Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules

We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field may acquire an attractive $1/r^3$ dipole-dipole interaction leading to superfluid $p$-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological $p_x+i{p}_y$ phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities $\sim {10}^8{\mathrm{cm}}^{-2}$.