Intense-field-stimulated multiphoton transitions in a two-level system

We study the interaction of an intense classical field with a two-level system coupled to a bosonic quantized field. We focus on the regime where the classical field and the two-level system characteristic frequencies are the same, while the quantized mode is set off resonance with both. We show that a parameter governing the dynamics of the system is the ratio between the classical field's intensity and the quantized mode detuning. Depending on this parameter, multiple excitations can be created in the quantized mode in a single cycle of the two-level system. Examples of physical setups allowing for the application of the presented ideas are superconducting circuits in strip-line resonators, laser cooled trapped ions, and neutral atoms coupled to the quantized field of a cavity. We focus on the latter in order to show that, with realistic experimental parameters, it is possible to generate up to four photons in a single Rabi cycle.