Analog quantum simulation of the Rabi model in the ultra-strong coupling   regime
  The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation (RWA). The RWA breaks down in the ultra-strong coupling (USC) regime, where the effective coupling strength $g$ is comparable to the energy $\omega$ of the bosonic mode, and remarkable features in the system dynamics are revealed. We demonstrate an analog quantum simulation of an effective quantum Rabi model in the USC regime, achieving a relative coupling ratio of $g/\omega \sim 0.6$. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model. 
Jochen Braum\"uller, Michael Marthaler, Andre Schneider, Alexander   Stehli, Hannes Rotzinger, Martin Weides, Alexey V. Ustinov
quant-ph