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The quantum Rabi model, involving a two-level system and a bosonic fieldmode, is arguably the simplest and most fundamental model describing quantumlight-matter interactions. Historically, due to the restricted parameterregimes of natural light-matter processes, the richness of this model has beenelusive in the lab. Here, we experimentally realize a quantum simulation of thequantum Rabi model in a single trapped ion, where the coupling strength betweenthe simulated light mode and atom can be tuned at will. The versatility of thedemonstrated quantum simulator enables us to experimentally explore the quantumRabi model in detail, including a wide range of otherwise unaccessiblephenomena, as those happening in the ultrastrong and deep strong couplingregimes. In this sense, we are able to adiabatically generate the ground stateof the quantum Rabi model in the deep strong coupling regime, where we are ableto detect the nontrivial entanglement between the bosonic field mode and thetwo-level system. Moreover, we observe the breakdown of the rotating-waveapproximation when the coupling strength is increased, and the generation ofphonon wave packets that bounce back and forth when the coupling reaches thedeep strong coupling regime. Finally, we also measure the energy spectrum ofthe quantum Rabi model in the ultrastrong coupling regime.

Quantum simulation of the quantum Rabi model in a trapped ion