Sidebands in optically detected magnetic resonance signals of nitrogen vacancy centers in diamond

We study features in the optically detected magnetic resonance (ODMR) signals associated with negatively charged nitrogen-vacancy (NV${}^{-}$) centers coupled to other paramagnetic impurities in diamond. Our results are important for understanding ODMR line shapes and for optimization of devices based on NV${}^{-}$ centers. We determine the origins of several side features to the unperturbed NV${}^{-}$ magnetic resonance by studying their magnetic field and microwave power dependences. Side resonances separated by around 130 MHz are due to hyperfine coupling between NV${}^{-}$ centers and nearest-neighbor ${}^{13}$C nuclear spins. Side resonances separated by approximately $\{40,260,300\}$ MHz are found to originate from simultaneous spin flipping of NV${}^{-}$ centers and single substitutional nitrogen atoms. All results are in agreement with the presented theoretical calculations.

Figure 1

(a) Energy-level structure of the NV${}^{-}$ center. Gray areas represent phonon sidebands. ${}^3{A}_2$ and ${}^{3}E$ are the spin-triplet ground and excited states, respectively. The electron spin projection along the NV${}^{-}$ axis is denoted $m_S$. (b) Confocal-microscopy setup.

Figure 2

(a) Side-resonance features in ODMR are observed on either side of the central resonance at 2870 MHz. Measurements were done at zero magnetic field with a laser power of 0.7 mW on sample W5. ${\Omega }_R$ denotes the resonant microwave Rabi frequency. (b) Measurement contrast of side resonances A, C, D, and E is plotted as a function of ${\Omega }_R$, which is proportional to the square root of microwave power applied to the sample. The contrast of side-resonance group C is multiplied by 20 for clarity. We only plot the contrasts of the C resonances for resonant microwave Rabi frequencies ${\Omega }_R\le 0.6$ MHz because the C resonances overlap with the B resonances for higher resonant microwave Rabi frequencies. The relative uncertainties of the contrasts are less than 5$\%$, which is smaller than the size of the markers on the plot.

Figure 3

Mixed energy-level diagrams for (a) hyperfine coupling of NV${}^{-}$ centers to ${}^{13}$C nuclear spins and (b) simultaneous spin flipping of NV${}^{-}$ centers and P1 centers. Each transition causing a resonance in Fig. 2a is labeled with the appropriate letter.

Figure 4

Comparison of ODMR signals of CVD and HPHT diamonds. The nitrogen concentration is different between the samples, while the ${}^{13}$C concentration is the same. Measurements were done at zero magnetic field with a laser power of 1.7 mW on diamond samples W2 and W5. The resonant microwave Rabi frequencies were (a) 0.35 and (b) 2.5 MHz. Measurements on the S8 sample were taken under slightly different experimental conditions than for the W2 and W5 samples. For the S8 measurements, the microwave power had some frequency dependence due to an etalon effect.

Figure 5

Magnetic-field dependence of side resonances for the W5 sample. A magnetic field was applied along the [100] orientation. ODMR measurements at low and high microwave powers corresponding to resonant microwave Rabi frequencies of (a) 0.18 and (b) 3.0 MHz. Signals are normalized and offset for clarity. Low-microwave-power measurements show C resonances, and high-microwave-power measurements show $\{\mathrm{B},\mathrm{D},\mathrm{E}\}$ resonances. The magnetic field strength is indicated near each curve. Note that the magnetic field along the NV${}^{-}$ axis is $B_z=B\cos 54.7^{\circ }.$ The values used for labeling purposes reflect the total $B$ value. (c) Frequency differences between group C resonances and their associated group A resonance as a function of applied magnetic field. Solid and dashed lines show theoretically predicted frequency differences for the $m_S=0\to m_S=+1$ and $m_S=0\to m_S=-1$ transitions, respectively. Points are experimental data from the measurements presented in (a). (d) Frequency differences between group $\{\mathrm{B},\mathrm{D},\mathrm{E}\}$ resonances and their associated group A resonance as a function of applied magnetic field. Solid lines show the theoretically predicted P1 center transition energies. Points are experimental data from the measurements presented in (b). Circles and squares represent frequency differences between group A resonances and their associated group E and group B side resonances, respectively. Triangles represent all resonance groups observed for magnetic fields higher than 100 G. The estimated uncertainties on the experimentally determined frequencies in (c) and (d) are 2 and 4 MHz, respectively.

Figure 6

Measurement contrast of side resonance E plotted as a function of magnetic field. Circles correspond to the contrast of the E resonances, and squares correspond to the contrast of the E resonances relative to that of the A resonances. Data are taken at ${\Omega }_R=3.0$ MHz.

Figure 7

The theoretically predicted dependence of the eigenenergy levels of the P1 center on the magnetic field applied in the [100] crystallographic direction.

Figure 8

Dashed lines: energy-level structure (three levels) of an NV${}^{-}$ center located in a magnetic field applied along one of the (a) [100] crystallographic directions and (b) the NV${}^{-}$ axis (which is one of the [111] directions) as a function of magnetic field strength. Solid lines: energy-level structure of the combined system consisting of an NV${}^{-}$ center and a nearest-neighbor ${}^{13}$C nuclear spin (six levels).