Gap solitons in superfluid boson-fermion mixtures

TL;DR

This paper constructs and analyzes stable gap solitons in a one-dimensional superfluid Bose-Fermi mixture within an optical lattice, revealing families of intra-gap and inter-gap solutions through variational and numerical methods.

Contribution

It introduces a novel framework for creating and studying gap solitons in superfluid Bose-Fermi mixtures using coupled equations and variational techniques.

Findings

Families of stable gap solitons are constructed in the first two bandgaps.

Both intra-gap and inter-gap solitons are identified and characterized.

Solutions are stable against strong perturbations.

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.