  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.

Quantum Gases