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.
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