  We investigate a system of fermions trapped in a quasi-periodic potential
from an open quantum system theory perspective, designing a protocol in which
an impurity atom (a two level system) is coupled to a trapped fermionic cloud
described by the non-interacting Aubry-Andr\'e model. The Fermi system is
prepared in a charge density wave state before it starts its relaxation. In
this work we focus our attention on the time evolution of the impurity in such
an out of equilibrium environment, and study whether the induced dynamics can
be classified as Markovian or non-Markovian. We find how the localised phase of
the Aubry-Andr\'{e} model displays evidence of strong and stable memory effects
and can be considered as a controllable and robust non-Markovian environment.
