============

The interaction between a two-level system and a harmonic oscillator is ubiquitous in modern physics. This universality allows us to extrapolate ideas and techniques across different physical backgrounds which—appealing to the developed intuition—may appear more natural on one field over another. In a quantum optical context, the harmonic oscillator and the two-level system compose the quintessential model for the quantum theory of radiation and its interaction with matter, with the former modelling a single electromagnetic field mode and the latter describing two discrete energy levels of a material system. The dynamics of the coupled system are described up to a very good approximation by the Jaynes–Cummings (JC) model if the coupling is dipolar in character and the rotating wave approximation is valid [@Jaynes_1963]. While deceptively simple, these dynamics allow for deep physical insight and conceptual understanding of quantum concepts, as exemplified in the experimental demonstration of the discrete nature of the electromagnetic field [@Meekhof_1996; @Brune_1996; @Hofheinz_2008].

The operational simplicity of the model seems to translate to the driven Jaynes–Cummings model. The driven JC model describes a two-level system interacting with a field mode that is being driven out of the ground state by an external coherent field. When the 