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 ``supe
rplaquettes 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.
We show that entanglement monotones can characterize the pronounced enhancement of entanglement at a quantum phase transition if they are sensitive to long-range high order correlations. These monotones are found to develop a sharp peak at the critic
al point and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlations and verify that these experimentally accessible quantities indeed encode entanglement information and probe separability.
