  We study the role of periodically driven time-dependent Rashba spin-orbit
coupling (RSOC) on a monolayer graphene sample. After recasting the originally
$4\times 4$ system of dynamical equations as two time-reversal related
two-level problems, the quasi-energy spectrum and the related dynamics are
investigated via various techniques and approximations. In the static case the
system is a gapped at the Dirac point. The rotating wave approximation (RWA)
applied to the driven system unphysically preserves this feature, while the
Magnus-Floquet approach as well as a numerically exact evaluation of the
Floquet equation show that this gap is dynamically closed. In addition, a
sizable oscillating pattern of the out-of-plane spin polarization is found in
the driven case for states which completely unpolarized in the static limit.
Evaluation of the autocorrelation function shows that the original uniform
interference pattern corresponding to time-independent RSOC gets distorted. The
resulting structure can be qualitatively explained as a consequence of the
transitions induced by the ac driving among the static eigenstates, i.e., these
transitions modulate the relative phases that add up to give the quantum
revivals of the autocorrelation function. Contrary to the static case, in the
driven scenario, quantum revivals (suppresions) are correlated to spin up
(down) phases.
