Microwave saturation spectroscopy of nitrogen-vacancy ensembles in diamond

Negatively charged nitrogen-vacancy (NV${}^{-}$) centers in diamond have generated much recent interest for their use in sensing. The sensitivity improves when the NV ground-state microwave transitions are narrow, but these transitions suffer from inhomogeneous broadening, especially in high-density NV ensembles. To better understand and remove the sources of broadening, we demonstrate room-temperature spectral “hole burning” of the NV ground-state transitions. We find that hole burning removes the broadening caused by magnetic fields from ${}^{13}$C nuclei and demonstrate that it can be used for magnetic-field-insensitive thermometry.

Figure 1

(a) The NV${}^{-}$ ground-state energy level structure [3, 12]. The ${}^{14}$N hyperfine interaction is included, but the ${}^{14}$N Zeeman splitting (0.3 kHz/G) is not. The MW transitions conserve nuclear $m_I$ (colored arrows, also shown in Fig. 2). (b) The pulse sequence used for pulsed hole burning. (c) The result of a pulsed-hole experiment in sample CVD1 (see Table 1). The 0.3 MHz FWHM hole is Fourier-limited and is narrower than what was achieved with CW hole-burning (Table 1). The model for the fit is described in the Appendix.

Figure 2

(a) CW ODMR spectra in sample HPHT1 with a static magnetic field along an arbitrary direction, which splits the resonances of the four NV-axis alignments into four pairs of frequencies. Burning a hole at any frequency only affects NVs of the associated alignment. The slight asymmetries in ODMR contrast are likely due to differences in MW power delivered to the NVs. (b) ODMR spectra of the $m_s=0$ to $+1$ transition, now with an axial magnetic field. (c) Here we amplitude modulate the pump field and perform lock-in detection on the NV fluorescence intensity.

Figure 3

The experimental apparatus for CW hole burning. We amplitude modulated the hole MW field at 1.3 kHz. In a pulsed hole-burning experiment, the hole MW field is not modulated and there is no lock-in amplifier.

Figure 4

(a) The effect of changing the pump frequency ($f_{+}$ = 2934.2 MHz + $\Delta f$) on the hole center frequency $f_{-}$ (diamond sample HPHT1). The lock-in signal when the probe is off resonance is due to the NV fluorescence being modulated by the pump MW at the lock-in frequency and is a measure of the pump absorption. Varying $f_{+}$ confirms the prediction made in Eq. (2). (b) Here we keep $f_{+}$ constant but vary $B$ near 23 G. Frequency pulling causes a $\pm$0.2-MHz shift when $B$ changes by $\pm$0.9 G (dashed lines). Additional data are included in the Supplemental Material [18].

Figure 5

Temperature dependence of $f_{-}$ in sample HPHT2. The solid line is a fit done with Eq. (4), and the dashed line is the linear part of this fit. Note that the oscillation period is not an independent free parameter, but is fixed by the model.

Figure 6

The actions of the $\pi$ pulses on the sublevel populations. After being initialized into the $m_s=0$ state, two $\pi$ pulses are applied, yielding different final-state populations depending on the experiment and $f_r$. Open circles represent NVs removed by the $\pi$ pulse, and filled circles represent the NV population after the pulse has acted. A red cross indicates that the probe does not affect the populations. Note that in case I of experiment 2, the NVs that were pumped are detected at $f_r=2D-f_h$.

Figure 7

The expected results of pulsed ODMR (a) and pulsed hole-burning experiments 1 (b) and 2 (c). We assume that the $m_s=0$ to $+1$, $m_I=0$ transition has frequency $f_0$. The red labels identify the expected fluorescence for the above three cases.

Figure 8

An illustrative picture of CW ODMR. Here we compare the differences in NV fluorescence when probing the $m_s=0$ to $+1$ and $m_s=0$ to $-1$ transitions, ignoring the effect of CPO. From this we see that pumping and probing the same transition produces a more prominent feature in the ODMR spectrum.

Figure 9

Final-state population fractions $P_0\left(f_r\right)$ and $P_{+1}\left(f_r\right)$ for ${\gamma }_{\pi }/{\gamma }_i=$ 0.05, 0.20, and 0.5.

Figure 10

The maximum slope achievable for a pulsed hole-burning experiment, where the readout $\pi$-pulse probes the $m_s=0$ to $-1$ transition. The slope increases with narrower pulse widths, improving $\delta f_{\mathrm{shot}}$, $\delta f_{\mathrm{white}}$, and $\delta f_{\mathrm{tech}}$.