Exact quantum Monte Carlo study of one dimensional trapped fermions with attractive contact interactions

TL;DR

This study uses exact quantum Monte Carlo methods to analyze one-dimensional trapped fermions with attractive interactions, exploring density profiles, spin imbalance effects, and signatures of exotic pairing states relevant for experiments.

Contribution

It provides a detailed, exact analysis of 1D trapped fermions with attractive contact interactions, including the validity of the Thomas-Fermi approximation and experimental parameter suggestions.

Findings

Thomas-Fermi approximation accurately predicts large particle number density profiles

Small oscillations and shell sizes are not well captured by the approximation

Identifies experimental conditions to observe FFLO states and double shell structures

Abstract

Using exact continuous quantum Monte Carlo techniques, we study the zero and finite temperature properties of a system of harmonically trapped one dimensional spin 1/2 fermions with short range interactions. Motivated by experimental searches for modulated Fulde-Ferrel-Larkin-Ovchinikov states, we systematically examine the impact of a spin imbalance on the density profiles. We quantify the accuracy of the Thomas-Fermi approximation, finding that for sufficiently large particle numbers (N > 100) it quantitatively reproduces most features of the exact density profile. The Thomas-Fermi approximation fails to capture small Friedel-like spin and density oscillations and overestimates the size of the fully paired region in the outer shell of the trap. Based on our results, we suggest a range of experimentally tunable parameters to maximize the visibility of the double shell structure of the system and the Fulde-Ferrel-Larkin-Ovchinikov state in the one dimensional harmonic trap. Furthermore, we analyze the fingerprints of the attractive contact interactions in the features of the momentum and pair momentum distributions.