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The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in 2Dsuperconductors about 50 years ago, but so far unambiguous experimentalevidences are still lacked. The recently experimentally realizedspin-imbalanced Fermi gases may potentially unveil this elusive state, butrequire very stringent experimental conditions. In this Letter, we show thatFFLO phases may be observed even in a 3D degenerate Fermi gas with spin-orbitcoupling and in-plane Zeeman field. The FFLO phase is driven by the interplaybetween asymmetry of Fermi surface and superfluid order, instead of theinterplay between magnetic and superconducting order in solid materials. Thepredicted FFLO phase exists in a giant parameter region, possesses a stablelong-range superfluid order due to the 3D geometry, and can be observed withexperimentally already achieved temperature ($T\sim 0.05E_{F}$), thus opens anew fascinating avenue for exploring FFLO physics.

Route to Observable Fulde-Ferrell-Larkin-Ovchinnikov Phases in 3D Spin-Orbit Coupled Degenerate Fermi Gases