Imaging the phase of an evolving Bose-Einstein condensate wave function

We demonstrate a spatially resolved autocorrelation measurement with a Bose -Einstein condensate and measure the evolution of the spatial profile of it s quantum mechanical phase. Upon release of the condensate from the magneti c trap, its phase develops a form that we measure to be quadratic in the sp atial coordinate. Our experiments also reveal the effects of the repulsive interaction between two overlapping condensate wave packets and we measure the small momentum they impart to each other.