Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity

TL;DR

This paper evaluates the local density approximation for the ground state energy of a one-dimensional Fermi gas with a single impurity, comparing it with exact numerical results and experimental data, highlighting its limitations and strengths.

Contribution

It provides a detailed comparison of theoretical models with numerical and experimental results for few-atom Fermi gases, revealing the regimes where the local density approximation is effective or breaks down.

Findings

LDA shows ambiguity in few-atom systems but performs well in some models.

Strong interaction theories fail as particle number increases or interaction weakens.

The contact coefficient is calculated in the strongly interacting regime.

Abstract

We discuss the local density approximation approach to calculating the ground state energy of a one-dimensional Fermi gas containing a single impurity, and compare the results with exact numerical values that we have for up to 11 particles for general interaction strengths and up to 30 particles in the strongly interacting case. We also calculate the contact coefficient in the strongly interacting regime. The different theoretical predictions are compared to recent experimental results with few-atom systems. Firstly, we find that the local density approximation suffers from great ambiguity in the few-atom regime, yet it works surprisingly well for some models. Secondly, we find that the strong interaction theories quickly break down when the number of particles increase or the interaction strength decreases.