Fulde-Ferrell-Larkin-Ovchinnikov critical polarization in one-dimensional fermionic optical lattices

We deduce an expression for the critical polarization P-C below which the Fulde-Ferrell-Larkin-Ovchinnikov state emerges in one-dimensional lattices with spin-imbalanced populations. We provide and explore the phase diagram of unconfined chains as a function of polarization, interaction, and particle density. For harmonically confined systems, we supply a quantitative mapping, which also allows applying our phase diagram for confined chains. We find analytically and confirm numerically that the upper bound for the critical polarization is universal: P-C(max) = 1/3 for any density, interaction, and confinement strength.