  The mechanism of fermionic pairing is the key to understanding various
phenomena such as high-temperature superconductivity and the pseudogap phase in
cuprate materials. We study the pair correlations in the attractive Hubbard
model using ultracold fermions in a two-dimensional optical lattice. By
combining the fluctuation-dissipation theorem and the compressibility equation
of state, we extract the interacting pair correlation functions and deduce a
characteristic length scale of pairs as a function of interaction and density
filling. At sufficiently low filling and weak on-site interaction, we observe
that the pair correlations extend over a few lattice sites even at temperatures
above the superfluid transition temperature.
