Fig. 2

Cross-relaxation induced polarisation of ¹³C spins in diamond. a Cross-relaxation spectra of a single NV spin near the ¹³C resonance (\(\omega _{{\mathrm{N}}V} = 1.1\) MHz), obtained with an interaction time τ = 4 µs using the CRIP sequence (blue) and the depolarisation sequence (orange, only the readout following the NV initialisation in \(|0\rangle\) is shown). Sequences were repeated N = 10⁵ times at each point. b Cross-relaxation curves obtained by increasing τ at the ¹³C resonance with the CRIP sequence (blue) and depolarisation sequence (orange), and off-resonance to obtain the background relaxation curve (green). Zoom-in at short times for the polarised (blue) and unpolarised case (orange, top and bottom curves correspond to the NV initialised in \(|0\rangle\) and \(| - 1\rangle\), respectively). c Calculated radial polarisation profiles relative to the NV spin (averaged over all angles), calculated from Eq. (1) for a random 1.1% ¹³C spin ensemble for varying total polarisation times, T = Nτ. Inset: profile along dashed line, corresponding to T = 2 h. d Three-dimensional representation of the polarisation distribution at T = 2 h