Theory of the neutral nitrogen-vacancy center in diamond and its application to the realization of a qubit

The negatively charged nitrogen-vacancy defect $\left({\text{NV}}^{-}\right)$ in diamond has attracted much attention in recent years in qubit and biological applications. The negative charge is donated from nearby nitrogen donors that could limit or stem the successful application of ${\text{NV}}^{-}$. In this study, we identify the neutral nitrogen-vacancy defect $\left({\text{NV}}^0\right)$ by ab initio supercell calculations through the comparison of the measured and calculated hyperfine tensors of the ${{}^{4}A}_2$ excited state. Our analysis shows that (i) the spin state can be selectively occupied optically, (ii) the electron spin state can be manipulated by time-varying magnetic field, and (iii) the spin state may be read out optically. Based on this ${\text{NV}}^0$ is a hope for realizing qubit in diamond without the need of nitrogen donors. In addition, we propose that ${\text{NV}}^0$ may be more sensitive magnetometer than the ultrasensitive ${\text{NV}}^{-}$.

Figure 1

(Color online) Calculated spin-density isosurfaces. Left panel: ground state ($M_{\text{S}}=\frac{1}{2}$ of ${}^{2}E$) and right panel: excited state ($M_{\text{S}}=\frac{3}{2}$ of ${{}^{4}A}_2$). Nitrogen and carbon atoms are depicted by very light gray and dark gray balls, respectively. We show two values of spin-density isosurfaces in the left panel: opaque red(dark gray) shows 0.128 (high spin density) while transparent yellow(light gray) shows 0.006 (very small spin density). Right panel shows normalized values in order to show the same effective magnetization density on the atoms as for $S=\frac{1}{2}$ state. The atoms are shown within the radius of $7.3\text{Å}$ around the nitrogen-atom cut from the 512-atom supercell. The spin density is negligible outside this region. Note that no spin density can be found on nitrogen atom in the ground state while sizeable spin density is localized on nitrogen atom in the excited state. The lobes at the nitrogen and carbon atoms near the vacant site may also represent the corresponding ${\sigma }_4$ and ${\sigma }_{1–3}$ dangling bonds in Eq. (1).

Figure 2

(Color online) The process of the manipulation of a qubit in ${\text{NV}}^0$ defect. Straight red(dark gray) arrow dotted in the middle: radiative recombination. Curved green(lighter gray) arrow: spin-orbit coupling $\left({\widehat{H}}_{\text{SO}}\right)$ possibly mediated by phonons. Light gray dotted arrows represent very weak interaction. Blue(dark gray) straight line: microwave-alternating magnetic-field pulse. Filled(empty) circle: initial(final) state of the electron. Setting the qubit state: (i) excitation from the ${}^{2}E$ ground state to the ${{}^{2}A}_1$ excited state, (ii) spin flip to the appropriate ${{}^{4}A}_2$ states iii) setting either $M_{\text{S}}=3/2$ or $M_{\text{S}}=-3/2$ state by $\pi$ pulse. Readout the qubit state: i) $\pi$ pulse to go back to $M_{\text{S}}=\pm 1/2$ states ii) spin flip to the ${{}^{2}A}_1$ state, and (iii) radiative recombination to the ${}^{2}E$ ground state. We show the fine structure of ${{}^{4}A}_2$ states in the absence of external magnetic field $\left(\mathbf{B}=0\right)$ (2nd column) and at $\mathbf{B}>0$ with typical EPR conditions in the next columns. $D\approx 1685\text{MHz}$ fine-structure constant was determined by EPR (Ref. 21). The figure does not show the true scale for the sake of clarity.