Multipulse Double-Quantum Magnetometry with Near-Surface Nitrogen-Vacancy Centers

We discuss multipulse magnetometry that exploits all three magnetic sublevels of the $S=1$ nitrogen-vacancy center in diamond to achieve enhanced magnetic field sensitivity. Based on dual frequency microwave pulsing, the scheme is twice as sensitive to ac magnetic fields as conventional two-level magnetometry. We derive the spin evolution operator for dual frequency microwave excitation and show its effectiveness for double-quantum state swaps. Using multipulse sequences of up to 128 pulses under optimized conditions, we show enhancement of the SNR by up to a factor of 2 in detecting NMR statistical signals, with a $4\times$ enhancement theoretically possible.

Figure 1

(a) The ground state energy levels for the spin-1 nitrogen-vacancy center, showing the zero-field splitting $D=2.87\mathrm{GHz}$ and the additional Zeeman splitting of the $m_s=\pm 1$ sublevels. (b) Double-quantum dynamic decoupling sequence using a superposition of the $m_s=\pm 1$ states, where the state amplitudes are periodically swapped. The final accumulated phase difference is insensitive to static magnetic fields, but proportional to twice the amplitude of the ac magnetic field (sine wave). Each “swap” is accomplished with a single dual-frequency pulse. (c),(d) Time evolution of the spin wave function under dual frequency microwave irradiation of the form $B_{MW}(t)=B_1\cos (\omega {}_{1}t+{\delta }_1)+B_2\cos (\omega {}_{2}t+{\delta }_2)$, plotted as probabilities, demonstrating the ability to perform a swap operation. In this example, $B_1=B_2$, and the $m_s=1(-1)$ state is initially populated with probability 0.75 (0.25) (red square and blue dot). (c) ${\delta }_1={\delta }_2=0°$, (d) ${\delta }_1=-{\delta }_2=90°$. In both cases, the wave function component probabilities are swapped when $t/t_0=1/2$, where $t_0=2\pi /\gamma B_1$. “Prepare” and “read” pulses are similarly achieved with $t/t_0=1/4$. (e) Circuit for generating the dual frequency pulses (see the Supplemental Material [19]). The mixer creates sum and difference frequencies $f_{\text{sum}}$ and $f_{\text{diff}}$ centered around 2.87 GHz.

Figure 2

Experimental comparison of (a) single-quantum (SQ) and (b) double-quantum (DQ) responses to identical ac magnetic test signals. A simple echo sequence with a single swap was used ($\text{echo}\text{time}=40\mu \mathrm{s}$). The DQ response oscillates with roughly half the period, as expected. (c) Echo response versus echo time. Solid curve is a fit to the data using the model $\xi (t)={\xi }_0\exp [-{(t/T_2)}^n]$. For the SQ (DQ) decay, $T_2=82\mu \mathrm{s}$, $n=2.2$ ($T_2=49\mu \mathrm{s}$, $n=1.9$).

Figure 3

Comparison of (a) SQ and (b) DQ magnetometry using a multipulse sequence of 64 “swap” pulses in response to a magnetic test signal. The repetition time $\tau$ was 528 ns, making the total evolution time $33.8\mu \mathrm{s}$. The test signal was at 947 kHz and was applied synchronously with the pulses ($\text{pulse}\text{width}=16\mathrm{ns}$). (a) was an $XY8–64$ sequence, while (b) was a related DQ version where the phases were cycled as $\{90°,0°,90°,0°,0°,90°,0°,90°,-90°,-180°,-90°,-180°,-180°,-90°,-180°,-90°\}$ and repeated four times. The DQ curve has roughly twice the maximum slope and 4 times the maximum curvature as the SQ curve.

Figure 4

Detection of NMR signals using multipulse dynamic decoupling sequences with scanned pulse spacing. (a) Signal versus pulse spacing for a SQ $XY8–128$ sequence. The external field was 24.1 mT, corresponding to a proton Larmor frequency $f_L=1.026\mathrm{MHz}$. A slight dip due to the proton signal is observed at a pulse repetition time of 488 ns, corresponding to $1/2f_L$ (arrow). Each point is the average of 5 million sequence repetitions ($\sim 5\text{min}\text{per}\text{point}$). (b) Identical measurement taken with the DQ protocol with phase sequence $\{90°,0°,90°,0°,0°,90°,0°,90°,-90°,-180°,-90°,-180°,-180°,-90°,-180°,-90°\}$ repeated eight times. A clear enhancement of the SNR is evident.