Open Hybrid Quantum Systems in the Ultra-Strong Coupling Regime

Quantum mechanics has always provided a conceptual framework for the description of microscopic phenomena and has been applied to explain properties and behaviour of a wide range of natural systems. In particular, the main developments have been achieved through the rst half of the twentieth century thanks to the understanding of the interaction of matter with electromagnetic elds. Several achievements in the understanding of these properties have been obtained treating the electromagnetic eld classically. However, in order to fully understand the light-matter interactions a full quantum theory is required. For example, quantum mechanics allowed to understand the transport and optical properties of materials. Nowadays, the eld studying these light-matter interactions using a fully quantum description for both light and matter is the so called Quantum Optics. This widespread eld is attracting great growing interest and is driving the second quantum revolution. Indeed, during the last several decades much efforts have been directed at exploiting the most puzzling effects of quantum mechanics, like, for example, the quantum superpositions and the entanglement, for the development of practical technologies.