We use quantum Monte Carlo methods to compute the density profile, the nonclassical moment of inertia, and the condensate fraction of an interacting quasi-two-dimensional trapped Bose gas with up to one million particles, and parameters closely related to recent experiments.
We locate the Kosterlitz-Thouless transition temperature T_KT, and discuss intrinsic signatures of the onset of superfluidity in the density profile. Above T_KT, the system can be described very accurately by a semiclassical theory taking into account the transverse degrees of freedom, but it differs notably from the strictly two-dimensional case. Below T_KT, the condensate fraction is macroscopic even for our largest systems, and it decays only slowly with system size. We discuss the relevance of our findings for analyzing ulta-cold-atom experiments in quasi-two-dimensional traps.