Tightly bound gap solitons in a Fermi gas

TL;DR

This paper investigates the formation of tightly-bound fundamental gap solitons in a one-dimensional degenerate Fermi gas trapped in an optical lattice, using numerical and variational methods, and explores their stability and experimental realization.

Contribution

It introduces a detailed analysis of gap solitons in a 1D Fermi gas within an optical lattice, including the discovery of antisymmetric subfundamental solitons and their stability properties.

Findings

Fundamental gap solitons are tightly confined within a single optical lattice cell.

Antisymmetric subfundamental solitons are found but are unstable.

Predicted solitons involve 10^4 to 10^5 atoms and are experimentally feasible.

Abstract

Within the framework of the mean-field-hydrodynamic model of a degenerate Fermi gas (DFG), we study, by means of numerical methods and variational approximation (VA), the formation of fundamental gap solitons (FGSs) in a DFG (or in a BCS superfluid generated by weak interaction between spin-up and spin-down fermions), which is trapped in a periodic optical-lattice (OL) potential. An effectively one-dimensional (1D) configuration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG (which amounts to the known quintic equation for the Tonks-Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL-induced spectrum (unless they are very close to edges of the gaps) feature a tightly-bound shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly-bound subfundamental solitons (SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of $\sim 10^4 - 10^5$ atoms, can be created by available experimental techniques in the DFG of $^6$Li atoms.