We show that dipolar interactions between ultracold polar alkali-metal dimers 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 model features long-range spin-spin interactions $J_z$ and $J_{\perp }$ of $XXZ$ type, long-range density-density interaction $V$, and long-range density-spin interaction $W$, all of which can be controlled in both magnitude and sign independently of each other and of the tunneling $t$. 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. Furthermore, we show that nuclear spins of the molecules can be used to implement an additional (orbital) degree of freedom that is coupled to the original rotational degree of freedom in a tunable way. The presented system is expected to exhibit exotic physics and to provide insights into strongly correlated phenomena in condensed-matter systems. Realistic experimental imperfections are discussed.

• Received 11 June 2011

DOI:https://doi.org/10.1103/PhysRevA.84.033619