Universal Bound States with Bose-Fermi Duality in Microwave-Shielded Polar Molecules

We report universal bound states of microwave-shielded ultracold molecules that solely depend on the strengths of long-range dipolar interaction and microwave coupling. Under a highly elliptic microwave field, few-molecule scatterings in three dimension are shown to be governed by effective one-dimensional (1D) models, which well reproduce the tetratomic bound state and the Born-Oppenheimer potential in three-molecule sector. For hexatomic systems comprising three identical molecules, we find much deeper bound state than the tetratomic one, with binding energy exceeding twice of the latter. Strikingly, these bound states display Bose-Fermi duality as facilitated by the effective 1D scattering with a large repulsive core from angular fluctuations. For large molecule ensembles, our results suggest the formation of elongated self-bound droplets with crystalline patterns in both bosonic and fermionic molecules.