  The experimental realizations of degenerate Bose and Fermi atomic samples
have stimulated a new wave of studies of quantum many-body systems in the
dilute and weakly interacting regime. The intriguing prospective of extending
these studies into the domain of strongly correlated phenomena is hindered by
the apparent relative weakness of atomic interactions. The effects due to
interactions can, however, be enhanced if the atoms are confined in optical
potentials created by standing light waves. The present letter shows that these
techniques, when applied to ensembles of cold fermionic atoms, can be used to
dramatically increase the transition temperature to a superfluid state and thus
make it readily observable under current experimental conditions. Depending
upon carefully controlled parameters, a transition to a superfluid state of
Cooper pairs, antiferromagnetic states or more exotic d-wave pairing states can
be induced and probed. The results of proposed experiments can provide a
critical insight into the origin of high-temperature superconductivity in
cuprates.
