  We investigate the phase diffusion of a Bose-Einstein condensate (BEC)
confined in the combined potential of a magnetic trap and a one-dimensional
optical lattice. We show that the phase diffusion of the condensate in the
whole optical lattice is evident and can be measured from the interference
pattern of expanding subcondensates after the optical lattice is switched off.
The maximum density of the interference pattern decreases significantly due to
the mixing of the phase diffusion appearing in different subcondensates. This
suggests a way to detect experimentally the notable phase diffusion of BECs.
