Hyperfine Dependence of Nuclear-Spin Rabi Frequencies in Silicon Donors

Nuclear-spin qubits in donor systems have emerged as promising platforms for quantum computing. Here, we demonstrate individual, high-fidelity coherent control of four phosphorus nuclear spins in a silicon donor cluster, where each nucleus is coupled to a central electron via a distinct hyperfine interaction. We investigate theoretically and experimentally how hyperfine interactions modulate nuclear Rabi frequencies under different electron-spin states. By calibrating the driving magnetic field using the ionized bare nucleus as an in situ atomic-scale sensor, we validate the theoretical model and find excellent agreement with the experiment. These results highlight the role of hyperfine interactions in nuclear-spin control and provide a new perspective for designing fast, high-fidelity, single-qubit gates in donor-based quantum processors.