Quantum simulation of the ultrastrong coupling dynamics in circuit QED

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We propose a method to get experimental access to the physics of the ultrastrong (USC) and deep strong (DSC) coupling regimes of light-matter interaction through the quantum simulation of their dynamics in standard circuit QED. The method makes use of a two-tone driving scheme, using state-of-the-art circuit-QED technology, and can be easily extended to general quantum optical cavity-QED setups. We provide examples of USC/DSC quantum effects that would be otherwise unaccessible.