  We use the variational cluster approximation to study the superconducting
ground state in the two-dimensional attractive Hubbard model, putting
particular emphasis on the significance of quantum fluctuations of the system.
We first show that the order parameter is suppressed in comparison with that
obtained using the mean-field theory owing to the effects of spatial
fluctuations in two-dimensional systems. We then show that the calculated
Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the
character of Cooper pairs in momentum space and that the pair coherence length
$\xi$ evaluated from the condensation amplitude demonstrates a smooth crossover
in real space from a weakly paired BCS state ($\xi\gg a$) to a BEC state of
tightly bound pairs ($\xi\ll a$), where $a$ is the lattice constant. The
calculated kinetic and potential energies in the superconducting and normal
ground states indicate that the superconducting state in the weak-coupling
region is driven by the gain in potential energy, while that in the
strongcoupling region is driven by the gain in kinetic energy.

Strongly Correlated Electrons;Superconductivity