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

TL;DR

This paper proposes a theoretical model for creating a stable, self-bound three-dimensional boson-fermion quantum ball using attractive interactions, repulsive three-boson interactions, and Lee-Huang-Yang corrections, supported by variational and numerical analysis.

Contribution

It introduces a mean-field model for a stable boson-fermion quantum ball incorporating three-boson interactions and LHY correction, with analysis specific to the $^7$Li-$^6$Li system.

Findings

Stable self-bound boson-fermion quantum balls are theoretically possible.

Repulsive three-boson interactions and LHY correction prevent collapse.

Numerical and variational solutions support the existence of such quantum balls.

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 three-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 $^7$Li- $^6$Li system.