Figure 1

(a) Nitrogen-vacancy (NV) color center in a diamond lattice. NV electronic spin decoherence is dominated by ${}^{13}$C nuclear spin and N electronic spin impurities. (b) Energy level structure of negatively charged NV center. (c) Hahn echo and $n$-pulse CPMG control sequences. Timing of ac magnetic field to be measured is shown in green.Reuse & Permissions

Figure 2

Measurements of NV multispin coherent evolution using $n$-pulse CPMG control sequences for three diamond samples of differing NV densities and spin impurity environments: (a) NV $\sim 60$ ppb, N $\sim 100$ ppm, and 1.1$\%$ ${}^{13}\mathrm{C}$; (b) NV $\sim 0.2$ ppb, N $\sim 0.1$ ppm, and 1.1$\%$ ${}^{13}\mathrm{C}$; and (c) NV $\sim 0.6$ ppb, N $\sim 1$ ppm, and 0.01$\%$ ${}^{13}\mathrm{C}$, where the solid lines denote fits to the decoherence envelope of the form $\exp [-{\left(\tau {/}_{T_2}\right)}^p]$. Note that the time axis of (b) is plotted with a linear scale due to the periodic collapses and revivals in the NV spin coherence of sample B associated with ${}^{13}\mathrm{C}$ Larmor precession.[29] These collapses and revivals occur in samples where the ${}^{13}$C abundance is high enough to contribute significantly to NV decoherence. (d) Scaling of measured NV multispin coherence times with the number $n$ of CPMG pulses: $T_2\propto {\left(n\right)}^s$.Reuse & Permissions

Figure 3

Measured ac magnetic field sensitivity for a 30 $\mu {\text{m}}^3$ sensing volume of sample C ($\sim$${10}^3$ sensing NV spins). (a) Examples of measured normalized fluorescence signals as functions of ac field magnitude $b_{\text{ac}}$ using a Hahn echo sequence (green/light gray) (wider amplitude range shown in the inset) and multipulse XY sequences with 28 (red/gray) and 54 (blue/dark gray) control pulses, illustrating how the uncertainty in the measured signal ($\delta S$) limits the uncertainty in the extracted magnetic field magnitude ($\delta B$). The sine behavior of the signal with respect to $b_{\text{ac}}$ is achieved by shifting the phase of the last microwave pulse by ${90}^{\circ }$ from what is shown in Fig. 1c. (b) Measured multipulse magnetic field sensitivity as a function of number of pulses for an 84.5 kHz ac field (circles). The solid line is calculated using Eq. (2) with experimental parameters $C=0.1$, $T_2=250\mu \text{s}$, $p=1$, and $s=0.37$. (c) Comparison of calculated (lines) and measured (points) magnetic field sensitivity at several ac field frequencies, for both Hahn echo and multipulse XY sequences (using the measured optimum number of pulses for each frequency).Reuse & Permissions