K-Rb Fermi-Bose mixtures: vortical states and sag

TL;DR

This paper investigates the stability and density distribution of K-Rb Bose-Fermi mixtures under attractive interactions, considering vortical states and trap displacements, providing analytical and numerical insights into collapse conditions.

Contribution

It introduces analytical expressions for the fermion effective potential in the presence of vortices and sag, enhancing understanding of mixture stability near collapse.

Findings

Analytical formulas for fermion density maxima

Validation of formulas up to collapse thresholds

Impact of vortical states and sag on stability

Abstract

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.