Triangular vortex lattices and giant vortices in rotating bubble Bose-Einstein condensates

We show that three-dimensional spherical-shell condensates respond to rotation by forming two aligned triangular Abrikosov-like vortex lattices on each hemispherical surface. The centrifugal force due to rotation causes an elliptical deformation of the spherical shell condensate shape and for faster rotation rates, drives the formation of a central multicharged vortex-antivortex pair at the poles surrounded by a ring of singly charged vortices in the bulk density. The vortex distributions observed in each hemisphere take a similar form to those found in rotating harmonic plus quartic traps.

Figure 1

Isosurfaces of constant density of shell-shaped Bose-Einstein condensates under rotation, with rotation frequencies from left to right of $0.21{\omega }_r, 0.25{\omega }_r, 0.27{\omega }_r$, and $0.3{\omega }_r$. The minimum energy states show the numbers of vortices increase as the external rotation frequency is increased. (a) Top row: Top view of holes in the isosurface (plotted at $50\%$ of the maximum condensate density) show the position of vortex cores. (b) Bottom row: Side view of lines in the isosurface (plotted at $10\%$ of the maximum condensate density) show the line length of vortex cores ending on an inner central sphere, which corresponds to the inner surface of the shell.

Figure 2

(a) Top view of isosurfaces plotted at $10\%$ of the maximum condensate density for shell-shaped Bose-Einstein condensates under a rotation of $0.4{\omega }_r$ (left column) and $0.54{\omega }_r$ (right column). (b) The corresponding side view of the constant density isosurface for an external rotation of $0.4{\omega }_r$, showing vortex lines through the bulk condensate density and an elliptical shaped density distribution. (c) The phase profile of a condensate experiencing an external rotation frequency of $0.54{\omega }_r$ at $\theta (x,y,0)$ illustrates the giant multicharged vortex of winding 22 that has formed at the poles. This multicharged vortex is surrounded by 19 singly charged vortices in the bulk condensate density.