We present a coherent filtering scheme which dramatically reduces the site
occupation number defects for atoms in an optical lattice, by transferring a
chosen number of atoms to a different internal state via adiabatic passage.
With the addition of superlattices it is possible to engineer states with a
specific number of atoms per site (atomic crystals), which are required for
quantum computation and the realisation of models from condensed matter
physics, including doping and spatial patterns. The same techniques can be used
to measure two-body spatial correlation functions. We illustrate these ideas
with a scheme to study the creation of a BCS state with a chosen filling factor
from a degenerate Fermi gas in an optical lattice.Comment: 4 Pages, 5 Figures, REVTex