Anderson localization of Cooper pairs and Majorana fermions in an ultracold atomic Fermi gas with synthetic spin-orbit coupling

TL;DR

This paper explores how disorder affects localization and superfluidity in a spin-orbit coupled ultracold Fermi gas, revealing differences between s-wave and p-wave interactions and analyzing the stability of Majorana fermions.

Contribution

It provides a theoretical analysis of Anderson localization in spin-orbit coupled Fermi gases, highlighting the robustness of topological superfluidity and Majorana fermions against disorder.

Findings

Disorder increases two-particle binding energy at low Zeeman fields.

Superfluidity disappears above a certain disorder threshold at low Zeeman fields.

Topological superfluidity with p-wave interactions is more robust against disorder.

Abstract

We theoretically investigate two-particle and many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasi-periodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional $s$-wave interactions. As the disorder strength increases, the two-particle binding energy increases and the fermionic superfluidity of many particles disappears above a threshold. At a large Zeeman field, where the interatomic interaction behaves effectively like a $p$-wave interaction, the binding energy decreases with increasing disorder strength and the resulting topological superfluidity shows a much more robust stability against disorder than the conventional $s$-wave superfluidity. We also analyze the localization properties of the emergent Majorana fermions in the topological phase. Our results could be experimentally examined in future cold-atom experiments, where the spin-orbit coupling can be induced artificially by using two Raman lasers, and the quasi-periodic potential can be created by using bichromatic optical lattices.