Mott-insulator phase of coupled one-dimensional atomic gases in a two-dimensional optical lattice

We consider the 2D Mott-insulator state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time-of-flight experiments is a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.