  We study the quantum dynamics of a two-mode Bose-Einstein condensate in a
time-dependent symmetric double-well potential using analytical and numerical
methods. The effects of internal degrees of freedom on the visibility of
interference fringes during a stage of ballistic expansion are investigated
varying particle number, nonlinear interaction sign and strength as well as
tunneling coupling. Expressions for the phase resolution are derived and the
possible enhancement due to squeezing is discussed. In particular, the role of
the superfluid - Mott insulator cross-over and its analog for attractive
interactions is recognized.
