Different scattering regimes in two-dimensional Bose-Einstein condensates

Motivated by the recent efforts to produce low-dimensional condensates, we study the ground-state density profiles of two-dimensional Bose-Einstein condensed atoms at zero temperature within a mean-field theory. The interplay between the tight harmonic confinement in the axial direction and collisional properties of the condensate atoms help identify three distinct regimes of experimental interest. Each regime is described by a different atom-atom coupling which depends on the density of the condensate as the system starts to be influenced by two-dimensional collisions. We trace the regions of experimentally accessible system parameters for which the crossover between different dimensionality behaviors in the scattering properties may become observable.