  A Bose-Einstein "double-slit" interferometer has been recently realized
experimentally by (Y. Shin et. al., Phys. Rev. Lett. 92 50405 (2004)). We
analyze the interferometric steps by solving numerically the time-dependent
Gross-Pitaevski equation in three-dimensional space. We focus on the
adiabaticity time scales of the problem and on the creation of spurious
collective excitations as a possible source of the strong dephasing observed
experimentally. The role of quantum fluctuations is discussed.
