Vortex lattices in three-component Bose-Einstein condensates under rotation: Simulating colorful vortex lattices in a color superconductor

We study vortex lattices in three-component Bose-Einstein condensates (BECs) under rotation, where three kinds of fractional vortices winding one of three components are present. Unlike the cases of two-component BECs where the phases of square and triangular lattices are present depending on the intercomponent coupling constant and the rotation speed, we find triangular ordered "colorful" vortex lattices where three kinds of fractional vortices are placed in order without defects, in all parameter regions where the intercomponent coupling g^′ is less than the intracomponent coupling g. When g>g^′ on the other hand, we find the phase separation: In a region where one component is present, the other two components must vanish, where we find ghost vortices in these two components whose positions are separated. In the boundary g=g^′, the accidental U(3) symmetry is present, in which case two vortices in different components are close to each other in some regions.