Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices

Abstract

We formulate the Collective Quantum Field Theory for three-dimensional bosonic optical lattices and evaluate its consequences in a mean-field approximation to two collective fields, proposed by Fred Cooper et al. and in a lowest-order Variational Perturbation Theory (VPT). It is shown that present mean-field approximation predicts some essential features of the experimentally observed dependence of the critical temperature on the coupling strength and a second - order quantum phase transition.In contrast to a recent prediction for atomic gases by Fred Cooper et. al., we find no superfluid state with zero condensate fraction.

21 pages, revtex, 4 figures. In this version the figures have been replaced, and the text extended

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• Thermodynamics of the Bose-Hubbard model in a Bogoliubov+U theory