Dissipative Superfluidity in a Molecular Bose-Einstein Condensate

Motivated by recent experimental realization of a Bose-Einstein condensate (BEC) of dipolar molecules, we develop superfluid transport theory for a dissipative BEC to show that a weak uniform two-body loss can induce phase rigidity, leading to superfluid transport of bosons even without repulsive interparticle interactions. A generalized $f$-sum rule is shown to hold for a dissipative superfluid as a consequence of weak U(1) symmetry. We also demonstrate that dissipation enhances the stability of a molecular BEC with dipolar interactions. Possible experimental signature of dissipative superfluidity are discussed.