Gap solitons in a model of a superfluid fermion gas in optical lattices

TL;DR

This paper models gap solitons in a superfluid Fermi gas within optical lattices, deriving stable 1D and 2D soliton solutions and analyzing their properties and dynamics.

Contribution

It introduces a nonlinear equation with a 7/3 power term for Fermi superfluids and constructs stable gap solitons in 1D and 2D optical lattice settings using numerical and variational methods.

Findings

Stable 1D and 2D gap solitons are numerically constructed.

The variational approximation accurately predicts band positions.

Gap solitons can be moved by optical lattices without significant distortion.

Abstract

We consider a dynamical model for a Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) superfluid state, trapped in a combination of a 1D or 2D optical lattice (OL) and a tight parabolic potential acting in the transverse direction(s). The model is based on 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 1D or 2D form, we construct families of stable 1D 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 1D GSs are constructed too. We also demonstrate that the GS can be dragged without much distortion by an OL moving at a moderate velocity ($\sim $ 1 mm/s, in physical units). The predicted GSs contain $\sim 10^{3}-10^{4}$ and $\sim 10^{3}$ atoms per 1D and 2D settings, respectively.