%0 Journal Article %J Physical Review A %D 2011 %T d-Wave Superfluidity in Optical Lattices of Ultracold Polar Molecules %A Kevin A. Kuns %A Ana Maria Rey %A Alexey V. Gorshkov %X Recent work on ultracold polar molecules, governed by a generalization of the t-J Hamiltonian, suggests that molecules may be better suited than atoms for studying d-wave superfluidity due to stronger interactions and larger tunability of the system. We compute the phase diagram for polar molecules in a checkerboard lattice consisting of weakly coupled square plaquettes. In the simplest experimentally realizable case where there is only tunneling and an XX-type spin-spin interaction, we identify the parameter regime where d-wave superfluidity occurs. We also find that the inclusion of a density-density interaction destroys the superfluid phase and that the inclusion of a spin-density or an Ising-type spin-spin interaction can enhance the superfluid phase. We also propose schemes for experimentally realizing the perturbative calculations exhibiting enhanced d-wave superfluidity. %B Physical Review A %V 84 %8 2011/12/29 %G eng %U http://arxiv.org/abs/1110.5330v2 %N 6 %! Phys. Rev. A %R 10.1103/PhysRevA.84.063639