Fermi one-dimensional quantum gas: Luttinger liquid approach and spin-charge separation

We discuss the properties of quasi-one-dimensional quantum gases of fermionic atoms using the Luttinger liquid theory, including the presence of an optical lattice and of a longitudinal trapping potential. We analyse in particular the nature and manifestations of spin-charge separation, where in the case of atoms 'spin' and 'charge' refers to two internal atomic states and the atomic mass density, respectively.