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Due to interest in both solid state based quantum computing architectures andthe application of quantum mechanical systems to nanomagnetometry, there hasbeen considerable recent attention focused on understanding the microscopicdynamics of solid state spin baths and their effects on the coherence of acontrollable, coupled central electronic spin. Many analytic approaches arebased on simplified phenomenological models in which it is difficult to capturemuch of the complex physics associated with this system. Conversely, numericalapproaches reproduce this complex behaviour, but are limited in the amount oftheoretical insight they can provide. Using a systematic approach based on thespatial statistics of spin bath constituents, we develop a purely analytictheory for the central spin decoherence problem of Nitrogen Vacancy centres indiamond that reproduces the experimental and numerical results found in theliterature, whilst correcting a number of limitations and inaccuraciesassociated with existing analytical approaches.

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