Luttinger liquid of polarons in one-dimensional boson-fermion mixtures
  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. 
L. Mathey, D.-W. Wang, W. Hofstetter, M. D. Lukin, Eugene Demler