Deep Three-Dimensional Solid-State Qubit Arrays with Long-Lived Spin Coherence

Nitrogen-vacancy centers (NVCs) in diamond show promise for quantum computing, communication, and sensing. However, the best current method for entangling two NVCs requires that each one is in a separate cryostat, which is not scalable. We show that single NVCs can be laser written 6–15-µm deep inside of a diamond with spin coherence times that are an order of magnitude longer than previous laser-written NVCs and at least as long as naturally occurring NVCs. This depth is suitable for integration with solid immersion lenses or optical cavities and we present depth-dependent ${\mathrm{T}}_2$ measurements. 200 000 of these NVCs would fit into one diamond.

Figure 1

Laser writing of 3D arrays of nitrogen vacancy centers in diamond with long spin coherence. (a) Schematic of the laser-writing setup. SLM is a spatial light modulator. CCD is a camera. (b) Wide-field transmission microscopy of the laser-written markers surrounding the arrays. The large boxes labeled A-G are 110 µm across.

Figure 2

Confocal imaging of a three-dimensional array of defects in diamond. Top row: (a)–(d) are in the X-Y plane at depths of 6, 9, 12, and 15 µm, respectively, before annealing: each spot is an ensemble of vacancies. (e) A vertical section in the X-Z plane. Bottom row: The same volume after annealing out the vacancies: the spots are nitrogen vacancy centers. In 9% of the target sites, NVCs are created, almost all as single centers (circled).

Figure 3

Fraction of single nitrogen vacancy centers compared to doubles and triples. (a) HBT measurement of the photon arrival time for NVC1. (b) HBT measurements reveal the fraction of single, double, and triple NVCs produced in three of the 3-µm pitch arrays with different laser-write pulse energies. (c) The frequency of the measured g²(0) for array M with no background subtraction.

Figure 4

Nitrogen vacancy center electron spin coherence times. (a) Spin-echo decays for adjacent, aligned NVCs [labeled NVC1 and NVC2, as shown in Figs. 4 and 1] fitted with $A{e}^{-{(t/T_2)}^n}$. NVC1 has T₂ = 710 ± 40 µs with n = 2.4 ± 0.4, while NVC2 has T₂ = 690 ± 90 µs with n = 2.0 ± 0.8. (b) Enlarged confocal image of NVC1 and NVC2. (c) Confocal image of a NVC between two laser-written electrical wires from another region of the same diamond. (d) Spin-echo coherence times measured for sites in arrays M (17.5 nJ) and I (17 nJ), which have a 3-µm pitch, as a function of NVC depth. (e) Using XY8-4 dynamic decoupling achieves T₂ = 2.4 ± 0.6 ms with n = 1.1 ± 0.4 on NVC1. For comparison, the longitudinal lifetime, T₁, of this site is 3.0 ± 0.7 ms.

Figure 5

Photoluminescence spectrum of (a) a single site at 25-µm depth in array A (19 nJ) before the sample was annealed at 1000 °C. (b) A single site M9-4 (labeled NVC2 above), which shows the characteristic emission of NVC⁻ (a negatively charged NVC) with a zero phonon line (ZPL) at 637.7 nm.

Figure 6

Proportion of sites fluorescing after the annealing process.

Figure 7

Array I has the most variation in strain as determined by crossed-polarizer microscopy (a) and Metripol measurements of $|\sin (\delta )|$ (b) and orientation (d). These images are orientated to match confocal microscopy. (c) Probability of single or double NVC formation in any of the layers of array I, binned by relative crossed-polarizer intensity (normalized over the diamond). Metripol measurements show only one order of phase shift so the brightness in the cross-polar image indicates higher birefringence, and hence strain, aggregated through the diamond. The fit to a binary logistic regression model is shown with a 1 standard deviation confidence interval, however, the correlation is not significant (p = 0.3), indicating that NVC yield is not correlated with strain. The probability of forming NVCs is taken as the fraction of sites in each cross-polar brightness grouping which develop a single or double NVC (optically resolvable or not).

Figure 8

Hanbury Brown-Twiss measurements are used to identify single NVC sites. (a)–(c) HBT photon arrival time auto-correlation measurements for three NVC sites in array H showing examples of single, double, and triple NVC classifications, respectively. (d) Statistics for all 3-µm pitch arrays, which show fluorescence, including incomplete measurement coverage of array H with approximately 20% yield of single NVCs, 2.5% double NVCs, and 0.3% triple NVCs, trading increased yield for a higher proportion of multiple NVC sites.

Figure 9

Layers of array M (17.5 nJ, 3 µm pitch) with single NVC (circle) and double NVC (diamond: determined by HBT, square: optically resolvable). Single NVC sites where T₂ is measured are labeled (M9-5 and M9-4 are the highlighted sites NVC1 and NVC2 in the main paper). (a)–(e) are, respectively, at depths of 3, 6, 9, 12, and 15 µm below the surface.

Figure 10

Layers of array I (17 nJ, 3 µm pitch) with single NVC (circle) and double NVC (diamond: determined by HBT, square: optically resolvable). Single NVC sites where T₂ is measured are labeled. (a)–(d) are, respectively, at depths of 6, 9, 12, and 15 µm below the surface.

Figure 11

Examples of T₂ spin-echo coherence time measurements from arrays M and I along with a histogram of the echo decay coherence times

Figure 12

Positioning precision of single nitrogen vacancy centers in array M. (a),(c) In the X-Y plane of the array. (b) In the vertical Z direction. Standard deviations are 220 and 250 nm, respectively, which is consistent with the mean separation of nitrogen in EL grade CVD diamond. (d) Change in the relative displacement between two points over time as measured by fitting the PSF and using a third point as a reference between each measurement.