Creation of coherence in Bose-Einstein condensates by atom detection

We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for the creation of the interference is of the order of the detection time for a few single atoms and another, for the preparation of coherent states, of the order of the detection time for a significant fraction of the total number of atoms. Approximate analytic solutions are derived and compared with exact numerical results.