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

## TL;DR

This paper demonstrates controlled weak measurements on single-atom electron and nuclear spins in silicon, enabling state manipulation, coherence preservation, and measurement-based quantum control techniques.

## Contribution

It introduces a method for single-shot variable-strength weak measurements on $^{31}$P spins, showing coherence preservation and state reversibility, advancing quantum measurement and control in solid-state systems.

## Key findings

- Partial nuclear spin collapse can be used for coherent state rotation
- Phase coherence is maintained through sequential weak measurements
- Measurement strength relates to tunneling rate estimation

## Abstract

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 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 measurement can be used to coherently rotate the spin to a desired pure state. We explicitly demonstrate that phase coherence is preserved 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 tunneling rates between the $^{31}$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.