  In order to have a better understanding of ultrafast electrical control of
exchange interactions in multi-orbital systems, we study a two-orbital Hubbard
model at half filling under the action of a time-periodic electric field. Using
suitable projection operators and a generalized time-dependent canonical
transformation, we derive an effective Hamiltonian which describes two
different regimes. First, for a wide range of non-resonant frequencies, we find
a change of the bilinear Heisenberg exchange $J_{\textrm{ex}}$ that is
analogous to the single-orbital case. Moreover we demonstrate that also the
additional biquadratic exchange interaction $B_{\textrm{ex}}$ can be enhanced,
reduced and even change sign depending on the electric field. Second, for
special driving frequencies, we demonstrate a novel spin-charge coupling
phenomenon enabling coherent transfer between spin and charge degrees of
freedom of doubly ionized states. These results are confirmed by an exact
time-evolution of the full two-orbital Mott-Hubbard Hamiltonian.
