  We quantify the effect of phase fluctuations on atom chip interferometry of
Bose-Einstein condensates. At very low temperatures, we observe small phase
fluctuations, created by mean-field depletion, and a resonant production of
vortices when the two clouds are initially in anti-phase. At higher
temperatures, we show that the thermal occupation of Bogoliubov modes makes
vortex production vary smoothly with the initial relative phase difference
between the two atom clouds. We also propose a technique to observe vortex
formation directly by creating a weak link between the two clouds. The position
and direction of circulation of the vortices is subsequently revealed by kinks
in the interference fringes produced when the two clouds expand into one
another. This procedure may be exploited for precise force measurement or
motion detection.
