Open quantum systems -- A brief introduction

TL;DR

This paper provides a concise overview of driven-dissipative many-body open quantum systems, emphasizing the Lindblad master equation's role in modeling and understanding their complex, out-of-equilibrium phenomena, especially in bosonic and spin systems.

Contribution

It offers a brief, focused introduction to the physics of open quantum systems, highlighting their significance in quantum hardware and the challenges of their theoretical description.

Findings

Emphasizes the importance of Lindblad master equation in modeling open quantum systems.

Discusses the exotic phenomena arising from non-equilibrium conditions.

Highlights the relevance of dissipative phenomena in quantum hardware platforms.

Abstract

This text is a short introduction to the physics of driven-dissipative many-body systems, focusing on a few selected topics. Beyond its more ``historical'' interest in the study of atomic physics and quantum optics, presently the modeling and studying dissipative phenomena in open quantum systems is pivotal to understanding quantum hardware platforms. While the lack of a thermodynamic potential for these out-of-equilibrium open systems makes it theoretically challenging to investigate their physics, at the same time it allows going beyond the thermodynamic paradigms and investigating new and exotic phenomena. We will focus on one of the simplest, yet most effective, descriptions of open quantum systems, namely the (Gorini-Kossakowski-Sudarshan-) Lindblad master equation. This phenomenological approach describes quantum systems that weakly interact with their surrounding environment. Although many of the results derived below will apply to any quantum system, we will focus in particular on bosonic/spin systems.