  We find that a model Hamiltonian of s-wave superconductors in the presence of
spin-orbit interactions and a Zeeman field is exactly solvable. Most
intriguingly, based on the exact solutions, an unconventional type of
Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in
which the center-of-mass momentum of the fermion pair is proportional to the
Zeeman field. We also elaborate on the drifting effect of the Zeeman field on
the spin-orbit-coupled Bose-Einstein condensate.
