Gap solitons in superfluid boson-fermion mixtures

Abstract

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 BEC and BCS 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 bandgaps of the OL-induced spectrum, by means of variational and numerical methods, which are found to be in good agreement. The families include both intra-gap and inter-gap solitons, with the chemical potentials of the boson and fermion components falling in the same or different bandgaps, respectively.Nonfundamental states, extended over several lattice cells, are constructed too. The GSs are stable against strong perturbations.

9 pages, 14 figures

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• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Hydrodynamics of Bose and Fermi superfluids at zero temperature: the superfluid nonlinear Schrodinger equation
• Symbiotic gap and semi-gap solitons in Bose-Einstein condensates
• Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
• Trapping of two-component matter-wave solitons by mismatched optical lattices