Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions

TL;DR

This paper investigates dark-soliton-like excitations in a one-dimensional attractive Fermi gas using the exactly solvable Yang-Gaudin model, revealing their properties and mass ratios across interaction regimes, with implications for experiments.

Contribution

It provides an exact analysis of yrast states in the Yang-Gaudin model, characterizing soliton-like excitations and their mass ratios, contrasting with mean-field predictions.

Findings

Mass ratio is unity in strong and weak attraction limits.

Mass ratio drops to approximately 0.78 in the crossover regime.

Results suggest dark-soliton-like excitations exist in related super Tonks-Girardeau gases.

Abstract

Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly-interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin-$\frac{1}{2}$ Fermi gas with attractive delta-function interactions in one dimension with the exactly solvable Yang-Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to $\approx 0.78$ in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks-Girardeau gas. The prospects for experimental observations are briefly discussed.