Structural change of vortex patterns in anisotropic Bose-Einstein condensates

We study the changes in the spatial distribution of vortices in a rotating Bose-Einstein condensate due to an increasing eccentricity of the trapping potential. By breaking the rotational symmetry, the vortex system undergoes a rich variety of structural changes, including the formation of zigzag and linear configurations. These spatial rearrangements are well signaled by the change in the behavior of the vortex-pattern eigenmodes against the eccentricity parameter. This behavior allows to actively control the distribution of vorticity in many-body systems and opens the possibility of studying interactions between quantum vortices over a large range of parameters.

Figure 1

Distance $\Delta x$ of the vortices from the soft trapping axis (in units of $\sqrt{2Ng\Omega /\hslash {\omega }_x}$) against the eccentricity of the trap, $\lambda$. We show the cases of $N_v=7$ and $8$ [panels (a) and (b), respectively] and plot only the changes in positions of four vortices in the lattice (the association with the curves is irrelevant), with the remaining showing analogous behavior. At $\lambda ={\lambda }_L$ the vortices suddenly align along the $y$ axis ($\Delta x=0$). We have used a BEC of ${10}^6$ ${}^{87}\mathrm{Rb}$ atoms with a scattering length $a=5.23\times {10}^{-9}$ m in a trap of frequencies ${\omega }_z/2\pi =100$ Hz and $\sqrt{{\omega }_x{\omega }_y}/2\pi =50$ Hz (independent of $\lambda$).

Figure 2

Phase distribution of the condensate carrying a vortex lattice in the x-y plane with $N_v=8$ for different values of $\lambda$. The black dots mark the positions of the vortices (in units of $\sqrt{2Ng\Omega /\hslash {\omega }_x}$). The appearance of different structural vortex patterns is clearly visible.

Figure 3

Phase distribution of the condensate carrying a vortex lattice in the x-y plane with $N_v=7$ for different values of $\lambda$. All other values are as in Fig. 2.

Figure 4

Phase distribution of the condensate carrying a vortex lattice in the x-y plane with $N_v=18$ for different values of $\lambda$. The black dots mark the positions of the vortices (in units of $\sqrt{2Ng\Omega /\hslash {\omega }_x}$).

Figure 5

Superfluid velocity field in the rotating frame for $N_v=8$ (other parameters as in Fig. 1). From (a) to (d) the asymmetry parameter is given by $\lambda =1,0.76,0.56,0.36$. Darkest (dark purple) regions correspond to zero velocity and the velocities close to the vortex cores are not shown on the chosen color map.

Figure 6

Spectrum of a BEC with $N_v=7$ vortices against the eccentricity $\lambda$. The points ${\lambda }_{C,L}$, where the vortex pattern undergoes a structural change, are visible.