Vortex liquids and vortex quantum Hall states in trapped rotating Bose gases

We discuss the feasibility of quantum Hall states of vortices in trapped low-density two-dimensional Bose gases with large particle interactions. For interaction strengths larger than a critical dimensionless 2D coupling constant $g_c \approx 0.6$, upon increasing the rotation frequency, the system is shown to spatially separate into vortex lattice and melted vortex lattice (vortex liquid) phases. At a first critical frequency, the lattice melts completely, and strongly correlated vortex and particle quantum Hall liquids coexist in inner respectively outer regions of the gas cloud. Finally, at a second critical frequency, the vortex liquid disappears and the strongly correlated particle quantum Hall state fills the whole sample.