Abstract:Année de publication : 2019
My PhD was devoted to the study of driven-dissipative quantum many-body systems. These systems represent natural platforms to explore fundamental questions about matter under non-equilibrium conditions, having at the same time a potential impact on emerging quantum technologies. My goal was to investigate new physical phenomena determined by the interplay of interactions, dissipation and non-equilibrium conditions as well as to develop new techniques to study these systems. The outline of the thesis is the following. In chapter 1 we will introduce the research field, at the boundaries of condensed matter physics, quantum optics and quantum information. We will discuss my motivations to do research in this field as well as the main ideas behind it, or at least my point of view, and go through some recent theoretical and experimental developments. In chapter 2 we will introduce some theoretical techniques and concepts that will be useful in the rest of the thesis. Rather than entering in technical details, for which we will refer to books and papers, we will try to make connections between different techniques that are not often discussed in literature. In chapter 3 we will discuss the spectral properties of Markovian open quantum systems, looking in particular at a quantum van der Pol oscillator, in presence of an additional non-linear term in its Hamiltonian. This chapter is mostly based on . In chapter 4, we will study the phase transition between a normal and a superfluid phase in a prototype system of driven-dissipative bosons on a lattice, which is characterized by an instability of dynamical modes. This chapter is mostly based on . In chapter 5 we will discuss the phase boundary of a Mott insulating phase stabilized by dissipation, which is potentially relevant for undergoing experiments. The results of this chapter are preliminary and unpublished. Finally, in chapter 6 we will discuss some developments towards using the technique of dynamical mean field theory (DMFT) for studying driven-dissipative lattice systems. We will revisit and extend some well known techniques for impurity systems in the context of Markovian open systems, which are potentially useful both in the context of DMFT and to go beyond Markovian master equations into more complicated scenarios of non-Markovian dissipation. This chapter is mostly based on .