Tunable state-dependent interactions in collisionally stable mixtures of polar molecules

We propose encoding a pseudo-spin-$1/2$ system in the ground ($v=0$) and first excited ($v=1$) vibrational states of polar molecules. Double microwave shielding simultaneously shields molecules in both states, suppressing two-body losses by orders of magnitude while strictly avoiding three-body recombination. The microwave dressing is state-dependent and results in highly tunable, long-range dipolar Ising exchange ($J_z$), density-density ($V$), and spin-density ($W$) interactions. These interaction length scales readily exceed the typical interparticle spacing, pushing the molecules deep into the strongly interacting regime. In bulk gases, this enables the exploration of itinerant quantum magnetism and quantum droplets with novel anisotropic spin textures; in optical lattices, it naturally realizes extended Hubbard and $t$-$J_z$ models, opening new directions in quantum simulation.