Energy levels and decoherence properties of single electron and nuclear spins in a defect center in diamond

The coherent behavior of the single electron and single nuclear spins of a defect center in diamond and a ${}^{13}\mathrm{C}$ nucleus in its vicinity, respectively, are investigated. The energy levels associated with the hyperfine coupling of the electron spin of the defect center to the ${}^{13}\mathrm{C}$ nuclear spin are analyzed. Methods of magnetic resonance, together with the optical readout of single defect centers, have been applied in order to observe the coherent dynamics of the electron and nuclear spins. Long coherence times, in the order of microseconds for electron spins and tens of microseconds for nuclear spins, recommend the studied system as a good experimental approach for implementing a two-qubit gate.