Optically detected nuclear quadrupolar interaction of ${}^{14}\mathrm{N}$ in nitrogen-vacancy centers in diamond

We report sensitive detection of the nuclear quadrupolar interaction of the ${}^{14}\mathrm{N}$ nuclear spin of the nitrogen-vacancy (NV) center using the electron spin-echo envelope modulation technique. We applied a weak transverse magnetic field to the spin system so that certain forbidden transitions became weakly allowed due to second-order effects involving the nonsecular terms of the hyperfine interaction. The weak transitions cause modulation of the electron spin-echo signal, and a theoretical analysis suggests that the modulation frequency is primarily determined by the nuclear quadrupolar frequency; numerical simulations confirm the analytical results and show excellent quantitative agreement with experiments. This is an experimentally simple method of detecting quadrupolar interactions, and it can be used to study spin systems with an energy structure similar to that of the NV center.

Figure 1

Optically detected ESEEM of the NV center in diamond. Solid lines represent experimental results (circle or square markers are used only for the purpose of figure legends), and dashed lines represent simulation results. An external magnetic field of 75 G was applied along the NV axis (θ = 0°) or perpendicular to the NV axis (θ = 90°). Modulation of the exponential decay for θ = 90° is due to the ${}^{14}\mathrm{N}$ nuclear quadrupolar coupling of the NV center. The inset shows the experimental result for the CPMG pulse sequence with 10 π pulses when the magnetic field is orientated at θ = 90°.

Figure 2

Illustration of the negatively charged NV center in diamond. The blue sphere with a blue arrow represents the ${}^{14}\mathrm{N}$ nuclear spin, and the light gray sphere with a gray arrow at the vacancy represents the NV electron spin. The green arrow represents the $z$ component of the electric field gradient at the ${}^{14}\mathrm{N}$ nuclear site. Dark gray spheres represent carbon atoms in the diamond lattice. The red arrow represents the external magnetic field along the $x$ axis.

Figure 3

Energy-level diagram for the NV center in diamond in the presence of a transverse magnetic field of 75 G along the $x$ axis. The Hamiltonian $H_{\mathrm{ZFS}}$ is responsible the zero-field splitting of the NV center, $H_{\mathrm{B}}$ governs the Zeeman interaction, $H_{\mathrm{Q}}$ governs the quadrupolar interaction, and $H_{\mathrm{HF}}$ governs the hyperfine interaction. Approximate energy eigenstates are indicated next to the corresponding energy levels, where $|{\psi }_x\rangle$, $|{\psi }_y\rangle$, and $|{\psi }_z\rangle$ are electron spin states and $|{\varphi }_x\rangle$, $|{\varphi }_y\rangle$, and $|{\varphi }_z\rangle$ are nuclear spin states. On the right side of the figure, the product state making the dominant contribution to each energy eigenstate is shown. Allowed (solid arrows) and forbidden (dashed arrows) spin transitions are also shown.

Figure 4

Fourier transform spectra of the ESEEM signal of the NV center in an external magnetic field of 75 G applied perpendicular to the NV axis. Solid lines with circles or squares represent experimental data obtained using the HE pulse sequence or the CPMG pulse sequence, respectively. The dotted line with triangles represents a simulation that used the HE pulse sequence. The inset shows the ESEEM signal after the exponential decay was subtracted.