  We propose the effective simulation of light-matter ultrastrong-coupling
phenomena with strong-coupling systems. Recent theory and experiments have
shown that the quantum Rabi Hamiltonian can be simulated by a Jaynes--Cummings
system with the addition of two classical drives. This allows to implement
nonlinear processes that do not conserve the total number of excitations.
However, parity is still a conserved quantity in the quantum Rabi Hamiltonian,
which forbids a wide family of processes involving virtual transitions that
break this conservation. Here, we show that these parity-non-conserving
processes can be simulated, and that this can be done in an even simpler setup:
a Jaynes-Cummings type system with the addition of a single classical drive. By
shifting the paradigm from simulating a particular model to simulating a
particular process, we are able to implement a much wider family of nonlinear
coherent protocols than in previous simulation approaches, doing so with fewer
resources and constraints. We focus our analysis on three particular examples:
a single atom exciting two photons, frequency conversion, and a single photon
exciting two atoms.
