Topological States in a One-Dimensional Fermi Gas with Attractive Interactions

TL;DR

This paper predicts a topological superfluid phase in a one-dimensional Fermi gas with spin-orbit coupling and attractive interactions, featuring Majorana-like modes and unique collective excitations, with potential experimental detection via Zeeman field sweeps.

Contribution

It introduces a new topological superfluid state in a 1D Fermi gas with Rashba-like spin-orbit coupling, Zeeman field, and attractive interactions, highlighting Majorana-like modes and their experimental signatures.

Findings

Majorana-like zero modes appear despite number conservation.

Degeneracy of collective excitations such as phonons.

Topological state can be detected via Zeeman field sweep pumping.

Abstract

We describe a novel topological superfluid state, which forms in a one-dimensional Fermi gas with Rashba-like spin-orbit coupling, a Zeeman field and intrinsic attractive interactions. In spite of total number conservation and the presence of gapless excitations, Majorana-like zero modes appear in this system and can be linked with interfaces between two distinct phases that naturally form at different regions of the harmonic trap. As a result, the low lying collective excitations of the system, including the dipole oscillations and the long-wavelength phonons, are doubly degenerate. While backscattering from point impurities can lead to a splitting of the degeneracies that scales algebraically with the system size, the smooth confining potential can only cause an exponentially small splitting. We show that the topological state can be uniquely probed by a pumping effect induced by a slow sweep of the Zeeman field from a high initial value down to zero field.