Kosterlitz-Thouless physics in a one-dimensional optical lattice

We study a system of quasi two-dimensional Bose gases formed in the nodes of a one-dimensional optical lattice potential. We focus on the effect of the tunneling of the atoms between adjacent planes on the Kosterlitz-Thouless crossover recently observed in the experiments of the Paris group [Z. Hadzibabic \emph{et al}., Nature (London) \textbf{441}, 1118 (2006)]. We compute the contrast of the interference pattern between two condensates, finding a behavior different from the one observed in the Kosterlitz-Thouless crossover. Finally, we consider the stack of a large number of pancakes.