Mapping the Two-Component Atomic Fermi Gas to the Nuclear Shell-Model

TL;DR

This paper demonstrates how a two-component atomic Fermi gas in a tight trap can be mapped onto the nuclear shell model, enabling the use of nuclear many-body techniques like SMMC to study pairing correlations in small cold atom systems.

Contribution

It introduces a mapping between cold Fermi gases and the nuclear shell model, allowing nuclear physics methods to analyze cold atom systems.

Findings

Applied Shell Model Monte Carlo to estimate pairing correlations.

Showed the mapping enables use of nuclear many-body techniques.

Demonstrated the approach on a small Fermi system with attractive interactions.

Abstract

The physics of a two-component cold fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1-100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic fermi gas in a tight external trap can be mapped to the nuclear shell model so that readily available many-body techniques in nuclear physics, such as the Shell Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.