Phenomenological Study of Decoherence in Solid-State Spin Qubits due to Nuclear Spin Diffusion

TL;DR

This paper investigates how nuclear spin diffusion affects coherence in solid-state spin qubits and evaluates dynamical decoupling protocols through simulations based on experimentally validated noise models.

Contribution

It introduces a phenomenological noise model for nuclear spin diffusion and validates it against experimental data, providing insights into coherence preservation strategies.

Findings

Reproduces experimental coherence decay using a 1/ω² noise spectrum

Identifies key factors affecting qubit coherence, such as nuclear programming and high-frequency noise

Provides bounds and metrics for improving qubit coherence in solid-state systems

Abstract

We present a study of the prospects for coherence preservation in solid-state spin qubits using dynamical decoupling protocols. Recent experiments have provided the first demonstrations of multipulse dynamical decoupling sequences in this qubit system, but quantitative analyses of potential coherence improvements have been hampered by a lack of concrete knowledge of the relevant noise processes. We present simulations of qubit coherence under the application of arbitrary dynamical decoupling pulse sequences based on an experimentally validated semiclassical model. This phenomenological approach bundles the details of underlying noise processes into a single experimentally relevant noise power spectral density. Our results show that the dominant features of experimental measurements in a two-electron singlet-triplet spin qubit can be replicated using a $1/\omega^{2}$ noise power spectrum associated with nuclear-spin-flips in the host material. Beginning with this validation we address the effects of nuclear programming, high-frequency nuclear-spin dynamics, and other high-frequency classical noise sources, with conjectures supported by physical arguments and microscopic calculations where relevant. Our results provide expected performance bounds and identify diagnostic metrics that can be measured experimentally in order to better elucidate the underlying nuclear spin dynamics.