Gap solitons of superfluid Fermi gas in one-dimensional optical lattices

Yan Chen, Kezhi Zhang, Yong-Lin He +2 more

Sadhan K. Adhikari, Boris A. Malomed

Sadhan K. Adhikari, Boris A. Malomed

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 ∼10 4 –10 5 atoms, can be created by available experimental techniques in the DFG of 6 Li atoms.

Yang Shu-Rong, Cai Hong-Qiang, Qi Wei +1 more

Based on the hydrodynamic model, gap soliton of a superfluid fermion gas in optical lattices was discussed. By using the variational method, the condition for existing gap soliton is obtained. It is found that, when the system crosses from Bose-Eingtein condensation side to the BCS side, the condition for existing gap soliton and the structure of gap soliton are very different.

Boris A. Malomed, V.A. Nascimento, Sadhan K. Adhikari

Sadhan K. Adhikari, Boris A. Malomed

Using coupled equations for the bosonic and fermionic order parameters, we construct families of gap solitons (GSs) in a nearly one-dimensional Bose-Fermi mixture trapped in a periodic optical-lattice (OL) potential, the boson and fermion components being in the states of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer superfluid, respectively. Fundamental GSs are compact states trapped, essentially, in a single cell of the lattice. Full families of such solutions are constructed in the first two band gaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intragap and intergap solitons, with the chemical potentials of the boson and fermion components falling in the same or different band gaps, respectively. Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.