# Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond

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## Abstract

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“The only thing you can do easily is be wrong, and that’s hardly worth the effort.”—Norton Juster, The Phantom Tollbooth

## 1. Introduction

## 2. Quantifying Readout Performance

#### 2.1. Photon Summation

#### 2.2. Thresholding

#### 2.3. Spin-Readout Noise

#### 2.4. Averaging

#### 2.5. Sensitivity

#### 2.6. Summary

## 3. Traditional Spin Readout

## 4. Maximizing Photon Collection Efficiency

#### 4.1. Crystal Alignment

#### 4.2. Photonic Structures

#### 4.3. Waveguides and Cavities

#### 4.4. Summary

## 5. Radiative Lifetime Engineering

## 6. Low-Temperature Resonant Readout

## 7. Nuclear-Assisted Readout

## 8. Spin-to-Charge Conversion

## 9. Photocurrent Readout

## 10. Accounting for Measurement Overhead

## 11. Real-Time Signal Processing Techniques

## 12. Discussion

## 13. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NV | Nitrogen-Vacancy |

PL | Photoluminescence |

SNR | Signal-to-noise ratio |

SCC | Spin-to-charge conversion |

ISC | Intersystem crossing |

LAC | Level anti-crossing |

SQL | Standard quantum limit |

ZPL | Zero-phonon line |

## Appendix A. Spin-Readout Noise Calculations

#### Appendix A.1. Photon Summation

#### Appendix A.2. Thresholding

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**Figure 1.**The diamond NV center. (

**a**) Room temperature electronic structure. Solid lines indicate radiative transitions (with corresponding rate ${\gamma}^{\mathrm{r}}$), and dashed lines represent nonradiative intersystem crossing (ISC) transitions (with rates ${\gamma}_{i}^{\mathrm{r}}$ and ${\kappa}_{i}$ for the excited and ground-state spin projection i, respectively). Solid black arrows represent the zero phonon lines of the triplet and singlet manifolds. (

**b**) Low temperature electronic structure of the nitrogen-vacancy (NV) center triplet manifold. Individual transitions used for spin pumping and resonant readout are indicated. (

**c**) Room temperature transient fluorescence response for the spin states ${m}_{s}=0,1$ produced by 532 $\mathrm{n}$$\mathrm{m}$ illumination. The optimal counting duration is indicated by the dashed vertical lines. Reprinted with permission from [42], Optical Society of America. (

**d**) Rabi nutations of the ground-state spin at room temperature, measured using traditional PL readout for an NV center beneath a planar diamond surface, with an NA = 0.9 objective. The left and right axes plot the average detected photons per measurement and normalized PL, respectively. The solid curve is a fit to the data.

**Figure 2.**Photonic devices for improving collection efficiency (

**a**) Scanning electron micrograph (SEM) of a solid immersion lens fabricated around an NV center. Inset: confocal PL image. (

**b**) Diamond nanopillar array fabricated on a [111]-oriented diamond. Source: Neu et al. [58]. (

**c**) Metalens fabricated above an NV center to act as an immersion objective. Inset: SEM of nanopillar metalens elements. Source: Grote et al. [57]. (

**d**) Schematic of diamond membrane embedded in an open micro-cavity. Source: Riedel et al. [59]. (

**e**) SEM of a hybrid diamond/silicon-nitride waveguide and a PL map of an NV center within the diamond waveguide. Source: Mouradian et al. [60].

**Figure 3.**Radiative lifetime engineering with plasmonic devices. Recent examples of plasmonic device geometries include: (

**a**) a shallow NV center situated below an optical plasmonic antenna; (

**b**) nanodiamonds containing NV ensembles deposited over TiN plasmonic resonators; and (

**c**) a hybrid dielectric-metal hourglass structure designed to couple to a shallow NV. Panel (

**d**) shows the highly directional angular emission distribution that results from hybrid hourglass plasmonic devices (the device shown in (c) is labeled MD2). “MD” stands for metal-dielectric. See [91] for details on the design variations in (d). Panel (a) is reprinted with permission from [76]. Copyright 2015 by the American Physical Society. Panel (b) is reprinted with permission from [92]. Copyright 2017 by the American Physical Society. Panels (c,d) are from Karamlou et al. [91].

**Figure 4.**Nuclear-assisted readout. (

**a**) Energy-level diagram showing the splitting of the ${m}_{s}=-1$ spin state into a triplet through hyperfine coupling with ${}^{14}$N (${A}_{\left|\right|}=2.16\mathrm{MHz}$). The data at the right show the normalized PL response to a pulsed electron-spin resonance measurement. (

**b**) Quantum circuit and measurement timing diagram used to detect proteins on the diamond surface using a nitrogen nuclear spin as a memory for storage. (

**c**) The readout fidelity, the inverse of spin readout noise (Equation (24)), as a function of repetitive readout cycles. Panels (b,c) are from [17]. Reprinted with permission from AAAS.

**Figure 5.**Spin-to-charge conversion (SCC). (

**a**,

**b**) Schematics of the spin-dependent ionization pathways for singlet spin-to-charge conversion (S-SCC) and triplet-SCC (T-SCC), respectively. Solid lines represent laser induced transitions, while dashed lines represent decay transitions. (

**c**) Histogram of photon counts during a 3 $\mathrm{m}$$\mathrm{s}$ charge readout measurement with 592 $\mathrm{n}$$\mathrm{m}$ illumination [43]. (

**d**) Timing diagram for the S-SCC protocol. (

**e**) NV${}^{-}$ population for different initial spin states as a function of the number of S-SCC repeats, N [43]. (

**f**) Single-shot (S.S.) SNR for S-SCC as a function of N for the protocol as-demonstrated and for the optimal case assuming $100\%$ singlet ionization probability. The corresponding traditional-PL SNR is the dashed line at SNR = 0.055 [43]. Panels (

**c**–

**f**) are from [43]. Copyright 2016 by the American Physical Society.

**Figure 6.**Quantifying SCC improvements in experiments. (

**a**) Time averaged SNR scaled by $\sqrt{\tau}$, for the traditional PL and triplet-SCC protocols as a function of saturation green-illumination count rate, assuming ${t}_{W}=200\mathsf{\mu}\mathrm{s}$. The T-SCC SNR is numerically calculated using the model in [33]. (

**b**) Speedup comparison for the various SCC techniques as a function of green saturation count rate, assuming ${t}_{W}=200\mathsf{\mu}\mathrm{s}$. (

**c**) Speedup comparison as a function of ${t}_{W}$, assuming a green saturation count rate of 250 $\mathrm{k}$$\mathrm{Cts}$/$\mathrm{s}$. The dashed line indicates the “break-even” point, where SCC provides a more efficient readout than traditional PL. The speedup in (b,c) is calculated using data reported in [33,43].

**Figure 7.**Complementary approaches for enhanced spin readout. Existing techniques have advantages for particular applications. Future research can consider the potential for combining multiple techniques in order to achieve fast, high-fidelity, single-shot readout (SSRO) of the NV center’s electron spin at room temperature. The highest reported traditional PL SNR, as well as the SCC SNR, are from Shields et al. [33]. The highest nuclear assisted SNR is from Neumann et al. [14].

**Table 1.**Compilation of spin-readout metrics, their formal relation to differential SNR, and common use cases. PL, photoluminescence; SNR, Signal-to-noise ratio.

Metric | Relation to SNR | Use Case |
---|---|---|

Contrast, C, & Count rate, ${\alpha}_{0}$ | $\mathrm{SNR}=\sqrt{{\alpha}_{0}}\frac{C}{\sqrt{2-C}}$ | traditional PL readout |

Spin-readout noise, ${\sigma}_{R}$ | $\mathrm{SNR}=\sqrt{\frac{2}{{\sigma}_{R}^{2}-1}}$ | magnetometry |

Fidelity, $\mathcal{F}$ | $\mathrm{SNR}=\frac{{p}_{0|0}-{p}_{0|1}}{\sqrt{{p}_{0|0}(1-{p}_{0|0})+{p}_{0|1}(1-{p}_{0|1})}}$ | quantum algorithms, large signals |

Repeats for $\langle \mathrm{SNR}\rangle =1$ | $N={\left(\frac{1}{\mathrm{SNR}}\right)}^{2}$ | magnetometry, general experiments |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Hopper, D.A.; Shulevitz, H.J.; Bassett, L.C.
Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond. *Micromachines* **2018**, *9*, 437.
https://doi.org/10.3390/mi9090437

**AMA Style**

Hopper DA, Shulevitz HJ, Bassett LC.
Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond. *Micromachines*. 2018; 9(9):437.
https://doi.org/10.3390/mi9090437

**Chicago/Turabian Style**

Hopper, David A., Henry J. Shulevitz, and Lee C. Bassett.
2018. "Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond" *Micromachines* 9, no. 9: 437.
https://doi.org/10.3390/mi9090437