Abstract
The quantum phase of boson-fermions mixtures (BFM) of atoms confined to one dimension by an anisotropic optical lattice were investigated. The study was carried out by using bosonization approach. A charge-density wave phase, a fermion pairing phase and a phase separation regime were found for a BFM with a single species of fermions. The result shows a similarity to the Luttinger liquid (LL) phase diagrams of 1D interacting electron systems, suggesting that 1D BFM can be understood as LLs of polarons.