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We describe an imbalanced superfluid Fermi gas in three dimensions within thepath-integral framework. To allow for the formation of theFulde-Ferell-Larkin-Ovchinnikov-state (FFLO-state), a suitable form of thesaddle-point is chosen, in which the pairs have a finite centre-of-massmomentum. To test the correctness of this path-integral description, thezero-temperature phase diagram for an imbalanced Fermi gas in three dimensionsis calculated, and compared to recent theoretical results. Subsequently, weinvestigate two models that describe the effect of imposing a one-dimensionaloptical potential on the 3D imbalanced Fermi gas. We show that this 1D opticalpotential can greatly enlarge the stability region of the FFLO-state, relativeto the case of the 3D Fermi gas without 1D periodic modulation. Furthermore itis show that there exists a direct connection between the centre-of-massmomentum of the FFLO-pairs and the wavevector of the optical potential. Wepropose that this concept can be used experimentally to resonantly enhance thestability region of the FFLO-state.

Resonant enhancement of the FFLO-state in 3D by a one-dimensional optical potential