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 (13)C 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 (13)C nuclear spins are compared and analyzed. Reduction in a free-induction- decay time T(2)* and a coherence time T(2) upon increase in nuclear spin concentration has been found. For pure diamond, T(2)* as long as 30 mu s and T(2) of up to 0.65 ms for the electron spin has been observed. The (13)C concentration dependence of T(2)* is explained by Fermi contact and dipolar interactions with nuclei in the lattice. It has been found that T(2) decreases approximately as 1/n, where n is (13)C concentration, which corresponds to the reported theoretical line of T(2) for an electron spin interacting with a nuclear spin bath.