FFLO vs Bose-Fermi mixture in polarized 1D Fermi gas on a Feshbach resonance: a 3-body study

TL;DR

This paper investigates the evolution of FFLO-like states into Bose-Fermi mixtures in a 1D Fermi gas near a Feshbach resonance, using exact three-body solutions and Monte Carlo simulations to understand correlation behaviors.

Contribution

It provides an exact three-body analysis and Monte Carlo insights into the transition from FFLO to Bose-Fermi states in a 1D Fermi gas.

Findings

FFLO-like oscillating correlations are present at the three-body level.

Correlations become monotonic in the Bose-Fermi mixture regime.

The study offers a detailed understanding of the crossover behavior.

Abstract

We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the FFLO-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is is already present at the 3-body level. We present an exact study of the 3-body problem, and gain extra insights by considering worldlines of a path integral Monte-Carlo calculation.