Bogoliubov-de Gennes study of trapped spin-imbalanced unitary Fermi gases

TL;DR

This paper uses advanced numerical methods to solve the Bogoliubov-de Gennes equations for trapped spin-imbalanced unitary Fermi gases, revealing how trapping geometry and imbalance influence phase behavior and the applicability of the local density approximation.

Contribution

It introduces novel numerical techniques to self-consistently solve the Bogoliubov-de Gennes equations for complex trapped Fermi gases, providing insights into phase structures and approximation validity.

Findings

Validity of LDA depends on trap geometry and spin imbalance

Identifies novel superfluid phases in spin-imbalanced gases

Demonstrates the impact of atom number on phase behavior

Abstract

It is quite common that several different phases exist simultaneously in a system of trapped quantum gases of ultra-cold atoms. One such example is the strongly-interacting Fermi gas with two imbalanced spin species, which has received a great amount of attention due to the possible presence of exotic superfluid phases. By employing novel numerical techniques and algorithms, we self-consistently solve the Bogoliubov de-Gennes equations, which describe Fermi superfluids in the mean-field framework. From this study, we investigate the novel phases of spin-imbalanced Fermi gases and examine the validity of the local density approximation (LDA), which is often invoked in the extraction of bulk properties from experimental measurements within trapped systems. We show how the validity of the LDA is affected by the trapping geometry, number of atoms and spin imbalance.