Emergence of fermion-mediated interactions in Bose-Fermi mixtures

TL;DR

This paper mathematically demonstrates how fermion-mediated interactions induce a stability-instability transition in Bose-Fermi mixtures, confirming experimental observations and analyzing the spectral properties of the many-body Hamiltonian.

Contribution

It provides the first rigorous proof of the stability transition in Bose-Fermi mixtures due to fermion-mediated interactions, linking spectral convergence to physical stability.

Findings

Attractive fermion-mediated interactions lead to a stability-instability transition.

Eigenvalues of the many-body Hamiltonian converge to those of an effective Bose Hamiltonian.

The transition is driven by the Bose-Fermi coupling strength $g$, causing collapse at large $|g|$.

Abstract

This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, as well as a stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. More precisely, we show the convergence of its eigenvalues towards those of an effective Bose Hamiltonian, which includes fermion-mediated effects. Applying this result to a model with short-range potentials, we derive a stability-instability transition in the bosonic subsystem, driven by the Bose-Fermi coupling strength $g$. For small $|g|$, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large $|g|$, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate.