.5em}\mathrm{s}$. Panel (c) shows the disturbed crystal as outer vortices pass the narrow direction of the condensate as they rotate around the central vortex, and panel (d) shows the reformation of the linear crystal. At this time, the left and right pairs of vortices have rotated around the central vortex, and the inner and outer vortices on each side have swapped positions. The phase plots show that the charge of the vortices is maintained throughout the time evolution.

Figure 6

Position of the vortices along the $x$ direction for $\Omega =0$ and for $\lambda =2.5$. The values for the initially outer pair of vortices are given by the full line, and the values for the inner pair of vortices are given by the broken line. It can be seen that the paths remain symmetrical for the respective pairs, however, they switch positions periodically.