Quantum Simulation of Non-Perturbative Cavity QED with Trapped Ions

Abstract

The simulation of non-perturbative cavity-QED effects is discussed using systems of trapped ions. Specifically, the implementation of extended Dicke models with both collective dipole-field and direct dipole–dipole interactions is addressed, which represent a minimal set of models for describing light–matter interactions in the ultrastrong and deep-strong coupling regime. It is shown that this approach can be used in state-of-the-art trapped ion setups to investigate excitation spectra or the transition between sub- and superradiant ground states, which are currently not accessible in any other physical system. The analysis also reveals the intrinsic difficulty of accessing this non-perturbative regime with larger numbers of dipoles, which makes the simulation of many-dipole cavity QED a particularly challenging test case for future quantum simulation platforms.