  We present a numerical study of the one-dimensional BCS-BEC crossover of a
spin-imbalanced Fermi gas. The crossover is described by the Bose-Fermi
resonance model in a real space representation. Our main interest is in the
behavior of the pair correlations, which, in the BCS limit, are of the
Fulde-Ferrell-Larkin-Ovchinnikov type, while in the BEC limit, a superfluid of
diatomic molecules forms that exhibits quasi-condensation at zero momentum. We
use the density matrix renormalization group method to compute the phase
diagram as a function of the detuning of the molecular level and the
polarization. As a main result, we show that FFLO-like correlations disappear
well below full polarization close to the resonance. The critical polarization
depends on both the detuning and the filling.
