Charge and spin dynamics of interacting Fermions in a one dimensional harmonic trap

TL;DR

This paper investigates the charge and spin dynamics of interacting one-dimensional Fermi gases in harmonic traps, revealing spatially varying spin-charge separation effects through Bethe-Ansatz and Tomonaga-Luttinger models.

Contribution

It introduces a detailed analysis of inhomogeneous spin-charge separation in trapped Fermi gases using Bethe-Ansatz solutions and low-energy effective models.

Findings

Conventional spin-charge separation occurs at the trap center.

Edge regions exhibit significantly enhanced spin-charge separation.

Inhomogeneous models capture spatial variation in excitation dynamics.

Abstract

We study an atomic Fermi gas interacting through repulsive contact forces in a one dimensional harmonic trap. Bethe-Ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation the edges cause a giant increase of the separation between these modes.