Phase diagram of rotating Bose-Einstein condensates trapped in power-law and hard-wall potentials

We investigate the rotational phase diagram of a quasi-two-dimensional, weakly-interacting Bose-Einstein condensate confined in power-law and in hard-wall trapping potentials.

For weak interactions, the system undergoes discontinuous transitions between multiply-quantized vortex states as the rotation frequency of the trap increases.

In contrast, stronger interactions induce continuous phase transitions toward mixed states involving both singly and multiply-quantized vortex states.

A central result is the qualitative (and experimentally observable) difference between power-law and hard-wall confinement: In hard-wall traps, the leading instability always involves states with nonzero density at the trap center, whereas in power-law traps the density vanishes as the rotation frequency increases.

The two different types of confinement give rise to scaling properties in the derived phase diagrams.