Analytic solutions to the central-spin problem for nitrogen-vacancy centers in diamond

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. Using a systematic approach based on the spatial statistics of the spin-bath constituents, we develop a detailed, purely analytic theory for the central-spin decoherence problem of a nitrogen-vacancy center electron coupled to its native 1.1% bath of 13C nuclear spins. Our theory reproduces the experimental and numerical results found in the lit..