The classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

TL;DR

This study investigates whether nuclear spin noise near clock transitions of Bi donors in silicon can be effectively modeled as classical Gaussian noise, demonstrating that classical approximation is valid when qubit back-action on the bath is minimal.

Contribution

The paper develops and experimentally validates a Gaussian noise model for nuclear spin baths near clock transitions, clarifying when classical noise models are appropriate in quantum decoherence.

Findings

Classical Gaussian noise models agree well with quantum calculations near clock transitions.

Quantum back-action becomes significant far from clock transitions, requiring quantum models.

Electron spin coherence times approach one second in natural silicon samples.

Abstract

Whether a quantum bath can be approximated as classical noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock-transitions (CTs). This system is therefore ideal for studying the quantum/classical nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a classical noise model. We develop a Gaussian noise model with noise correlations determined by quantum calculations and compare the classical noise approximation to the full quantum bath theory. We experimentally test our model through dynamical decoupling sequence of up to 128 pulses, finding good agreement with simulations and measuring electron spin coherence times approaching one second - notably using natural silicon. Our theoretical and experimental study demonstrates that the noise from a nuclear spin bath is analogous to classical Gaussian noise if the back-action of the qubit on the bath is small compared to the internal bath dynamics, as is the case close to CTs. However, far from the CTs, the back-action of the central spin on the bath is such that the quantum model is required to accurately model spin decoherence.