  A Bose-Einstein condensate exhibiting a nontrivial phase induces an
artificial magnetic field in immersed impurity atoms trapped in a stationary,
ring-shaped optical lattice. We present an effective Hamiltonian for the
impurities for two condensate setups: the condensate in a rotating ring and in
an excited rotational state in a stationary ring. We use Bogoliubov theory to
derive analytical formulas for the induced artificial magnetic field and the
hopping amplitude in the limit of low condensate temperature where the impurity
dynamics is coherent. As methods for observing the artificial magnetic field we
discuss time of flight imaging and mass current measurements. Moreover, we
compare the analytical results of the effective model to numerical results of a
corresponding two-species Bose-Hubbard model. We also study numerically the
clustering properties of the impurities and the quantum chaotic behavior of the
two-species Bose-Hubbard model.
