A self-bound matter-wave boson–fermion quantum ball

Abstract

We demonstrate the possibility of creating a self-bound stable three-dimensional matter-wave spherical boson–fermion quantum ball in the presence of an attractive boson–fermion interaction and a small repulsive three-boson interaction. The two-boson interaction could be attractive or repulsive whereas the fermions are taken to be in a fully-paired super-fluid state in the Bardeen–Cooper–Schreifer (quasi-noninteracting weak-coupling) limit. We also include the Lee–Huang–Yang (LHY) correction to a repulsive bosonic interaction term. The repulsive three-boson interaction and the LHY correction can stop a global collapse while acting jointly or separately. The present study is based on a mean-field model, where the bosons are subject to a Gross–Pitaevskii (GP) Lagrangian functional and the fully-paired fermions are described by a Galilean-invariant density functional Lagrangian. The boson–fermion interaction is taken to be the mean-field Hartree interaction, quite similar to the interaction term in the GP equation. The study is illustrated by a variational and a numerical solution of the mean-field model for the boson–fermion 7Li–6Li system.