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 O(gtT)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(gt \, T)$$\end{document}. Our approach relies on the concept of Kato stability and general theory on non-autonomous linear evolution equations.