  We study the entangled states that can be generated using two species of
atoms trapped in independently movable, two-dimensional optical lattices. We
show that using two sets of measurements it is possible to measure a set of
entanglement witness operators distributed over arbitrarily large regions of
the lattice, and use these witnesses to produce two-dimensional plots of the
entanglement content of these states. We also discuss the influence of noise on
the states and on the witnesses, as well as connections to ongoing experiments.
