Josephson tunneling between weakly interacting Bose-Einstein condensates

Based on a tunneling Hamiltonian description, we calculate the Josephson, and interference currents between two Bose-Einstein condensates by the Bogoliubov theory. The dominant Josephson term is of first in the tunneling with a critical current density proportional to the state pressure. In contrast to superconductors, the normal current finite at zero temperature. We discuss the dynamics of the relative in a semiclassical approximation derived from an exact functional approach, which includes the interaction effects at fixed total number. It is shown that the normal current leads to a damping of the oscillations and, at long times, eliminates the macroscopic quantum trapping predicted by Smerzi et.al. Finally we give estimates for an realization of Josephson tunneling in cold atomic gases, which that coherent transfer of atoms might be realized with a ²³Na.