2025/02/25 by Esteban Felipe Molina Cardenas, Cárdenas, Esteban, Joseph K. Miller +5
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2502.18678
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.