Vortex lattices in fast rotating Bose-Einstein condensates between the Thomas-Fermi and the lowest-Landau-level regimes

We present an explicit analytical analysis of the ground state of vortex lattice structures, based on a minimization of the Gross-Pitaevskii energy functional in a fast rotating Bose-Einstein condensate between the Thomas-Fermi and the lowest-Landau-level regimes. By a Bogoliubov-like transformation we find that the coarse-grained average of the atomic density varies as [1−(x²+y²)∕R_⊥²]^3∕2 in the xy plane, and that the vortices form an almost regular triangular lattice. Our variational calculation is quantitatively and qualitatively consistent with recent analytical, numerical, and experimental data.