Interaction-induced dynamical phase locking of Bose-Einstein condensates

We show that interactions result in the emergence of a {\it definite} relative-phase between two initially incoherent Bose-Einstein condensates. The many-realization interference fringe visibility is universal at $g_{12}^{(1)}\sim 1\mathrm{/}3$ throughout the Josephson interaction regime, as evident from a semiclassical picture. Other types of incoherent preparation yield qualitatively different coherence dynamics.