Coherence of single spins coupled to a nuclear spin bath of varying density

The dynamics of single electron and nuclear spins in a diamond lattice with different ¹³C nuclear spin concentration is investigated. It is shown that coherent control of up to three individual nuclei in a dense nuclear spin cluster is feasible. The free-induction decays of nuclear spin Bell states and single nuclear coherences among ¹³C nuclear spins are compared and analyzed. Reduction in a free-induction-decay time T₂^ and a coherence time T₂ upon increase in nuclear spin concentration has been found. For pure diamond, T₂^ as long as 30 μs and T₂ of up to 0.65 ms for the electron spin has been observed. The ¹³C concentration dependence of T₂^ is explained by Fermi contact and dipolar interactions with nuclei in the lattice. It has been found that T₂ decreases approximately as $1/n$, where n is ¹³C concentration, which corresponds to the reported theoretical line of T₂ for an electron spin interacting with a nuclear spin bath.