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In order to have a better understanding of ultrafast electrical control ofexchange interactions in multi-orbital systems, we study a two-orbital Hubbardmodel at half filling under the action of a time-periodic electric field. Usingsuitable projection operators and a generalized time-dependent canonicaltransformation, we derive an effective Hamiltonian which describes twodifferent regimes. First, for a wide range of non-resonant frequencies, we finda change of the bilinear Heisenberg exchange $J_{\textrm{ex}}$ that isanalogous to the single-orbital case. Moreover we demonstrate that also theadditional biquadratic exchange interaction $B_{\textrm{ex}}$ can be enhanced,reduced and even change sign depending on the electric field. Second, forspecial driving frequencies, we demonstrate a novel spin-charge couplingphenomenon enabling coherent transfer between spin and charge degrees offreedom of doubly ionized states. These results are confirmed by an exacttime-evolution of the full two-orbital Mott-Hubbard Hamiltonian.

Optical control of competing exchange interactions and coherent spin-charge coupling in two-orbital Mott insulators