Superfluid Bose-Fermi mixture from weak-coupling to unitarity

TL;DR

This paper develops a unified theoretical framework using coupled nonlinear Schrödinger equations to describe superfluid Bose-Fermi mixtures across the entire interaction spectrum from weak-coupling to unitarity, including surface effects.

Contribution

It introduces a set of Galilei-invariant equations valid from weak-coupling to unitarity, incorporating beyond-mean-field corrections for both bosonic and fermionic components.

Findings

Equations accurately describe the mixture across interaction regimes.

Numerical tests confirm model validity over wide scattering length ranges.

Model captures surface effects in superfluid mixtures.

Abstract

We investigate the zero-temperature properties of a superfluid Bose-Fermi mixture by introducing a set of coupled Galilei-invariant nonlinear Schr\"odinger equations valid from weak-coupling to unitarity. The Bose dynamics is described by a Gross-Pitaevskii-type equation including beyond-mean-field corrections possessing the correct weak-coupling and unitarity limits. The dynamics of the two-component Fermi superfluid is described by a density-functional equation including beyond-mean-field terms with correct weak-coupling and unitarity limits. The present set of equations is equivalent to the equations of generalized superfluid hydrodynamics, which take into account also surface effects. The equations describe the mixture properly as the Bose-Bose repulsive (positive) and Fermi-Fermi attractive (negative) scattering lengths are varied from zero to infinity in the presence of a Bose-Fermi interaction. The present model is tested numerically as the Bose-Bose and Fermi-Fermi scattering lengths are varied over wide ranges covering the weak-coupling to unitarity transition.