  When two initially independent Bose-condensed gases are allowed to overlap,
we investigate the density expectation value of the whole system by using the
second quantization method. In the presence of interatomic interaction, based
on the exact expression of the density expectation value, it is found that
there is a nonzero interference term in the density expectation value of the
whole system. The evolution of the density expectation value is shown for
different coupling constants. The present work shows clearly that there is an
interaction-induced coherence process between two initially independent
condensates.
