Ab initio theory of the ${\mathrm{N}}_2\mathrm{V}$ defect in diamond for quantum memory implementation

The ${\text{N}}_2\mathrm{V}$ defect in diamond is characterized by means of ab initio methods relying on density functional theory calculated parameters of a Hubbard model Hamiltonian. It is shown that this approach appropriately describes the energy levels of correlated excited states induced by this defect. By determining its critical magneto-optical parameters, we propose to realize a long-living quantum memory by ${\text{N}}_2\mathrm{V}$ defect, i.e., $H3$ color center in diamond.

Figure 1

(a) Geometry of ${\text{N}}_2\mathrm{V}$ defect in diamond. (b) Representation of defect levels of double negatively charged ${\text{N}}_2\mathrm{V}$ with closed-shell orbitals relative to the valence-band maximum (VBM). (c) Analysis of ODMR contrast of the neutral ${\text{N}}_2\mathrm{V}$. Straight line illustrates radiative decay, dashed and dotted lines represent ISC with first-order and second-order spin-orbit couplings ($\lambda$), respectively. Curved lines and blue arrows indicate phonon and microwave transition, respectively. The calculated zero-field splitting parameters are given for ${}^{3}B_1$ state at 0 K temperature.

Figure 2

Visualization of geometric structure and defect wave functions of ${\text{N}}_2\mathrm{V}$. Brown and blue balls represent the carbon and nitrogen atoms, respectively. Defect states are labeled by their irreducible representation and localization. (a) $a_1\left(\text{N}\right)$, (b) $b_2\left(\text{N}\right)$, (c) $a_1\left(\text{C}\right)$, (d) $b_1\left(\text{C}\right)$, (e) defect levels.

Figure 3

Excitation energies of the neutral ${\text{N}}_2\mathrm{V}$ defect in diamond. States that are very close in energy are enclosed with brackets. The lowest optically allowed excitation energies are highlighted with red. Left panel: self-consistent unrestricted spin-polarized Kohn-Sham HSE06 $\mathrm{\Delta }\mathrm{SCF}$ results. The tilde on the labels of the wave functions denotes that not the true eigenstate of the system is calculated (see text for more details). Middle panel: experimental zero-phonon-line energies for the singlets (Ref. [7]) and the proposed energies of triplets (Ref. [11]). Right panel: Hubbard model Hamiltonian results.

Figure 4

Visualization of atomic sites with dominant hyperfine parameters shown in Table 3 for ${\text{N}}_2{V}^0$.