  We study a nonequilibrium dynamics of a one-dimensional spin-imbalanced
Fermi-Hubbard model following a quantum quench of on-site interaction,
realizable, for example, in Feshbach-resonant atomic Fermi gases. We focus on
the post-quench evolution starting from the initial BCS and
FuldeFerrell-Larkin-Ovchinnikov (FFLO) ground states and analyze the
corresponding spin-singlet, spin-triplet, density-density, and
magnetization-magnetization correlation functions. We find that beyond a
light-cone crossover time, rich post-quench dynamics leads to thermalized and
pre-thermalized stationary states that display strong dependence on the initial
ground state. For initially gapped BCS state, the long-time stationary state
resembles thermalization with the effective temperature set by the initial
value of the Hubbard interaction. In contrast, while the initial gapless FFLO
state reaches a stationary pre-thermalized form, it remains far from
equilibrium. We suggest that such post-quench dynamics can be used as a
fingerprint for identification and study of the FFLO phase.
