Tightly bound gap solitons in a Fermi gasS. K. Adhikari1 and B. A. Malomed2
1 Instituto de Física Teórica, UNESP - São Paulo State University - 01.405-900 São Paulo, São Paulo, Brazil
2 Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University - Tel Aviv 69978, Israel
received 12 February 2007; accepted in final form 18 July 2007; published September 2007
published online 8 August 2007
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 atoms, can be created by available experimental techniques in the DFG of 6Li atoms.
03.75.Ss - Degenerate Fermi gases .
03.75.Lm - Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations .
05.45.Yv - Solitons .
© Europhysics Letters Association 2007