Beyond spin-charge separation: Helical modes and topological quantum phase transitions in one-dimensional Fermi gases with spin-orbit and Rabi couplings

TL;DR

This paper explores how spin-orbit and Rabi couplings in one-dimensional Fermi gases lead to helical modes and topological phase transitions, providing a detailed phase diagram and experimental signatures.

Contribution

It introduces a comprehensive analysis of topological quantum phase transitions and the evolution of collective modes in spin-orbit coupled Fermi gases with Rabi fields.

Findings

Identification of helical collective modes due to spin-charge mixing

Mapping of phase diagram with topological Lifshitz transitions

Analysis of dynamical structure factors for experimental detection

Abstract

Motivated by the experimental observation of spin-charge separation in one-dimensional interacting Fermi gases, we investigate these systems in the presence of spin-orbit coupling and Rabi fields. We demonstrate that spin-charge-separated modes evolve into helical collective modes due to the special mixing of spin and charge induced by spin-orbit coupling and Rabi fields. We obtain the phase diagram of chemical potential versus Rabi fields for given spin-orbit coupling and interactions, and find several topological quantum phase transitions of the Lifshitz type. We show that the velocities of the collective modes are nonanalytic at the boundaries between different phases. Lastly, we analyze the charge-charge, spin-charge and spin-spin dynamical structure factors to show that the dispersions, spectral weights and helicities of the collective modes can be experimentally extracted in systems such as $^{6}{\rm Li}$, $^{40}{\rm K}$ and $^{173}{\rm Yb}$.