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

We describe an imbalanced superfluid Fermi gas in three dimensions within the path-integral framework. To allow for the formation of the Fulde-Ferell-Larkin-Ovchinnikov-state (FFLO-state), a suitable form of the saddle-point is chosen, in which the pairs have a finite centre-of-mass momentum. To test the correctness of this path-integral description, the zero-temperature phase diagram for an imbalanced Fermi gas in three dimensions is calculated, and compared to recent theoretical results. Subsequently, we investigate two models that describe the effect of imposing a one-dimensional optical potential on the 3D imbalanced Fermi gas. We show that this 1D optical potential can greatly enlarge the stability region of the FFLO-state, relative to the case of the 3D Fermi gas without 1D periodic modulation. Furthermore it is show that there exists a direct connection between the centre-of-mass momentum of the FFLO-pairs and the wavevector of the optical potential. We propose that this concept can be used experimentally to resonantly enhance the stability region of the FFLO-state.