Universal control of superexchange in linear triple quantum dots with an empty mediator

Superexchange is one of the vital resources to realize long-range interaction between distant spins for large-scale quantum computing. Recent experiments have demonstrated coherent oscillations logical states defined by remote whose coupling given superexchange mediated central spins. Excavating potential requires a full understanding in terms control parameters, which still lacking literature. Here, using configuration calculations, we study two-electron system linear triple-quantum-dot device left and right dots are occupied single electron each, spin as qubits. The numerical nature calculations allows access microscopic details quantum-dot confining electronic wave functions, some overlooked celebrated Hubbard model but turn out be critical behavior superexchange. Following experimental demonstrations interactions, focus on detuning regime where charge ground state yields an empty middle dot. We found that, when detunings at leveled, can exhibit nonmonotonic behavior, ranges from positive negative values function middle-dot detuning. further show that larger relative causes magnitude increase (decrease) originally (negative) then proceed results much left-right dot Using Hubbard-like model, present analytical expressions they conform well qualitatively with results. Our suggest even simple delocalized exhibits energy nontrivial behaviors, could important applications spin-based