Electron spin decoherence of single nitrogen-vacancy defects in diamond

We present a detailed theoretical analysis of the electron spin decoherence in single nitrogen-vacancy defects in ultrapure diamond. The electron spin decoherence is due to the interactions with ^13C nuclear spins in the diamond lattice. Our approach takes advantage of the low concentration (1. 1%) of ^13C nuclear spins and their random distribution in the diamond lattice by an algorithmic aggregation of spins into small, strongly interacting groups. By making use of this disjoint cluster approach, we demonstrate a possibility of nontrival dynamics of the electron spin that cannot be described by a single time constant. This dynamics is caused by a strong coupling between the electron and few nuclei and exhibits large variations depending on the distribution of ^13C nuclei surrounding each individual electronic spin. This results, in particular, in a substantial echo signal even at microsecond time scales. Our results are in good agreement with recent experimental observations.