Phase-kicked control of counter-rotating interactions in the quantum Rabi model

We present an interaction scheme to control counter-rotating terms in the quantum Rabi model. We show that by applying a sequence of $\pi \mathrm{/}2$ phase kicks to a two-level atom and a single mode quantized field, the natural dynamics of the Rabi model can be interrupted in a way that counter-rotating transitions can be significantly enhanced. This is achieved by a suitable timing of the phase kicks determined by a phase matching condition. If the time between successive kicks is sufficiently short, our scheme is turned into a dynamical decoupling problem in which the effects of counter-rotating terms can be strongly suppressed under ultrastrong coupling.