  We study resolved sideband laser cooling of a one-dimensional optical lattice
with one atom per site, and in particular the effect of the dipole interaction
between radiating atoms. For simplicity, we consider the case where only a
single cooling laser is applied. We derive a master equation, and solve it in
the limit of a deep lattice and weak laser driving. We find that the dipole
interaction significantly changes the final temperature of the particles,
increasing it for some phonon wavevectors and decreasing it for others. The
total phonon energy over all modes is typically higher than in the
non-interacting case, but can be made lower by the right choice of parameters.
