Diamond Magnetometry and Gradiometry Towards Subpicotesla dc Field Measurement

Nitrogen-vacancy (N-$V$) centers in diamond have developed into a powerful solid-state platform for compact quantum sensors. However, high-sensitivity measurements usually come with additional constraints on the pumping intensity of the laser and the pulse control applied. Here, we demonstrate high-sensitivity N-$V$-ensemble-based magnetic field measurements with low-intensity optical excitation. Direct current magnetometry methods such as continuous-wave optically detected magnetic resonance and continuously excited Ramsey measurements combined with lock-in detection are compared to achieve an optimization. Gradiometry is also investigated as a step towards unshielded measurements of unknown gradients. The magnetometer demonstrates a minimum detectable field of 0.3–0.7 pT in a 73-s measurement when a flux guide with a sensing dimension of 2 mm is applied, corresponding to a magnetic field sensitivity of 2.6–6 $\mathrm{pT}/\sqrt{\mathrm{Hz}}$. Combined with our previous efforts on diamond ac magnetometry, the diamond magnetometer is promising for performing wide-bandwidth magnetometry with picotesla sensitivity and a cubic-millimeter sensing volume under ambient conditions.

Figure 1

(a) The experimental setup is installed in a magnetic field shield for high-sensitivity measurements. PD, photodetector. (b) Two identical diamond sensors are constructed to measure the noise floor in the gradiometer configuration. The reference channel uses a loop antenna. (c) A flux guide is placed between the diamond and a coil for enhancement of the magnetic field sensitivity. (d) Energy diagram of N-$V^{-}$ center.

Figure 2

(a) Lock-in-detected cw ODMR signal profile and the corresponding scalar factor. ${\delta }_{\mathrm{cm}}$ is a common-mode line shift of the two resonant lines. $S_{-1}$ and $S_{+1}$ are the corresponding signals, with the same amplitude but different signs. (b) A continuously excited Ramsey (CE Ramsey) sequence is used to promote the cw ODMR measurement. The blocks of solid color labeled “Laser” depict the laser pulses used in a traditional Ramsey measurement, while in the CE Ramsey method the laser is continuously applied in all the time bins, as shown by the cross-hatched area. The curve labeled FL (red line) depicts the fluorescence signal when the external field is zero. The signal in the time bins corresponding to the solid laser blocks is a valid signal for magnetic field sensing, as shown by the shaded area for Seq1. The remaining signal becomes negligible when ${\tau }_m\ll T_{\mathrm{seq}}$, which can be seen in (c), which shows the fluorescence readout for cycle times $T_{\mathrm{seq}}=1\mathrm{ms}$ (black solid curve) and $250\mu \mathrm{s}$ (red dotted curve). The Seq1 and Seq2 blocks on the top correspond to the signal for the 1-ms cycle. The figure shows both the conventional readout method (shown for the 1-ms-cycle signal) and the lock-in readout method (shown for the 250-$\mu \mathrm{s}$-cycle signal). The signals in the gray areas are calculated following the equations shown in the figure for conventional readout. For lock-in detection, the demodulation reference is applied according to the dashed sinusoidal line.

Figure 3

(a) Optimization of theoretical shot-noise-limited sensitivity with respect to laser pumping and MW driving strength based on the cw ODMR model. $T_2^{\ast }=8.5\mu \mathrm{s}$ and $T_1=6\mathrm{ms}$ are the parameters used in the calculation. The dashed line shows the optimized MW strength and sensitivity for different excitation powers. The triangle marks the best theoretical sensitivity. (b) Repolarization curves for both the experimental results and the simulation, indicating the effects of the two primary parameters, the pumping rate ($k$ in MHz) and $T_1$. (c) Experimental sensitivity parameter of linewidth divided by contrast for different Rabi frequencies. The Rabi frequency for the cw ODMR method is optimized at 17 kHz. (d) Contrast of simulated cw ODMR signal for different modulation frequencies (on logarithmic scale). The pumping rate and $T_1$ also affect the bandwidth and contrast of the magnetometer. The diamond magnetometer has a 3-dB bandwidth of around 1.5 kHz, and the signal contrast is reduced from 1 to 20 kHz.

Figure 4

(a) Linewidth measured with different Rabi frequencies by cw ODMR (black dotted line), pulsed ODMR (red solid line), and CE-pulsed-ODMR (blue dashed line). Both axes are logarithmic. The inset shows the cw ODMR linewidth for decreasing MW power. (b) Scalar factor of cw ODMR measurement with frequency-modulation (FM) signal $f_m=1$, 5, 10, and 20 kHz as a function of the modulation amplitude $f_d$. The data for $f_m=1$ and 5 kHz fit well with the derivative of a Lorentzian lineshape. However, the fitting cannot work (it is higher than the measured results) when the bandwidth $2(f_d+f_m)$ of the modulated MW signal approaches the ODMR linewidth. (c) Comparison of scalar factors for cw ODMR (MW phase-modulated) and CE Ramsey methods for different modulation frequencies. The demodulation frequency of the CE Ramsey measurement is $1/T_{\mathrm{seq}}$. The cw ODMR traces are plotted for different values of ${\varphi }_d$. For comparison, an extra cw ODMR curve is plotted with the FM MW signal bandwidth fixed at 100 kHz. (d) Noise floor (root-mean-square noise in volts, lower left $y$ axis) of the electronics and demodulated laser intensity, from 1 to 20 kHz. Both axes are logarithmic. The frequency resolution of the spectra is 13.7 mHz for a 73-s measurement time. In the upper part, the minimum detectable fields (right $y$ axis) of the CE Ramsey and cw ODMR measurements for a bandwidth $W=100$ kHz are plotted.

Figure 5

(a) Magnetic field noise spectrum measured by cw ODMR method with hyperfine driving and DR driving, compared with the spectrum measured by an OPM sensor. The black line is the off-resonant baseline showing the intrinsic noise of the diamond magnetometer. With a measurement time of 73 s, all of the spectra plotted in this figure have the same frequency resolution of 13.7 mHz. The magnitudes are plotted on a logarithmic scale here and in parts (b) and (c). (b) The green and red lines show the noise spectra obtained from the direct outputs of measurements with and without a FG. The blue line shows the measured magnetic field noise calibrated using the difference between the battery-discharging signals in the two measurements. In order to see the low-frequency noise spikes, the discharging ramp of the output is removed by linear fitting before the spectral analysis. (c) Noise spectra measured by the gradiometer setup: the probe channel 1 (blue), the reference channel 2 (red), and the gradiometry signal (black) are measured. The spectrum of each single channel is measured by applying single-resonance driving, and the spectrum of the gradiometer is measured by combining the two channels and operating it with the DR driving scheme.