Gap solitons in a model of a superfluid fermion gas in optical lattices
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We consider a dynamical model for a Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) superfluid state, trapped in a combination of a ID or 2D optical lattice (OL) and a tight parabolic potential, acting in the transverse direction(s). The model is based oil an equation for the order parameter (wave function), which is derived from the energy density for the weakly coupled BCS superfluid. The equation includes a nonlinear self-repulsive term of power 7/3, which accounts for the Fermi pressure. Reducing the equation to the I D or 2D form, we construct families of stable I D and 2D gap solitons (GSs) by means of numerical simulations, which are guided by the variational approximation (VA). The GSs are, chiefly. compact objects trapped in a single cell of the OL potential. In the linear limit, the VA predicts almost exact positions of narrow Bloch bands that separate the semi-infinite and first finite gaps, as well as the first and second finite ones. Families of stable even and odd bound states of I D GSs are constructed, too. We also demonstrate that the GS can be dragged without much distortion by an OL moving at a moderate velocity (similar to 1 mm/s, in physical units). The predicted GSs contain similar to 10(3)-10(4) and similar to 10(3) atoms per 1D and 2D settings, respectively. (C) 2008 Elsevier B.V. All rights reserved.