Figure 2

Dynamical nuclear polarization using the frequency-modulated microwave driving field. (a) The polarization dynamics of a ¹³C at a distance of 1.5 nm from the NV center with the transition frequency \(\omega=(D-\gamma B)+\delta\), where \({\delta =(2\pi)5\mbox{ MHz}}\), \(P_{\downarrow}\) is the nuclear spin down state population, and the frequency of microwave field changes at the speed of ν. (b) The average nuclear spin down state population \(\bar{P}_{\downarrow}\) as a function of the total polarization time for the frequency sweeping speed \(\nu=(2\pi)1 \mbox{ MHz} \cdot\mbox{ms}^{-1}\) and \({\nu=(2\pi)2 \mbox{ MHz}\cdot \mbox{ms} ^{-1}}\), using an ensemble of NV centers with a Lorentzian transition frequency distribution, the corresponding linewidth is \({\Delta=(2\pi) 10\mbox{ MHz}}\). In both (a) and (b), the magnetic field is \(B=200\mbox{ G}\) and is aligned along the NV axis, and the Rabi frequency of microwave field is \(\Omega=\gamma_{C} B\) where \(\gamma_{C}\) is the gyromagnetic ration of ¹³C, and the NV center is re-polarized every 120 μs.