Exact results of two-component Fermi gas in a hard wall trap

TL;DR

This paper provides exact solutions for the ground state of a one-dimensional two-component Fermi gas in a hard wall trap, revealing unique momentum distributions due to interactions, with potential experimental relevance.

Contribution

It offers an exact Bethe ansatz analysis of the system's wave function and correlations, highlighting differences from free fermions.

Findings

Momentum density distribution differs from free fermions in strong interactions

Position density distributions are similar regardless of interactions

Results are relevant for ultra-cold atom experiments

Abstract

We investigate the ground state properties of a one-dimensional two-component ultra-cold Fermi gas in an infinite potential well. Exact Bethe ansatz solution is used to calculate the many-body wave function of the system. Then we evaluate the single-particle reduced density matrix and two-particle density density correlations of the system for different interaction strengths. We find that the momentum density distributions of the strongly interacting two-component Fermi gas is distinct from that of free spinless Fermi gas although their position density distributions are similar. This interacting system may be experimentally accessible using ultra-cold atoms.