© William P. Reinhardt.

A feature common to all macroscopic quantum systems is the formation of vortices. These are quantum whirlpools (or tornadoes) created by rotation, or by phase imprinting via manipulation of atoms caught in a trap. The top image shows the density profile of a BEC with five vortex holes viewed from above. The lower image shows the phase of the same macroscopic wave function leading to the density shown in the upper image, labeled by colors as in Unit 6, Figure 23. Note that the holes in the density occur at exactly those points where the phase is "singular," that is at those five special points where the diverging colored lines of phase come together. At this point there is no way to assign a phase (a mathematical impossibility.) However, the density is zero at these points, so a choice of phase is meaningless. (Unit: 6)