Free induction decay of single spins in diamond

We study, both theoretically and experimentally, the free induction decay (FID) of the electron spin associated with a single nitrogen-vacancy defect in high-purity diamond, where the main source of decoherence is the hyperfine interaction with a bath of C-13 nuclear spins. In particular, we report a systematic study of the FID signal as a function of the strength of a magnetic field oriented along the symmetry axis of the defect. On average, an increment of the coherence time by a factor of root 5/2 is observed at high magnetic field in diamond samples with a natural abundance of C-13 nuclear spins, in agreement with numerical simulations and theoretical studies. Further theoretical analysis shows that this enhancement is independent of the concentration of nuclear-spin impurities. By dividing the nuclear-spin bath into shells and cones, we theoretically identify the nuclear spins responsible for the observed dynamics.