  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.
