  We calculate density-density correlations of an expanding gas of strongly
attractive ultra-cold spin-1/2 fermions in an optical lattice. The phase
diagram of the tightly bound fermion pairs exhibits a Bose-Einstein condensed
state and a Mott insulating state with a single molecule per lattice site. We
study the effects of quantum fluctuations on the correlations in both phases
and show that they are especially important in the Bose-Einstein condensate
state, leading to the appearance of singular peaks. In the Mott insulating
state the correlations are characterized by sharp dips. This can be utilized in
experiments to distinguish between these two phases.
