  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
cavity-QED setups. We provide examples of USC/DSC quantum effects that would be
otherwise unaccessible.
