Bunching-antibunching crossover in harmonically trapped few-body Bose-Fermi mixtures

TL;DR

This study explores the ground state behavior of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap, revealing a crossover from bunching to antibunching of bosons influenced by interaction strength and mass ratio, explained through correlations and an effective Bose-Hubbard model.

Contribution

It demonstrates the physical origin of the bunching-antibunching crossover using correlated ab initio methods and introduces a two-site Bose-Hubbard model for heavy fermions.

Findings

Bunching-antibunching crossover observed with increasing interspecies repulsion.

Crossover suppressed when bosonic repulsion exceeds a critical value depending on mass ratio.

Correlations induce an effective bosonic interaction explaining bunching behavior.

Abstract

We investigate the ground state of a few-body Bose-Fermi mixture in a one-dimensional harmonic trap with varying interaction strengths and mass ratio. A bunching-antibunching crossover of the bosonic species for increasing interspecies' repulsion is observed within our fully correlated \textit{ab~initio} studies. Interestingly, this crossover is suppressed if the bosonic repulsion exceeds a critical value which strongly depends on the mass ratio. In order to unveil the physical origin of this crossover, we employ different levels of approximations: while a species mean-field approach can account for the antibunching, only the inclusion of the interspecies correlations can lead to the bunching. We show that these correlations effectively create an induced bosonic interaction, which in turn elucidates the occurrence of the bosonic bunching. Finally, we derive a two-site extended Bose-Hubbard model which reveals the low-energy physics of the bosons for the case of much heavier fermions.