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Based on the matrix product states method, we investigate numerically theground state properties of one-dimensional mixtures of repulsive bosons andspin-imbalanced attractive fermions, the latter being in theFulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at afinite momentum $k=k_{FFLO}$. We find that the visibility of such a state isdramatically enhanced as the repulsive Bose-Fermi mixture is brought close tothe phase-separation point. In particular, large amplitude self-inducedoscillations with wave-vector $2k_{FFLO}$ appear in both the fermion totaldensity and the boson density profiles, leaving sharp fingerprints in thecorresponding static structure factors. We show that these features remain wellvisible in cold atoms systems trapped longitudinally by a smooth flat-bottompotential. Hence bosons can be used to directly reveal the modulated Fermisuperfluid in experiments.

Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point