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We consider a periodic vortex lattice in a rotating Bose-Einstein condensedgas, where the centrifugal potential is exactly compensated by the externalharmonic trap. By introducing a gauge transformation which makes theHamiltonian periodic, we solve numerically the 2D Gross-Pitaevskii equationfinding the exact mean field ground state. In particular, we explore thecrossover between the Thomas-Fermi regime, holding for large values of thecoupling constant, and the lowest Landau level limit, corresponding to theweakly interacting case. Explicit results are given for the equation of state,the vortex core size, as well as the elastic shear modulus, which is crucialfor the calculation of the Tkachenko frequencies.Comment: 4 pages, 4 figure

Vortex lattices in Bose-Einstein condensates: From the Thomas-Fermi regime to the lowest-Landau-level regime