In this work, we consider a model derived from energy density for a Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) superfluid state, trapped in a quasiperiodic one-dimensional optical lattice (OL). Reducing the equation to the 3D to 1D form, we construct families of stable 1D gap solitons (GSs) by the variational approximation (VA). In the linear limit, the VA predicts almost exact positions of narrow Bloch bands that separate the first gaps. Through the variational approximation, we show the possibility that the nonlinearity coefficient acting in a combination with the potential of the quasiperiodic one-dimensional optical lattice, allows one dimensional bright gap solitons to arise. Varying the amplitude of the optical lattice, we analyze the existence and stability of bright gap solitons using a gaussian ansatz. GSs are stable against small variations of the quasiperiodic optical lattice. This paper can be used as a learning guide in the study of cold atoms. Students are encouraged to perform variational calculations for other amplitude values of optical lattices.
Keywords:
Optical lattice; Degenerate Fermi Gas; Variational Approximation (VA)
