Cavity QED simulation of qubit-oscillator dynamics in the ultrastrong coupling regime

We propose a quantum simulation of a two-level atom coupled to a single mode of the electromagnetic field in the ultrastrong-coupling regime based upon resonant Raman transitions in an atom interacting with a high finesse optical cavity mode. We show by numerical simulation the possibility of realizing the scheme with a single rubidium atom, in which two hyperfine ground states make up the effective two-level system, and for cavity QED parameters that should be achievable with, for example, microtoroidal whispering-gallery-mode resonators. Our system also enables simulation of a generalized model in which a nonlinear coupling between the atomic inversion and the cavity photon number occurs on an equal footing with the (ultrastrong) dipole coupling and can give rise to critical-type behavior even at the single-atom level. Our model takes account of dissipation, and we pay particular attention to observables that would be readily observable in the output from the system.