Solitons of Bose-Fermi mixtures in a strongly elongated trap

Abstract

It is shown that a Bose-Fermi mixture of a degenerate gas of spin-polarized fermions, whose number significantly exceeds the number of bosons, embedded in a strongly anisotropic trap, is described by the one-dimensional coupled nonlinear Schrodinger equation for the boson component and the wave equation with external source for the fermion component. Depending on the type of boson-fermion interaction, the system may display modulational instability and the existence of solitons in the fermion and boson components respectively. Such solitons represent either a local decrease (increase) of the density of both the components or a decrease of the density in one component and an increase of the density in the other component. It is shown that the type of the effective interactions can be easily managed by varying the trap geometry or by means of Feshbach resonance.