Tightly bound gap solitons in a Fermi gas

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.

6 pages, 8 figures

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Cited by in corpus (9)

• Superfluid Bose-Fermi mixture from weak-coupling to unitarity
• Spontaneous symmetry breaking of gap solitons in double-well traps
• Solitons in Tonks-Girardeau gas with dipolar interactions
• Hydrodynamics of Bose and Fermi superfluids at zero temperature: the superfluid nonlinear Schrodinger equation
• Symbiotic gap and semi-gap solitons in Bose-Einstein condensates
• Solitons in one-dimensional photonic crystals
• Gap solitons in superfluid boson-fermion mixtures
• Josephson oscillation of a superfluid Fermi gas
• Trapping of two-component matter-wave solitons by mismatched optical lattices