  Adiabatically varying the driving frequency of a periodically-driven
many-body quantum system can induce controlled transitions between resonant
eigenstates of the time-averaged Hamiltonian, corresponding to adiabatic
transitions in the Floquet spectrum and presenting a general tool in quantum
many-body control. Using the central spin model as an application, we show how
such controlled driving processes can lead to a polarization-based decoupling
of the central spin from its decoherence-inducing environment at resonance.
While it is generally impossible to obtain the exact Floquet Hamiltonian in
driven interacting systems, we exploit the integrability of the central spin
model to show how techniques from quantum quenches can be used to explicitly
construct the Floquet Hamiltonian in a restricted many-body basis and model
Floquet resonances.
