  We propose a controlled method to create and detect d-wave superfluidity with
ultracold fermionic atoms loaded in two-dimensional optical superlattices. Our
scheme consists in preparing an array of nearest-neighbor coupled square
plaquettes or ``superplaquettes'' and using them as building blocks to
construct a d-wave superfluid state. We describe how to use the coherent
dynamical evolution in such a system to experimentally probe the pairing
mechanism. We also derive the zero temperature phase diagram of the fermions in
a checkerboard lattice (many weakly coupled plaquettes) and show that by tuning
the inter-plaquette tunneling spin-dependently or varying the filling factor
one can drive the system into a d-wave superfluid phase or a Cooper pair
density wave phase. We discuss the use of noise correlation measurements to
experimentally probe these phases.
