Motivated by the observation of multiphoton electric dipole spin resonance processes in InAs nanowires, we theoretically study the transport dynamics of a periodically driven five-level system, modeling the level structure of a two-electron double quantum dot. We show that the observed multiphoton resonances, which are dominant near interdot charge transitions, are due to multilevel Landau-Zener-Stuckelberg-Majorana interference. Here a third energy level serves as a shuttle that transfers population between the two resonant spin states. By numerically integrating the master equation we replicate the main features observed in the experiments: multiphoton resonances (as large as 8 photons), a robust odd-even dependence, and oscillations in the electric dipole spin resonance signal as a function of energy level detuning.
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