Long spin coherence times of nitrogen vacancy centers in milled nanodiamonds

Nanodiamonds containing negatively charged nitrogen vacancy centers (${\text{NV}}^{-}$) have applications as localized sensors in biological materials and have been proposed as a platform to probe the macroscopic limits of spatial superposition and the quantum nature of gravity. A key requirement for these applications is to obtain nanodiamonds containing ${\text{NV}}^{-}$ with long spin coherence times. Using milling to fabricate nanodiamonds processes the full 3D volume of the bulk material at once, unlike etching pillars, but has, up to now, limited ${\text{NV}}^{-}$ spin coherence times. Here, we use natural isotopic abundance nanodiamonds produced by ${\text{Si}}_3{\text{N}}_4$ ball milling of chemical vapor deposition grown bulk diamond with an average single substitutional nitrogen concentration of $121\text{ppb}$. We show that the electron spin coherence times of ${\text{NV}}^{-}$ centers in these nanodiamonds can exceed 400 $\mu \text{s}$ at room temperature with dynamical decoupling. Scanning electron microscopy provides images of the specific nanodiamonds containing ${\text{NV}}^{-}$ for which a spin coherence time was measured.

Figure 1

(a) Confocal fluorescence microscopy (CFM) image in red and blue (lighter gray scale), of nanodiamond KNMO13ND1 (ND1) overlaid onto a reflection image, in purple and orange (darker grayscale), of the grid-marked silicon. Image plotted using the Qudi software suite [45]. ND1 is identified by the solid green (gray) ring. The dashed green (gray) rings around nearby features are overlaid on both (a) and (b) which, along with the grid, verify that the CFM and scanning electron microscopy (SEM) are both viewing the same nanodiamonds. (b) SEM imaging of the same area in (a) is necessary to provide a measurement of size. The inset shows a higher magnification image of ND1. (c) A lower magnification SEM image of an etched silicon map before nanodiamonds are introduced. Vertical and horizontal grid lines are visible along with arcs that are centered on the center of the silicon map. The grid lines visible in (a), (b) are the intersection of horizontal, vertical, and arc markings. In (a), the grid lines are the dark lines to the right of ND1, and in (b) the grid lines are the bright lines to the right of ND1. Each small square has dimensions $25\times 25\mu \mathrm{m}$. (d) ${\text{NV}}^{-}$ center schematic, three carbon atoms shown in blue (dark gray) at the bottom, one nitrogen in red (gray) at the top, and the transparent (light grey) central sphere is the vacant lattice site.

Figure 2

(a) Fluorescence intensity against $g^{\left(2\right)}\left(0\right)$ value. $0\le g^{\left(2\right)}\left(0\right)<0.5$ indicates a single center, $0.5\le g^{\left(2\right)}\left(0\right)<0.67$ indicates two, $0.67\le g^{\left(2\right)}\left(0\right)<0.75$ indicates three, and $g^{\left(2\right)}\left(0\right)\ge 0.75$ indicates more than three. A total of 175 nanodiamonds containing ${\text{NV}}^{-}$(s) were surveyed. (b) An example Hanbury Brown-Twiss (HBT) measurement of photon correlation for ND1. The black curve is a fit to $1-a[bexp(-\frac{\left|\tau \right|}{c})+(1-b)exp(-\frac{\left|\tau \right|}{d})]$, where $g^{\left(2\right)}\left(0\right)=1-a$. For this plot, $g^{\left(2\right)}\left(0\right)=0.38\pm 0.04$. After multiple measurements, the value quoted in the text of $g^{\left(2\right)}\left(0\right)=0.39\pm 0.02$ is reached.

Figure 3

(a) Spin-echo decay measurements of ND1. For the Hahn echo, XY8-1, and XY8-4 pulse sequences, we measure coherence times $T_2^{\text{HE}}=177\pm 24\mu \mathrm{s}, T_2^{\text{XY8-1}}=323\pm 21\mu \mathrm{s}$, and $T_2^{\text{XY8-4}}=462\pm 130\mu \mathrm{s}$, respectively. Lines fit by $a+bexp[-{(t/T_2)}^n]$. (b) The $532\mathrm{n}\mathrm{m}$ laser and microwave (MW) pulses applied for the Hahn echo and XY8-n sequences. The bracketed block in XY8-n is repeated n times.

Figure 4

Hahn echo measurements on six nanodiamonds other than ND1 containing single ${\text{NV}}^{-}$. Error bars are not shown as they are smaller than the data points. Dashed lines fit by $a+bexp[-{(t/T_2)}^n]$ or, for those figures that contain ${}^{13}\mathrm{C}$ revivals, $a+bexp[-{(t/T_2)}^n](1-c{sin\left(\frac{\pi t}{d}\right)}^2{sin\left(\frac{\pi t}{g}\right)}^2)$ [53, 55]. For the plots with revivals, the periods are as follows: for ND2: $d=3.6\pm 0.2\mu \mathrm{s}, g=4.0\pm 0.3\mu \mathrm{s}$, and for ND6: $d=6.96\pm 0.05\mu \mathrm{s}, g=13.9\pm 0.1\mu \mathrm{s}$.

Figure 5

Confocal fluorescence microscopy (CFM) images of ND1 identified by a green (light gray) dashed ring. (a) CFM taken prior to scanning electron microscopy (SEM) observation of ND1. (b) CFM taken after SEM observation of ND1. A bright rectangle of background fluorescence is visible surrounding ND1. This background is not present prior to SEM observation. Images plotted using the Qudi software suite [45].

Figure 6

Hahn echo measurement of ND1 with shorter inter-point spacing than in Fig. 3 of the main text. Revivals in spin-echo signal due to ${}^{13}\mathrm{C}$ spins are well fit by $a+bexp[-{(t/T_2)}^n](1-c{sin\left(\frac{\pi t}{d}\right)}^2{sin\left(\frac{\pi t}{g}\right)}^2)$ [53, 55], where $d=6.975\pm 0.007\mu \mathrm{s}$ and $g=11.44\pm 0.02\mu \mathrm{s}$.

Figure 7

Spin echo $T_2$ times against the estimated maximum distance the ${\text{NV}}^{-}$ could be from the surface ($R_{\text{max}}$), plotted for all seven nanodiamonds that contained an ${\text{NV}}^{-}$ for which a $T_2$ was measured.