Coherent control via weak measurements in P31 single-atom electron and nuclear spin qubits

The understanding of weak measurements and interaction-free measurements has greatly expanded the conceptual and experimental toolbox to explore the quantum world. Here we demonstrate single-shot variable-strength weak measurements of the electron and nuclear spin states of a ${}^{31}\mathrm{P}$ single-atom donor in silicon. We first show how the partial collapse of the nuclear spin due to measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved with high fidelity throughout multiple sequential single-shot weak measurements and that the partial state collapse can be reversed. Second, we use the relation between measurement strength and perturbation of the nuclear state as a physical meter to extract the tunnel rates between the ${}^{31}\mathrm{P}$ donor and a nearby electron reservoir from data conditioned on observing no tunneling events. Our experiments open avenues to measurement-based state preparation, steering and feedback protocols for spin systems in the solid state, and highlight the fundamental connection between information gain and state modification in quantum mechanics.