  We present a mapping between the Edwards model of disorder describing the
motion of a single particle subject to randomly-positioned static scatterers
and the Bose polaron problem of a light quantum impurity interacting with a
Bose-Einstein condensate (BEC) of heavy atoms. The mapping offers an
experimental setting to investigate the physics of Anderson localization where,
by exploiting the quantum nature of the BEC, the time evolution of the quantum
impurity emulates the disorder-averaged dynamics of the Edwards model. Valid in
any space dimension, the mapping can be extended to include interacting
particles, arbitrary disorder or confinement, and can be generalized to study
many-body localization. Moreover, the corresponding exactly-solvable disorder
model offers means to benchmark variational approaches used to study polaron
physics. Here, we illustrate the mapping by focusing on the case of an impurity
interacting with a one-dimensional BEC through a contact interaction. While a
simple wave function based on the expansion in the number of bath excitations
misses the localization physics entirely, a coherent state Ansatz combined with
a canonical transformation captures the physics of disorder and Anderson
localization.
