Fig. 2: Optical and spin dynamics of carbon-related hBN defects.

a Model used to fit the results of experiments in (b–d), including a spin-1 ground and optically excited states and a singlet metastable state. Optical excitation and radiative recombination processes are spin-conserving at zero magnetic field. b–d Blue circles correspond to the mean of measured data, light blue error bars indicate one standard deviation of the measured data, red curves correspond to a global fit of the model to the experimental data, and the grey shaded region corresponds to model predictions with  <3× the minimum fit error. The insets present the pulse protocols used in the measurements, with optical (green blocks) and microwave drive (red blocks) pulses and readout time (grey block). b (top) Background-corrected second-order autocorrelation (g⁽²⁾(t)). (bottom) Residuals of the fit of the model to the data. c Spin-dependent optical initialisation. Blue circles are the mean value of the contrast measured for various delay times τ_r. d Modified spin-relaxation experiment. The signal experiment probes the PL when we apply two microwave π pulses, before and after a delay time τ between the two optical pulses. The reference experiment probes the PL when a single microwave π pulse is applied at the end of τ. e Simulated ODMR contrast as a function of the spin-selectivity of the direct (\({k}_{{{{{\rm{E}}}}} \to {{{{\rm{S}}}}}_{{{{\rm{0}}}}}}\)) and reverse (\({k}_{{{{{\rm{S}}}}}_{{{{\rm{0}}}}}\to {{{{\rm{G}}}}}}\)) intersystem crossing rates. The size of the black circles represents cwODMR contrast of different defects, positioned according to their relative rates extracted from fits to second-order autocorrelation and pulsed ODMR experiments. The largest circle corresponds to a 30% contrast.