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

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We study an ultracold and dilute superfluid Bose-Fermi mixture confined in a strictly one-dimensional (1D) 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 interatomic strength g{sub 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{sub bf}>0 and may become a localized Bose-Fermi bright soliton for g{sub bf}<0. Finally, we show, using variational and numerical solutions 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.