Title: Bose-Hubbard lattice as a controllable environment for open quantum systems,
Abstract: We investigate the open dynamics of an atomic impurity embedded in a
one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation
for the impurity and show that the Bose-Hubbard lattice behaves as a tunable
engineered environment allowing to simulate both Markovian and non-Markovian
dynamics in a controlled and experimentally realisable way. We demonstrate that
the presence or absence of memory effects is a signature of the nature of the
excitations induced by the impurity, being delocalized or localized in the two
limiting cases of superfluid and Mott insulator, respectively. Furthermore, our
findings show how the excitations supported in the two phases can be
characterized as information carriers.