We theoretically investigate photoinduced phenomena induced by time-periodic driving fields in two-dimensional electron gases under perpendicular magnetic fields with Rashba spin-orbit coupling. Using perturbation theory, we provide analytical results for the Floquet-Landau energy spectrum appearing due to THz radiation. By employing the resulting photo-modulated states, we compute the dynamical evolution of the spin polarization function for an initially prepared coherent state. We find that the interplay of the magnetic field, Rashba spin-orbit interaction and THz radiation can lead to inversion of the spin polarization. The dynamics also induces fractional revivals and non-trivial beating patterns in the autocorrelation function due to interference of the photo-modulated quantum states. We also calculate the transverse photo-assisted conductivity in the linear response regime using Kubo formalism and analyze the impact of the radiation field and Rashba spin-orbit interaction. In the static limit, we find that our results reduce to well-known expressions of the conductivity in non-relativistic and quasi-relativistic (topological insulator surfaces) two-dimensional electron gas thoroughly described in the literature. We discuss the possible experimental detection of our theoretical prediction and their relevance for spin-orbit physics at high magnetic fields.
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