Spin-orbit coupling and operation of multivalley spin qubits

Spin qubits composed of either one or three electrons are realized in a quantum dot formed at a Si/SiO₂ interface in isotopically enriched silicon. Using pulsed electron-spin resonance, we perform coherent control of both types of qubits, addressing them via an electric field dependent g factor. We perform randomized benchmarking and find that both qubits can be operated with high fidelity. Surprisingly, we find that the g factors of the one-electron and three-electron qubits have an approximately linear but opposite dependence as a function of the applied dc electric field. We develop a theory to explain this g-factor behavior based on the spin-valley coupling that results from the sharp interface. The outer ``shell'' electron in the three-electron qubit exists in the higher of the two available conduction-band valley states, in contrast with the one-electron case, where the electron is in the lower valley. We formulate a modified effective mass theory and propose that intervalley spin-flip tunneling dominates over intravalley spin flips in this system, leading to a direct correlation between the spin-orbit coupling parameters and the g factors in the two valleys. In addition to offering all-electrical tuning for single-qubit gates, the g-factor physics revealed here for one-electron and three-electron qubits offers potential opportunities for different qubit control approaches.