Diamond-nitrogen-vacancy electronic and nuclear spin-state anticrossings under weak transverse magnetic fields

We report on detailed studies of electronic and nuclear spin states in the diamond-nitrogen-vacancy (NV) center under weak transverse magnetic fields. We numerically predict and experimentally verify a previously unobserved NV hyperfine level anticrossing (LAC) occurring at bias fields of tens of gauss—two orders of magnitude lower than previously reported LACs at $\sim 500$ and $\sim 1000$ G axial magnetic fields. We then discuss how the NV ground-state Hamiltonian can be manipulated in this regime to tailor the NV's sensitivity to environmental factors and to map into the nuclear spin state.

Figure 1

(a) Axial and transverse magnetic field directions with respect to the NV axis. As $B_{\perp }$ is increased from (b) 35 to (c) 45 G, the $m_I=0$ energy levels are separated from the $m_I=\pm 1$ energy levels, removing the degeneracy which results in an electron-nuclear spin flip anticrossing, which is detailed in the inset of (b). Nondressed states are indicated with colored lines and dressed states are indicated with black lines.

Figure 2

(a) Anticrossing coupling strength with increasing $B_{\perp }$. (b) Magnitude of small axial B fields at which the centers of these anticrossings are observed. In both plots, the double-electron spin flip anticrossing is marked $E$ and the electron-nuclear spin flip anticrossing is marked $N$. At fields greater than $B_{\perp }\sim 40$ G, $E_g$ continues to increase quadratically and $N_g$ goes to zero as the energy levels no longer overlap.

Figure 3

(a) Experimental setup. (b) The four orientation subensembles of NV centers are shown with an applied magnetic field. (c) An anticrossing strength of $\sim 2.6$ MHz is seen in subensemble 1 when the perpendicular component of the B field $\left(B_{1,\perp }\right)$ is equal to 30 G and the axial component of the B field $\left(B_{1,\left|\right|}\right)$ is varied around zero field. Inset shows a high resolution spectra of resonance 1 and $1^{\prime }$.

Figure 4

Plots of transition energies as a function of the axial magnetic field under fixed transverse magnetic fields. Transitions for $B_{\perp }=35$ and $B_{\perp }=45$ G are shown, which correspond to the energy levels in Fig. 1. Grayscale indicates normalized fluorescence. Double-electron spin anticrossings of coupling strength $E_g$ are seen at $E_p=0,\pm A_{\left|\right|}h/g_e{\mu }_B\simeq \pm 0.75$ G. ESR in diamond with a natural abundance of carbon isotopes has additional resonances due to hyperfine interactions with the $\sim 1\% \left(I=1/2\right) {}^{13}\mathrm{C}$ nuclear spins; these features are visible at correspondingly lower contrast in both (a) and (b), the highest contrast of which is labeled.

Figure 5

Detail of double-electron and electron-nuclear spin anticrossings at $B_{\perp }=30$ G, where grayscale represents normalized fluorescence. The rf excitation power was reduced by 10 dB to reduce power broadening. This allows the higher-resolution features to be observed; however it is at the expense of the signal-to-noise ratio. Electron-nuclear spin anticrossings of coupling strength $N_g\simeq 250$ kHz are seen centered around $N_p\simeq \pm 0.35$ G, separated in frequency by $P_{gs}$ at 2.877 and 2.872 GHz. Numerical solutions to ${\mathcal{H}}_{gs}$ are plotted over the data, with the diameter of the circles corresponding to the probability of the transition.

Figure 6

Comparison of (a) ${}^{15}\mathrm{N}$ and (b) ${}^{14}\mathrm{N}$ samples at $B_{\perp }=30$ G.