Analytic solutions to the central spin problem for Nitrogen Vacancy centres in diamond

TL;DR

This paper develops an analytic theory for the decoherence of Nitrogen Vacancy centers in diamond, improving understanding of spin bath dynamics relevant for quantum computing and nanomagnetometry.

Contribution

It introduces a systematic, purely analytic approach based on spatial statistics, addressing limitations of previous models and aligning with experimental and numerical results.

Findings

Reproduces experimental and numerical decoherence results

Corrects inaccuracies in previous analytical models

Provides deeper theoretical insight into spin bath dynamics

Abstract

Due to interest in both solid state based quantum computing architectures and the application of quantum mechanical systems to nanomagnetometry, there has been considerable recent attention focused on understanding the microscopic dynamics of solid state spin baths and their effects on the coherence of a controllable, coupled central electronic spin. Many analytic approaches are based on simplified phenomenological models in which it is difficult to capture much of the complex physics associated with this system. Conversely, numerical approaches reproduce this complex behaviour, but are limited in the amount of theoretical insight they can provide. Using a systematic approach based on the spatial statistics of spin bath constituents, we develop a purely analytic theory for the central spin decoherence problem of Nitrogen Vacancy centres in diamond that reproduces the experimental and numerical results found in the literature, whilst correcting a number of limitations and inaccuracies associated with existing analytical approaches.