  The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, a superconducting state
with non-zero total momentum Cooper pairs in a large magnetic field, was first
predicted about 50 years ago, and since then became an important concept in
many branches of physics. Despite intensive search in various materials,
unambiguous experimental evidence for the FFLO phase is still lacking in
experiments. In this paper, we show that both FF (uniform order parameter with
plane-wave phase) and LO phase (spatially varying order parameter amplitude)
can be observed using fermionic cold atoms in spin-orbit coupled optical
lattices. The increasing spin-orbit coupling enhances the FF phase over the LO
phase. The coexistence of superfluid and magnetic orders is also found in the
normal BCS phase. The pairing mechanism for different phases is understood by
visualizing superfluid pairing densities in different spin-orbit bands. The
possibility of observing similar physics using spin-orbit coupled
superconducting ultra-thin films is also discussed.
