Julen S. Pedernales

The quantum Rabi model, involving a two-level system and a bosonic field mode, is arguably the simplest and most fundamental model describing quantum light-matter interactions. Historically, due to the restricted parameter regimes of natural light-matter processes, the richness of this model has been elusive in the lab. Here, we experimentally realize a quantum simulation of the quantum Rabi model in a single trapped ion, where the coupling strength between the simulated light mode and atom can be tuned at will. The versatility of the demonstrated quantum simulator enables us to experimentally explore the quantum Rabi model in detail, including a wide range of otherwise unaccessible phenomena, as those happening in the ultrastrong and deep strong coupling regimes. In this sense, we are able to adiabatically generate the ground state of the quantum Rabi model in the deep strong coupling regime, where we are able to detect the nontrivial entanglement between the bosonic field mode and the two-level system. Moreover, we observe the breakdown of the rotating-wave approximation when the coupling strength is increased, and the generation of phonon wave packets that bounce back and forth when the coupling reaches the deep strong coupling regime. Finally, we also measure the energy spectrum of the quantum Rabi model in the ultrastrong coupling regime.

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a sideband cooling blockade, stopping the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We compare the linear and nonlinear cases of these models in the ultrastrong and deep strong coupling regimes. Moreover, we propose a scheme that simulates the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red and blue sideband interactions, yielding applications as a dynamical quantum filter.

This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations can be generated. We propose the use of an ancillary qubit to efficiently access both time-correlation functions and entanglement monotones, and we provide two experimental demonstrations of our methods, measuring time correlations in an NMR setup and entanglement monotones in a photonic system. Moreover, we explain how time-correlation functions could be exploited for the quantum simulation of open quantum dynamics, and we provide an experimental recipe for the measurement of entanglement monotones in trapped ion technologies. On the other hand, we explore the quantum simulation of quantum optical models of light-matter interaction for inaccessible coupling regimes, providing experimental proposals for their implementation, both in ions and superconducting circuits. Finally, we also provide an experimental proposal for the quantum simulation of spin models in trapped ions following a digital-analog simulation scheme.

Quantum field theories describe a wide variety of fundamental phenomena in physics. However, their study often involves cumbersome numerical simulations. Quantum simulators, on the other hand, may outperform classical computational capacities due to their potential scalability. Here, we report an experimental realization of a quantum simulation of fermion-antifermion scattering mediated by bosonic modes, using a multilevel trapped ion, which is a simplified model of fermion scattering in both perturbative and nonperturbative quantum electrodynamics. The simulated model exhibits prototypical features in quantum field theory including particle pair creation and annihilation, as well as self-energy interactions. These are experimentally observed by manipulating four internal levels of a $^{171}\mathrm{Yb}^{+}$ trapped ion, where we encode the fermionic modes, and two motional degrees of freedom that simulate the bosonic modes. Our experiment establishes an avenue towards the efficient implementation of fermionic and bosonic quantum field modes, which may prove useful in scalable studies of quantum field theories in perturbative and nonperturbative regimes.