Effective size and expansion energy of a Bose-Einstein condensate in a 3D non-cubic optical lattice

This work is devoted to study the temperature dependence of the effective size r^2 and expansion energy Ex,z of a Bose-Einstein condensate in a 3D non-cubic optical lattice. Correction due to the finite size, interatomic interaction and the deepness of the lattice potential are given simultaneously. The calculated results show that these two parameters increase with the lattice depth or the relative frequency at temperature less than the transition temperature, (T T0); yet it has little effect at temperatures higher than the transition temperature (T T0). Both the effective size and expansion energy follow a characteristic temperature dependence, i.e. r^2, E ∝ (T/T0)4 if T T0 and r^2, E ∝ (T/T0) if T T0. For a 3D non cubic optical potential the effect of relative frequency is much more than the effect of the optical potential depth. Thus for a non-cubic optical potential one has to use the pure harmonically trapped boson gas as the zeroth order approximation in any perturbation or numerically treatment for this system.