  Arrays of atoms trapped in optical lattices are appealing as storage media
for photons, since motional dephasing of the atoms is eliminated. The regular
lattice is also associated with band structure in the dispersion experienced by
incident photons. Here we study the influence of this band structure on the
efficiency of quantum memories based on electromagnetically induced
transparency (EIT) and on Raman absorption. We observe a number of interesting
effects, such as both reduced and superluminal group velocities, enhanced
atom-photon coupling and anomalous transmission. These effects are ultimately
deleterious to the memory efficiency, but they are easily avoided by tuning the
optical fields away from the band edges.
