  Anderson localisation -- the inhibition of wave propagation in disordered
media -- is a surprising interference phenomenon which is particularly
intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D
system of infinite size is always localised, the localisation length-scale may
be too large to be unambiguously observed in an experiment. In this sense, 2D
is a marginal dimension between one-dimension, where all states are strongly
localised, and three-dimensions, where a well-defined phase transition between
localisation and delocalisation exists as the energy is increased. Here we
report the results of an experiment measuring the 2D transport of ultracold
atoms between two reservoirs, which are connected by a channel containing
pointlike disorder. The design overcomes many of the technical challenges that
have hampered observation of localisation in previous works. We experimentally
observe exponential localisation in a 2D ultracold atom system.
