Nuclear spin dynamics and Zeno effect in quantum dots and defect centers

TL;DR

This paper investigates nuclear spin dynamics in quantum dots and defect centers, demonstrating how the quantum Zeno effect can extend the Overhauser field lifetime and analyzing the long-term behavior of nuclear spin polarization under electron-mediated interactions.

Contribution

It provides a detailed analysis of the short- and long-time nuclear spin dynamics, highlighting the potential to control nuclear spin coherence via measurement protocols and elucidating the effects of electron-mediated interactions.

Findings

Short-time Overhauser field dynamics are quadratic in time.

Quantum Zeno effect can prolong the Overhauser field lifetime.

Long-term Overhauser field decay is limited to a small fraction.

Abstract

We analyze nuclear spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction ("J-coupling" in NMR). Our analysis shows that the Overhauser field generated by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson series expansion and a generalized master equation approach, that for a nuclear spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount on the order of the inverse number of nuclear spins interacting with the electron.