Gap solitons in fermion superfluids

We consider a dynamical model of a superfluid Fermi gas in the Bardeen–Cooper–Schrieffer regime trapped in a periodic optical lattice (OL) potential. The model is based on an equation for complex order parameter ϕ of the superfluid, which is derived from the relevant energy density and includes a self-repulsive term ∼ϕ7/3. By means of the variational approximation (VA) and numerical simulations, we find families of stable one- and two-dimensional (1D and 2D) gap solitons (GSs) in this model. Chiefly, they are compact objects trapped in a single cell of the OL. Families of stable even and odd bound states of these GSs are also found in one dimension. A 3D GS family is constructed too, but solely within the framework of the VA. In the linear limit, the VA predicts an almost exact position of the left edge of the first band-gap in the OL-induced spectrum. The full VA provides an accurate description of families of 1D and 2D fundamental GSs. We also demonstrate that a 1D GS can be safely transported by an OL moving at a moderate velocity.