S. Maniscalco

We present an in-depth study of the non-equilibrium statistics of the irreversible work produced during sudden quenches in proximity to the structural linear-zigzag transition of ion Coulomb crystals in 1+1 dimensions. By employing both an analytical approach based on a harmonic expansion and numerical simulations, we show the divergence of the average irreversible work in proximity to the transition. We show that the non-analytic behaviour of the work fluctuations can be characterized in terms of the critical exponents of the quantum Ising chain. Due to the technological advancements in trapped ion experiments, our results can be readily verified.

We study the open system dynamics of a harmonic oscillator coupled with an artificially engineered reservoir. We single out the reservoir and system variables governing the passage between Lindblad type and non-Lindblad type dynamics of the reduced system's oscillator. We demonstrate the existence of conditions under which virtual exchanges of energy between system and reservoir take place. We propose to use a single trapped ion coupled to engineered reservoirs in order to simulate quantum Brownian motion.

The spectacular experimental results of the last few years in cavity quantum electrodynamics and trapped ions research has led to very high level laboratory performances. Such a stimulating situation essentially stems from two decisive advancements. The first is the invention of reliable protocols for the manipulation of single atoms. The second is the ability to produce desired bosonic environments on demand. These progresses have led to the possibility of controlling the form of the coupling between individual atoms and an arbitrary number of bosonic modes. As a consequence, fundamental matter-radiation interaction models like, for instance, the JC model and most of its numerous nonlinear multiphoton generalizations, have been realized or simulated in laboratory and their dynamical features have been tested more or less in detail. This topical paper reviews the state of the art of the theoretical investigations and of the experimental observations concerning the dynamical features of the coupling between single few-level atoms and two bosonic modes. In the course of the paper we show that such a configuration provides an excellent platform for investigating various quantum intermode correlation effects tested or testable in the cavity quantum electrodynamics and trapped ion experimental realms. In particular we discuss a mode-mode correlation effect appearing in the dynamics of a two-level atom quadratically coupled to two bosonic modes. This effect, named parity effect, consists in a high sensitivity to the evenness or oddness of the total number of bosonic excitations.

The heating of trapped ions due to the interaction with a {\it quantized environment} is studied {\it without performing the Born-Markov approximation}. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method.

We study the entanglement between the 2D vibrational motion and two ground state hyperfine levels of a trapped ion, Under particular conditions this entanglement depends on the parity of the total initial vibrational quanta. We study the robustness of this quantum coherence effect with respect to the presence of non-dissipative sources of decoherence, and of an imperfect initial state preparation.