Phase-space dynamics of Bose condensates: Interference versus interaction

We study theoretically the macroscopic interference of two independent Bose condensates released from a double potential trap. The observation of fringes could serve as a test for the paradigm of broken gauge symmetry. By numerical solution of the nonlinear Schrödinger equation in three dimensions, the consecutive stages of expansion, overlap, and interference are investigated in order to facilitate the design of future experiments. The phase-space dynamics of the condensates is analyzed by means of the Wigner function. It turns out that the distance of interference fringes grows linearly in time with a velocity inversely proportional to the initial distance of the two condensates. The collisional reduction of the fringe visibility is estimated.