  We present a scanning probe microscopy technique for spatially resolving
transport in cold atomic gases, in close analogy with scanning gate microscopy
in semiconductor physics. The conductance of a quantum point contact connected
to two atomic reservoirs is measured in the presence of a tightly focused laser
beam acting as a local perturbation that can be precisely positioned in space.
By scanning its position and recording the subsequent variations of
conductance, we retrieve a high-resolution map of transport through a quantum
point contact. We demonstrate a spatial resolution comparable to the extent of
the transverse wave function of the atoms inside the channel, and a position
sensitivity below 10nm. Our measurements agree well with an analytical model
and ab-initio numerical simulations, allowing us to identify a regime in
transport where tunneling dominates over thermal effects. Our technique opens
new perspectives for the high-resolution observation and manipulation of cold
atomic gases.
