  We use Quantum Monte Carlo (QMC) simulations to study the pairing mechanism
in a one-dimensional fermionic system governed by the Hubbard model with
attractive contact interaction and with imbalance between the two spin
populations. This is done for the uniform system and also for the system
confined in a harmonic trap to compare with experiments on confined ultra-cold
atoms. In the uniform case we determine the phase diagram in the
polarization-temperature plane and find that the
"Fulde-Ferrell-Larkin-Ovchinnikov" (FFLO) phase is robust and persists to
higher temperature for higher polarization. In the confined case, we also find
that the FFLO phase is stabilized by higher polarization and that it is within
the range of detection of experiments currently underway.
