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.
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