One-dimensional superfluid Bose-Fermi mixture: mixing, demixing and bright solitons

TL;DR

This paper investigates the behavior of a one-dimensional superfluid Bose-Fermi mixture, revealing conditions for stability, demixing, and bright soliton formation, with potential experimental realization.

Contribution

It introduces a coupled mean-field model for 1D Bose-Fermi mixtures and analyzes their stability, demixing, and soliton solutions under different boundary conditions.

Findings

Uniform mixture stable only at high fermionic density with periodic boundaries.

Demixing occurs at low fermionic density for positive inter-atomic interaction.

Bright solitons are stable and can be experimentally realized.

Abstract

We study a ultra-cold and dilute superfluid Bose-Fermi mixture confined in a strictly one-dimensional atomic waveguide by using a set of coupled nonlinear mean-field equations obtained from the Lieb-Liniger energy density for bosons and the Gaudin-Yang energy density for fermions. We consider a finite Bose-Fermi inter-atomic strength g_{bf} and both periodic and open boundary conditions. We find that with periodic boundary conditions, i.e. in a quasi-1D ring, a uniform Bose-Fermi mixture is stable only with a large fermionic density. We predict that at small fermionic densities the ground state of the system displays demixing if g_{bf}>0 and may become a localized Bose-Fermi bright soliton for g_{bf}<0. Finally, we show, using variational and numerical solution of the mean-field equations, that with open boundary conditions, i.e. in a quasi-1D cylinder, the Bose-Fermi bright soliton is the unique ground state of the system with a finite number of particles, which could exhibit a partial mixing-demixing transition. In this case the bright solitons are demonstrated to be dynamically stable. The experimental realization of these Bose-Fermi bright solitons seems possible with present setups.