Optical polarization of nuclear ensembles in diamond

We report polarization of a dense nuclear-spin ensemble in diamond and its dependence on magnetic field and temperature. The polarization method is based on the transfer of electron spin polarization of negatively charged nitrogen vacancy (NV) color centers to the nuclear spins via the excited-state level anticrossing of the center. We polarize 90$\%$ of the ${}^{14}$N nuclear spins within the NV centers, and 70$\%$ of the proximal ${}^{13}$C nuclear spins with hyperfine interaction strength of 13–14 MHz. Magnetic-field dependence of the polarization reveals a sharp decrease in polarization at specific field values corresponding to cross relaxation with substitutional nitrogen centers, while temperature dependence of the polarization reveals that high polarization persists down to 50 K. This work enables polarization of the ${}^{13}$C in bulk diamond, which is of interest in applications of nuclear magnetic resonance, in quantum memories of hybrid quantum devices, and in sensing.

Figure 1

Nuclear-spin polarization process of the ${}^{13}$C nuclear spin. The ${}^3$$A_2$ and the ${}^{3}E$ are the triplet ground and excited states, respectively. (a) Energy diagram of the electronic triplet levels of the NV center at room temperature as a function of the axial magnetic field. The ESLAC of the spin states $m_S=0$ and $m_S=-1$ can be seen in a field of ≈500 G. (b) The joint manifold of the nuclear spin of the ${}^{14}$N and the electronic spin of the NV center near the ESLAC. The states are labeled as $|m_S,m_I\rangle$. At 500 G, the electronic substates are nearly degenerate in the excited state, while in the ground state there is a splitting of ∼1.5 GHz. The axial hyperfine interaction can be seen as a splitting of the $m_S=-1$ states, while the off-axial hyperfine interaction mixing of the electronic and the nuclear spins is represented by the bidirectional curved arrow in the ${}^{3}E$ level. The intersystem crossing is represented by dashed arrows connecting the $m_S=-1$ in the excited state to the $m_S=0$ in the ground state. The optical transitions are represented by bidirectional straight arrows, which conserve spin.

Figure 2

Comparison of ODMR signal of the [111] orientation in a low magnetic field and near the ESLAC. Top figure: ODMR signal at 21 G. Bottom figure: ODMR signal near the ESLAC at 387 G. Thick dashed curve correspond to the experimental results, thick full curve correspond to the fitted multiple resonances. Narrow curves correspond to the fitted individual resonances. The high peak marked with an arrow corresponds to the ($m_S=0$, ${}^{14\mathrm{N}}{m}_I=+1\to m_S=+1$, ${}^{14\mathrm{N}}{m}_I=+1$) transition. The marked low peak corresponds to ($m_S=0$, $m_I{[}^{14}\mathrm{N}]=+1$, $m_I{[}^{13}\mathrm{C}]=+1/2\to m_S=+1$, $m_I{[}^{14}\mathrm{N}]=+1$, ${}^{13\mathrm{C}}{m}_I{[}^{13}\mathrm{C}]=+1/2$) transition, and it is due to hyperfine interaction with ${}^{14}$N and ${}^{13}$C nuclear spins. Top figure: $f_{\mathrm{resonance}}$ = 2.93 GHz. Bottom figure: $f_{\mathrm{resonance}}$ = 3.92 GHz.

Figure 3

Room-temperature ${}^{14}$N nuclear polarization as a function of the axial magnetic field. The circles are the experimental measurements, and the dashed curve is the simulation result at zero strain. Inset: ${}^{14}$N polarization in a narrower magnetic field range showing three dips of the nuclear polarization corresponding to cross-relaxation with P1 centers.

Figure 4

(a) Temperature dependence of ${}^{14}$N polarization. Circles represent experimental results; asterisks represent simulated ${}^{14}$N polarization, in which the strain distribution is extracted from the ESODMR measurements. (b) Temperature dependence of zero-field ESODMR. The main figure represents a product of the average over the central range of the resonance in the range of 1.38–1.44 GHz, and the FWHM. Inset: ESODMR at zero field for four different temperatures between 10 and 285 K.

Figure 5

A steady-state density matrix simulation of the ${}^{14}$N nuclear polarization as a function of the axial magnetic field and the spin-strain interaction.