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The understanding of weak measurements and interaction-free measurements hasgreatly expanded the conceptual and experimental toolbox to explore the quantumworld. Here we demonstrate single-shot variable-strength weak measurements ofthe electron and the nuclear spin states of a single $^{31}$P donor in silicon.We first show how the partial collapse of the nuclear spin due to measurementcan be used to coherently rotate the spin to a desired pure state. Weexplicitly demonstrate that phase coherence is preserved throughout multiplesequential single-shot weak measurements, and that the partial state collapsecan be reversed. Second, we use the relation between measurement strength andperturbation of the nuclear state as a physical meter to extract the tunnelingrates between the $^{31}$P donor and a nearby electron reservoir from data,conditioned on observing no tunneling events. Our experiments open avenues tomeasurement-based state preparation, steering and feedback protocols for spinsystems in the solid state, and highlight the fundamental connection betweeninformation gain and state modification in quantum mechanics.

Coherent control via weak measurements in $^{31}$P single-atom electron and nuclear spin qubits