Interference of Bose-Einstein condensates in momentum space

We suggest an experiment to investigate interference effects between two sp atially separated Bose-Einstein condensates. In the presence of coherence, the dynamic structure factor, measurable through inelastic photon scatterin g, is predicted to exhibit, at high momentum transfer q, interference fring es with frequency period Delta nu = q/md, where d is the distance between t he condensates. We show that this coherent configuration corresponds to an eigenstate of the physical observable measured in the experiment and that t he relative phase of the condensates can be, hence, created through the mea surement process.