| Trapped atomic Bose-Einstein condensates (BECs) have emerged as a promising experimental system to study many-body physics. In this work, we present a mean-field theory numerical study of the vortex lattices produced in these condensates. To capture the wide range of regimes which are possible in these new experimental systems, we employ finite element techniques to diagonalize the Bogoliubov deGennes equations for the normal modes. Our results show a remarkable quantitative and qualitative agreement with experiments. The normal modes of a vortex lattice have much to do with its nucleation, stability and eventual destruction. Our studies have uncovered a branch of excitations restricted to the boundary which appear to play a key role in the nucleation and decay of the lattice. For further understanding of these processes, we study the dissipative non-equilibrium dynamics of the lattice based on a successful model of condensate growth. The normal modes also carry information about the effects of two point correlations in the lattice, which in the case of trapped gases, are of paramount importance. At ultra-fast rotation the lattice is expected to melt to yield a host of highly entangled states analogous to the fractional Hall states. Our approach furnishes us with a panoramic view of the transformation of the lattice spectrum as the transition point is approached from the mean field regime. With reference to this unique advantage, we close with some comments about the cold melting of the lattice. |
