Bose-Einstein condensates in optical lattices (original) (raw)

We show that the GPE with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, presents a set of ground states which is orbitally stable for any value of the self-interaction (attractive and repulsive) parameter and laser intensity. We also derive a new formalism which gives explicit expressions for the minimum energy E min and the associated chemical potential µ 0 . Based on these formulas, we generalize the variational method to obtain approximate solutions, at any order of approximation, for E min , µ 0 and the ground state.