  We suggest two experimental methods for probing both short- and long-range
spin correlations of atoms in optical lattices using superlattice potentials.
The first method involves an adiabatic doubling of the periodicity of the
underlying lattice to probe neighboring singlet (triplet) correlations for
fermions (bosons) by the occupation of the new vibrational ground state. The
second method utilizes a time-dependent superlattice potential to generate
spin-dependent transport by any number of prescribed lattice sites, and probes
correlations by the resulting number of doubly occupied sites. For
experimentally relevant parameters, we demonstrate how both methods yield large
signatures of antiferromagnetic (AF) correlations of strongly repulsive
fermionic atoms in a single shot of the experiment. Lastly, we show how this
method may also be applied to probe d-wave pairing, a possible ground state
candidate for the doped repulsive Hubbard model.
