  We theoretically analyze the Bragg spectroscopic interferometer of two
spatially separated atomic Bose-Einstein condensates that was experimentally
realized by Saba et al. [Science 2005 v307 p1945] by continuously monitoring
the relative phase evolution. Even though the atoms in the light-stimulated
Bragg scattering interact with intense coherent laser beams, we show that the
phase is created by quantum measurement-induced back-action on the homodyne
photo-current of the lasers, opening possibilities for quantum-enhanced
interferometric schemes. We identify two regimes of phase evolution: a running
phase regime which was observed in the experiment of Saba et al., that is
sensitive to an energy offset and suitable for an interferometer, and a trapped
phase regime, that can be insensitive to applied forces and detrimental to
interferometric applications.
