Coupled 1D Bose gases in 2D optical lattices

Luis Santos

Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany

We analyze the physics of Bose gases confined in a 2D optical lattice, in which every lattice site is a finite 1D system coupled via tunneling with the neighboring sites. First we consider a regime in which the system is superfluid, and the local chemical potential at each lattice site can be considered as that provided by the Lieb-Liniger solution. Due to the weak coupling between sites and the form of the chemical potential, the 3D ground-state density profile and the excitation spectrum acquire remarkable cross-dimensional properties different from both 1D and 3D gases. Second, we discuss 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 will not be a signature of the Mott-insulator phase, but a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.