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 ex that is analogous to the single-orbital case. Moreover we demonstrate that also the additional biquadratic exchange interaction B 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. Contents arXiv:1803.03796v2 [cond-mat.str-el] 1 Feb 2019 SciPost Physics Submission A Projection operators 19 B Effective Hamiltonian 20 C Spin-one and pseudo spin-one operators 22 D Derivation of the effective spin-one Hamiltonian 23 E Effective Hamiltonian with Spin-Charge coupling 27 References 28
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