  Spin-polarized attractive Fermi gases in one-dimensional (1D) optical
lattices are expected to be remarkably good candidates for the observation of
the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with
an attractive Hubbard model with population imbalance. By means of the
density-matrix renormalization-group method we compute the pairing correlations
as well as the static spin and charge structure factors in the whole range from
weak to strong coupling. We demonstrate that pairing correlations exhibit
quasi-long range order and oscillations at the wave number expected from FFLO
theory. However, we also show by numerically computing the mixed spin-charge
static structure factor that charge and spin degrees of freedom appear to be
coupled already for small imbalance. We discuss the consequences of this
coupling for the observation of the FFLO phase, as well as for the
stabilization of the quasi-long range order into long-range order by coupling
many identical 1D systems, as in quasi-1D optical lattices.
