Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases

TL;DR

This paper reviews quantum dark solitons in ultracold one-dimensional Bose and Fermi gases, focusing on their relation to exact many-body eigenstates called yrast states, using Bethe ansatz solutions.

Contribution

It provides a comprehensive overview of quantum dark solitons in 1D Bose and Fermi gases and links them to exact yrast states via Bethe ansatz.

Findings

Quantum dark solitons correspond to yrast states in Lieb-Liniger and Yang-Gaudin models.

Exact solutions reveal the quantum nature of solitonic excitations.

The study bridges classical soliton concepts with quantum many-body physics.

Abstract

Solitons are ubiquitous phenomena that appear, among others, in the description of tsunami waves, fiber-optic communication and ultracold atomic gases. The latter systems turned out to be an excellent playground for investigations of matter-wave solitons in a quantum world. This Tutorial provides a general overview of the ultracold contact interacting Bose and Fermi systems in a one-dimensional space that can be described by the renowned Lieb-Liniger and Yang-Gaudin models. Both the quantum many-body systems are exactly solvable by means of the Bethe ansatz technique, granting us a possibility for investigations of quantum nature of solitonic excitations. We discuss in details a specific class of quantum many-body excited eigenstates called yrast states and show that they are strictly related to quantum dark solitons in the both considered Bose and Fermi systems.