Figure 4: Probing the spin–noise spectrum.

(a) Spin relaxation measurements for NV_A at three different external static magnetic fields B_ext. The NV centre is prepared in each of its three spin eigenstates (m_s=0, −1, +1), and the spin-dependent photoluminescence is measured as a function of waiting time t. We extract the m_s=0↔+1 and the m_s=0↔−1 relaxation rates by fitting with a three-level model. (b) Measured NV spin relaxation rates as a function of B_ext. As we lower B_ext, the m_s=0↔+1 and the m_s=0↔−1 relaxation rates consecutively increase by about an order of magnitude. Dots are measured data. Solid lines are fits based on a model of the magnetic noise spectrum at the site of the NV centre, from which we obtain d=35(5) nm. Error bars represent±1 standard deviation determined by the fit-uncertainty in the fitted relaxation rates. (c) Calculated magnetic noise spectrum at d=35 nm above an infinite magnetic plane as a function of external magnetic field B_ext. The increasing NV spin-state relaxation rates for decreasing B_ext observed in b are due to the increase in noise spectral density at the NV ESR frequencies, which are denoted by the yellow and white dashed line for the m_s=0↔+1 and m_s=0↔−1 transition, respectively.