Quantum Magnetism with Polar Molecules: Tunable Generalized $t$-$J$ Model

We show that dipolar interactions between ultracold polar molecules in optical lattices can be used to realize a highly tunable generalization of the $t$-$J$ model, which we refer to as the $t$-$J$-$V$-$W$ model. The ``spin" is encoded in the rotational degree of freedom of the molecules, while the interactions are controlled by applied static electric and continuous-wave microwave fields. We show that the tunability and the long-range nature of the interactions in the $t$-$J$-$V$-$W$ model enable enhanced superfluidity in one dimension and controllable preparation of robust d-wave superfluids in two dimensions. The latter may provide fundamental insights into high-temperature superconductivity. [References: Phys. Rev. Lett. 107, 115301 (2011); Phys. Rev. A 84, 033619 (2011); arXiv:1110.5330]