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

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.

6 pages main text + 3 pages supplementary

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• Quantum walks: the first detected transition time
• Beating the thermal limit of qubit initialization with a Bayesian Maxwell's demon
• Spin rotation by resonant electric field in few-level quantum dots: Floquet dynamics and tunneling
• Relationship between subjecting the qubit to dynamical decoupling and to a sequence of projective measurements
• Fast high-fidelity single-qubit gates for flip-flop qubits in silicon
• Balancing coherent and dissipative dynamics in a central-spin system
• Characterization of a quasi-static environment with a qubit
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• Hyperfine-assisted decoherence of a phosphorus nuclear-spin qubit in silicon
• Lyapunov-Based Stabilization and Control of the Stochastic Schrodinger Equation
• Compared study of Shannon, Tsallis and Gaussian entropy of bound magnetopolaron in nanostructures
• Maximizing the nondemolition nature of a quantum measurement via an adaptive readout protocol