  We use bosonization approach to investigate quantum phases in mixtures of
bosonic and fermionic atoms confined in one dimensional optical lattices. The
phase diagrams can be well understood in terms of polarons, which correspond to
atoms that are "dressed" by screening clouds of the other atom species. For a
mixture of single species of fermionic and bosonic atoms we find a charge
density wave phase, a phase with fermion pairing, and a regime of phase
separation. For a mixture of two species of fermionic atoms and one species of
bosonic atoms we obtain spin and charge density wave phases, a Wigner crystal
phase, singlet and triplet paired states of fermions, and a phase separation
regime. Equivalence between the Luttinger liquid description of polarons and
the canonical polaron transformation is established and the techniques to
detect the resulting quantum phases are discussed.
