  We analyze the recently measured anomalous transport properties of an
ultracold gas through a ballistic constriction [S. Krinner et al., PNAS
201601812 (2016)]. The quantized conductance observed at weak interactions
increases several-fold as the gas is made strongly interacting, which cannot be
explained by the Landauer theory of single-channel transport. We show that this
phenomenon is due to the multichannel Andreev reflections at the edges of the
constriction, where the interaction and confinement result in a superconducting
state. Andreev processes convert atoms of otherwise reflecting channels into
the condensate propagating through the constriction, leading to a significant
excess conductance. Furthermore, we find the spin conductance being suppressed
by superconductivity; the agreement with experiment provides an additional
support for our model.
