Suppression of Decoherence of a Spin-Boson System by Time-Periodic Control

We consider a finite-dimensional quantum system coupled to the bosonic radiation field and subject to a time-periodic control operator. Assuming the validity of a certain dynamic decoupling condition we approximate the system's time evolution with respect to the non-interacting dynamics. For sufficiently small coupling constants $g$ and control periods $T$ we show that a certain deviation of coupled and uncoupled propagator may be estimated by $\mathcal{O}(gt \, T)$. Our approach relies on the concept of Kato stability and general theory on non-autonomous linear evolution equations.