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

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.

Automated summary

The tutorial discusses the application of solitons in the quantum world and introduces the Lieb-Liniger and Yang-Gaudin models in ultracold Bose and Fermi systems. These models are exactly solvable using the Bethe ansatz technique, aiding in the exploration of the quantum nature of solitonic excitations.