  We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state
of weakly-bound Cooper pairs to the Bose-Einstein Condensate (BEC) of
strongly-bound molecular dimers in a gas of ultracold atoms loaded on a
two-dimensional optical lattice. By using the the mean-field BCS equations of
the emerging Hubbard model and the concept of off-diagonal-long-range-order for
fermions we calculate analytically and numerically the pair binding energy, the
energy gap and the condensate fraction of Cooper pairs as a function of
interaction strength and filling fractor of atoms in the lattice at zero
temperature.
