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We study the onset of dissipation in an atomic Josephson junction betweenFermi superfluids in the molecular Bose-Einstein condensation limit of strongattraction. Our simulations identify the critical population imbalance and themaximum Josephson current delimiting dissipationless and dissipative transport,in quantitative agreement with recent experiments. We unambiguously linkdissipation to vortex ring nucleation and dynamics, demonstrating that quantumphase slips are responsible for the observed resistive current. Our workdirectly connects microscopic features with macroscopic dissipative transport,providing a comprehensive description of vortex ring dynamics inthree-dimensional inhomogeneous constricted superfluids at zero and finitetemperatures.

Critical transport and vortex dynamics in a thin atomic Josephson junction