We measure the superfluid transport of strongly interacting fermionic lithium atoms via quantum point contacts with local spin-dependent particle losses. We find that the characteristic non-ohmic superfluid transport enabled by higher-order multiple Andreev reflections survives even at dissipation strengths larger than the superfluid gap. We develop a model with a mean-field reservoir connected to a dissipative site via a tunnel. Calculations in Keldysh form reproduce the observed non-equilibrium particle currents but do not fully explain the observed loss rates or spin currents.

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