Fermi Gas atoms trapped by one quasi-periodic lattice and a two-dimensional harmonic potential

Abstract In this work, we consider a dynamical three-dimensional model of a Bardeen-Cooper-Schrieffer superfluid Fermi gas trapped in a unidimensional quasiperiodic optical lattice and in the presence of a tight cigar-shaped trapping potential. By variational approximation, we study the possibility that the nonlinearity coefficient acting in a combination with the potential of the quasiperiodic optical lattice and cigar-shaped trapping potential, allows three dimensional bright gap solitons to arise. Families of three-dimensional fundamental gap soliton are stable for small values of amplitude of the quasiperiodic optical lattice. The manuscript presented may become a teaching and learning guide in studies involving fermionic gases trapped by light fields. Students are encouraged to perform variational calculations for the hydrodynamic equation in one dimension.