  Describing the behaviour of strongly interacting particles in the presence of
disorder is among the most challenging problems in quantum many-body physics.
The controlled setting of cold atom experiments provides a new avenue to
address these challenges [1], complementing studies in solid state physics,
where a number of puzzling findings have emerged in experiments using
superconducting thin films [2,3]. Here we investigate a strongly interacting
thin film of an atomic Fermi gas subject to a random potential. We use
high-resolution in-situ imaging [4-7] to resolve the atomic density at the
length scale of a single impurity, which would require scanning probe
techniques in solid state physics [8]. This allows us to directly observe the
fragmentation of the density profile and to extract its percolation properties.
Transport measurements in a two-terminal configuration indicate that the
fragmentation process is accompanied by a breakdown of superfluidity. Our
results suggest that percolation of paired atoms is responsible for the loss of
superfluidity, and that disorder is able to increase the binding energy of
pairs.
