Open quantum systems

A brief introduction

¹ Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
² Pitaevskii BEC Center, CNR-INO and Dipartimento di Fisica, Università di Trento, I-38123 Trento, Italy
³ INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy

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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 of dissipative phenomena in open quantum systems are pivotal to understanding quantum hardware platforms. Although 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 one to go beyond the thermodynamic paradigms and investigate new and exotic phenomena. We will focus on one of the simplest, yet most effective, descrip-tions of open quantum systems, namely the (Gorini-Kossakowski-Sudarshan-) Lindblad master equation. This phenomenological approach has been devel-oped to describe quantum systems that weakly interact (Born approximation) with a memoryless (Markovian) surrounding environment. However, it is often a remarkably simple and predictive tool to characterize the essential features of an open quantum system. Although many of the results derived below will ap-ply to any quantum system, we will focus in particular on bosonic/spin systems.