(color online) Nitrogen–vacancy (NV) centers in diamond. (a) An NV center is formed by a substitutional nitrogen atom and an adjacent vacancy in the diamond lattice. (b) The energy levels and optical transitions of the NV electron spin. The spin states can be polarized with green laser and readout by fluorescence intensity. (c) Ground states of an NV center under an external magnetic field . The degeneration of states are lifted by Zeeman effect. The hyperfine interaction with surrounding ¹³C nuclear spins brings an inhomogeneous broadening. (d) Typical optical detected magnetic resonance (ODMR) spectrum of an NV center. The strength of the external magnetic field can be extract from the resonant positions of the ODMR spectrum.