  We show that triplet pairing correlations are generated in purely s-waves
superfluids whenever population imbalance enforces anisotropic Fulde-Ferrell
(FF) or inhomogeneous Larkin-Ovchinikov (LO) states. The same set of
quasiparticle states contributes to the triplet component and to the
polarization, thus spatially correlating them. In the LO case, this set forms a
narrow band of Andreev states centered on the nodes of the s-wave order
parameter. This picture naturally provides a unifying explanation of previous
findings that attractive p-wave interaction stabilizes FFLO states. We also
study a similar triplet mixing which occurs when a balanced two-component
system displays FFLO type oscillations due to a spin-dependent optical lattice.
We discuss how this triplet component can be measured in systems of ultra-cold
atoms using a rapid ramp across a p-wave Feshbach resonance. This should
provide a smoking gun signature of FFLO states.
