  Superconductivity is a quantum phenomena arising, in its simplest form, from
pairing of fermions with opposite spin into a state with zero net momentum.
Whether superconductivity can occur in fermionic systems with unequal number of
two species distinguished by spin, atomic hyperfine states, flavor, presents an
important open question in condensed matter, cold atoms, and quantum
chromodynamics, physics. In the former case the imbalance between spin-up and
spin-down electrons forming the Cooper pairs is indyced by the magnetic field.
Nearly fifty years ago Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) proposed
that such imbalanced system can lead to exotic superconductivity in which pairs
acquire finite momentum. The finite pair momentum leads to spatially
inhomogeneous state consisting of of a periodic alternation of "normal" and
"superconducting" regions. Here, we report nuclear magnetic resonance (NMR)
measurements providing microscopic evidence for the existence of this new
superconducting state through the observation of spin-polarized quasiparticles
forming so-called Andreev bound states.
