  We present an exact Quantum Monte Carlo study of the attractive 1-dimensional
Hubbard model with imbalanced fermion population. The pair-pair correlation
function, which decays monotonically in the absence of polarization P, develops
oscillations when P is nonzero, characteristic of
Fulde-Ferrell-Larkin-Ovchinnikov phase. The pair momentum distribution peaks at
a momentum equal to the difference in the Fermi momenta. At strong coupling,
the minority and majority momentum distributions are shown to be deformed,
reflecting the presence of the other species, and its Fermi surface. The FFLO
oscillations survive the presence of a confining potential, and the local
polarization at the trap center exhibits a marked dip, similar to that observed
experimentally.
