  We present a theoretical model to investigate the interference of an array of
Bose-Einstein condensates loaded in a one-dimensional spin-dependent optical
lattice, which is based on an assumption that for the atoms in the entangled
single-atom state between the internal and the external degrees of freedom each
atom interferes only with itself. Our theoretical results agree well with the
interference patterns observed in a recent experiment by Mandel et al. [Phys.
Rev. Lett. 91, 010407 (2003)]. In addition, an experimental suggestion of
nonuniform phase distribution is proposed to test further our theoretical model
and prediction. The present work shows that the entanglement of a single atom
is sufficient for the interference of the condensates confined in a
spin-dependent optical lattice and this interference is irrelevant with the
phases of individual condensates, i.e., this interference arises only between
each condensate and itself and there is no interference effect between two
arbitrary different condensates.
