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 ${[1\ensuremath{-}({x}^{2}+{y}^{2})∕{R}_{\ensuremath{\perp}}^{2}]}^{3∕2}$ 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.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 ${[1\ensuremath{-}({x}^{2}+{y}^{2})∕{R}_{\ensuremath{\perp}}^{2}]}^{3∕2}$ 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.

Physical Review ANov 20, 20062 citations

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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.