We show that in a commensurate bosonic ladder, a quantum phase transition occurs between a Mott insulator and a superfluid when interchain hopping increases. We analyse the properties of this transition as well as the physical properties of the two phases. We discuss the physical consequences for experimental systems such as Josephson Junction arrays.

We study a half filled ladder of spinless fermions. We show that contrarily to a single chain, the ladder becomes a Mott insulator for arbitrarily small repulsive interactions. We obtain the full phase diagram and physical quantities such as the charge gap. We show that there is only a single insulating phase for repulsive interactions, regardless of the strength of the interchain hopping and single chain Mott gap. There is thus no confinement-deconfinement transition in this system but a simple crossover. We show that upon doping the system becomes a Luttinger liquid with a universal parameter K = 1/2 different from the one of the single chain (K = 1/4).