Suppression of Decoherence by Periodic Forcing

We consider a finite-dimensional quantum system coupled to a thermal reservoir and subject to a time-periodic, energy conserving forcing. We show that, if a certain dynamical decoupling condition is fulfilled, then the periodic forcing counteracts the decoherence induced by the reservoir: for small system-reservoir coupling $\lambda$ and small forcing period $T$, the system dynamics is approximated by an energy conserving and non-dissipative dynamics, which preserves coherences. For times up to order $(\lambda T)^{-1}$, the difference between the true and approximated dynamics is of size $\lambda +T$. Our approach is rigorous and combines Floquet and spectral deformation theory. We illustrate our results on the spin-fermion model and recover previously known, heuristically obtained results.