NONLINEAR QUANTUM OPTICS AND THERMODYNAMICS WITH THREE TRAPPED IONS

Abstract

Harmonic oscillators coupled via nonlinear interactions is a fundamental model in several branches of physics. Trapped ions are particularly attractive for the implementation of such models because their normal modes of motion form a set of harmonic oscillators, and the nonlinear coupling between these modes naturally arises due to mutual (anharmonic) Coulomb interaction. In this thesis I present experimental implementation of the trilinear Hamiltonian that couples three normal modes of motion in a system of three trapped 171Yb+ ions. I characterize the experimental realization of such interaction and show simulations of several physical systems of current relevance in their fields: the Jaynes-Cummings model, which describes the coupling of an optical mode in a cavity with a two-level atom; a model of Hawking radiation of evaporative black holes; and also describe the progress towards the absorption refrigerator in the quantum regime, studying its performance and effects due to coherence.