  We analyze theoretically the quantization of conductance occurring with cold
bosonic atoms trapped in two reservoirs connected by a constriction with an
attractive gate potential. We focus on temperatures slightly above the
condensation threshold in the reservoirs. We show that a conductance step
occurs, coinciding with the appearance of a condensate in the constriction.
Conductance relies on a collective process involving the quantum condensation
of an atom into an elementary excitation and the subsequent quantum evaporation
of an atom, in contrast with ballistic fermion transport. The value of the
bosonic conductance plateau is strongly enhanced compared to fermions and
explicitly depends on temperature. We highlight the role of weak repulsive
interactions between the bosons in preventing them from collapsing into the
constriction.
