I will show how a trapped ion system can simulate both the Quantum Rabi Model (QRM) and the Two-Photon Quantum Rabi Model (TPQRM), in all relevant parameter regimes. These two paradigmatic models of light-matter interaction show a plethora of interesting physical phenomena, such as the collapse of the spectrum of the TPQRM for certain parameter regimes. Moreover, I will explain how one can measure the g(1) & g(2) coherence functions of the phononic degree of freedom of an ion string. These functions are central to the quantum theory of light, and its measurement in trapped ions would open the door to the simulation of quantum optical experiments with trapped ions. If time permits, I will briefly review other theoretical results in the line of trapped ions at the QUTIS research group in Bilbao, such as the novel digital-analog techniques for the simulation of spin models, and embedding quantum simulators for the measurement of entanglement of mixed states.
Ph. D student of Prof. Enrique Solano's group