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Quantum guidelines for solid-state spin defects

An Author Correction to this article was published on 14 October 2021

This article has been updated

Abstract

Defects with associated electron and nuclear spins in solid-state materials have a long history relevant to quantum information science that goes back to the first spin echo experiments with silicon dopants in the 1950s. Since the turn of the century, the field has rapidly spread to a vast array of defects and host crystals applicable to quantum communication, sensing and computing. From simple spin resonance to long-distance remote entanglement, the complexity of working with spin defects is fast increasing, and requires an in-depth understanding of the defects’ spin, optical, charge and material properties in this modern context. This is especially critical for discovering new relevant systems for specific quantum applications. In this Review, we expand upon all the key components of solid-state spin defects, with an emphasis on the properties of defects and of the host material, on engineering opportunities and on other pathways for improvement. This Review aims to be as defect and material agnostic as possible, with some emphasis on optical emitters, providing broad guidelines for the field of solid-state spin defects for quantum information.

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Fig. 1: Spin defects in the solid state for quantum information science.
Fig. 2: Electron spin relaxation and coherence.
Fig. 3: Electron and nuclear spin control.
Fig. 4: Optical properties of spin defects in the solid state.
Fig. 5: Considerations for optical coherence.
Fig. 6: Charge state properties of solid-state defects.
Fig. 7: Defect host material considerations.

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References

  1. Steger, M. et al. Quantum information storage for over 180 s using donor spins in a 28Si “semiconductor vacuum”. Science 336, 1280–1283 (2012).

    CAS  Google Scholar 

  2. Gordon, J. P. & Bowers, K. D. Microwave spin echoes from donor electrons in silicon. Phys. Rev. Lett. 1, 368–370 (1958).

    CAS  Google Scholar 

  3. Maiman, T. H. Stimulated optical radiation in ruby. Nature 187, 493–494 (1960).

    Google Scholar 

  4. Abraham, M., Weeks, R. A., Clark, G. W. & Finch, C. B. Electron spin resonance of rare-earth ions in thorium oxide: Yb3+ and Er3+. Phys. Rev. 137, A138–A142 (1965).

    Google Scholar 

  5. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    CAS  Google Scholar 

  6. Ichimura, K. A simple frequency-domain quantum computer with ions in a crystal coupled to a cavity mode. Opt. Commun. 196, 119–125 (2001).

    CAS  Google Scholar 

  7. Gruber, A. et al. Scanning confocal optical microscopy and magnetic resonance on single defect centers. Science 276, 2012–2014 (1997).

    CAS  Google Scholar 

  8. Bradac, C., Gao, W., Forneris, J., Trusheim, M. E. & Aharonovich, I. Quantum nanophotonics with group IV defects in diamond. Nat. Commun. 10, 5625 (2019).

    CAS  Google Scholar 

  9. Son, N. T. et al. Developing silicon carbide for quantum spintronics. Appl. Phys. Lett. 116, 190501 (2020).

    CAS  Google Scholar 

  10. Barry, J. F. et al. Sensitivity optimization for NV-diamond magnetometry. Rev. Mod. Phys. 92, 15004 (2020).

    CAS  Google Scholar 

  11. Jaskula, J. C. et al. Improved quantum sensing with a single solid-state spin via spin-to-charge conversion. Phys. Rev. Appl. 11, 064003 (2019).

    CAS  Google Scholar 

  12. Bradley, C. E. et al. A ten-qubit solid-state spin register with quantum memory up to one minute. Phys. Rev. X 9, 031045 (2019).

    CAS  Google Scholar 

  13. Simmons, S. et al. Entanglement in a solid-state spin ensemble. Nature 470, 69–72 (2011).

    CAS  Google Scholar 

  14. Morello, A. et al. Single-shot readout of an electron spin in silicon. Nature 467, 687–691 (2010).

    CAS  Google Scholar 

  15. Hensen, B. et al. Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682–686 (2015).

    CAS  Google Scholar 

  16. Wolfowicz, G. et al. Coherent storage of microwave excitations in rare-earth nuclear spins. Phys. Rev. Lett. 114, 170503 (2015).

    Google Scholar 

  17. Toth, M. & Aharonovich, I. Single photon sources in atomically thin materials. Annu. Rev. Phys. Chem. 70, 123–142 (2019).

    CAS  Google Scholar 

  18. Liu, X. & Hersam, M. C. 2D materials for quantum information science. Nat. Rev. Mater. 4, 669–684 (2019).

    Google Scholar 

  19. Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013).

    CAS  Google Scholar 

  20. Casola, F., van der Sar, T. & Yacoby, A. Probing condensed matter physics with magnetometry based on nitrogen-vacancy centres in diamond. Nat. Rev. Mater. 3, 17088 (2018).

    CAS  Google Scholar 

  21. Lohrmann, A., Johnson, B. C., McCallum, J. C. & Castelletto, S. A review on single photon sources in silicon carbide. Rep. Prog. Phys. 80, 034502 (2017).

    CAS  Google Scholar 

  22. Morley, G. W. Towards spintronic quantum technologies with dopants in silicon. Electron. Paramagnetic Reson. 24, 62–76 (2015).

    CAS  Google Scholar 

  23. Zhong, T. & Goldner, P. Emerging rare-earth doped material platforms for quantum nanophotonics. Nanophotonics 8, 2003–2015 (2019).

    CAS  Google Scholar 

  24. Ivády, V., Abrikosov, I. A. & Gali, A. First principles calculation of spin-related quantities for point defect qubit research. NPJ Comput. Mater. 4, 76 (2018).

    Google Scholar 

  25. Heremans, F. J., Yale, C. G. & Awschalom, D. D. Control of spin defects in wide-bandgap semiconductors for quantum technologies. Proc. IEEE 104, 2009–2023 (2016).

    CAS  Google Scholar 

  26. Bassett, L. C., Alkauskas, A., Exarhos, A. L. & Fu, K. C. Quantum defects by design. Nanophotonics 8, 1867–1888 (2019).

    CAS  Google Scholar 

  27. Awschalom, D. D., Hanson, R., Wrachtrup, J. & Zhou, B. B. Quantum technologies with optically interfaced solid-state spins. Nat. Photonics 12, 516–527 (2018).

    CAS  Google Scholar 

  28. Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J. Material platforms for spin-based photonic quantum technologies. Nat. Rev. Mater. 3, 38–51 (2018).

    Google Scholar 

  29. Chatterjee, A. et al. Semiconductor qubits in practice. Nat. Rev. Phys. 3, 157–177 (2021).

    Google Scholar 

  30. Jin, J. et al. Telecom-wavelength atomic quantum memory in optical fiber for heralded polarization qubits. Phys. Rev. Lett. 115, 140501 (2015).

    Google Scholar 

  31. Tyryshkin, A. M., Lyon, S. A., Astashkin, A. V. & Raitsimring, A. M. Electron spin relaxation times of phosphorus donors in silicon. Phys. Rev. B 68, 193207 (2003).

    Google Scholar 

  32. Bar-Gill, N., Pham, L. M., Jarmola, A., Budker, D. & Walsworth, R. L. Solid-state electronic spin coherence time approaching one second. Nat. Commun. 4, 1743 (2013).

    CAS  Google Scholar 

  33. Gugler, J. et al. Ab initio calculation of the spin lattice relaxation time T1 for nitrogen-vacancy centers in diamond. Phys. Rev. B 98, 214442 (2018).

    CAS  Google Scholar 

  34. Norambuena, A. et al. Spin-lattice relaxation of individual solid-state spins. Phys. Rev. B 97, 094304 (2018).

    CAS  Google Scholar 

  35. Shrivastava, K. N. Theory of spin–lattice relaxation. Phys. Status Solidi 117, 437–458 (1983).

    CAS  Google Scholar 

  36. Abragam, A. & Bleaney, B. Electron Paramagnetic Resonance of Transition Ions (Oxford Univ. Press, 2012).

  37. Jarmola, A., Acosta, V. M., Jensen, K., Chemerisov, S. & Budker, D. Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond. Phys. Rev. Lett. 108, 197601 (2012).

    CAS  Google Scholar 

  38. Castner, T. G. Raman spin-lattice relaxation of shallow donors in silicon. Phys. Rev. 130, 58–75 (1963).

    CAS  Google Scholar 

  39. Green, B. L. et al. Neutral silicon-vacancy center in diamond: spin polarization and lifetimes. Phys. Rev. Lett. 119, 096402 (2017).

    CAS  Google Scholar 

  40. Orbach, R. Spin-lattice relaxation in rare-earth salts. Proc. R. Soc. Lond. A Math. Phys. Sci. 264, 458–484 (1961).

    CAS  Google Scholar 

  41. Xu, J. et al. Spin-phonon relaxation from a universal ab initio density-matrix approach. Nat. Commun. 11, 2780 (2020).

    CAS  Google Scholar 

  42. Park, J., Zhou, J.-J. & Bernardi, M. Spin-phonon relaxation times in centrosymmetric materials from first principles. Phys. Rev. B 101, 045202 (2020).

    CAS  Google Scholar 

  43. Kurkin, I. N. & Chernov, K. P. EPR and spin-lattice relaxation of rare-earth activated centres in Y2SiO5 single crystals. Phys. B+C. 101, 233–238 (1980).

    CAS  Google Scholar 

  44. Meesala, S. et al. Strain engineering of the silicon-vacancy center in diamond. Phys. Rev. B 97, 205444 (2018).

    CAS  Google Scholar 

  45. Wolfowicz, G. et al. Vanadium spin qubits as telecom quantum emitters in silicon carbide. Sci. Adv. 6, eaaz1192 (2020).

    CAS  Google Scholar 

  46. Gilardoni, C. M. et al. Spin-relaxation times exceeding seconds for color centers with strong spin–orbit coupling in SiC. New J. Phys. 22, 103051 (2020).

    CAS  Google Scholar 

  47. Kukharchyk, N., Sholokhov, D., Kalachev, A. A. & Bushev, P. A. Enhancement of optical coherence in 167Er:Y2SiO5 crystal at sub-Kelvin temperatures. Preprint at arXiv https://arxiv.org/abs/1910.03096 (2019).

  48. Paik, S.-Y., Lee, S.-Y., Baker, W. J., McCamey, D. R. & Boehme, C. T1 and T2 spin relaxation time limitations of phosphorous donor electrons near crystalline silicon to silicon dioxide interface defects. Phys. Rev. B 81, 075214 (2010).

    Google Scholar 

  49. Rosskopf, T. et al. Investigation of surface magnetic noise by shallow spins in diamond. Phys. Rev. Lett. 112, 147602 (2014).

    CAS  Google Scholar 

  50. Myers, B. A. et al. Probing surface noise with depth-calibrated spins in diamond. Phys. Rev. Lett. 113, 27602 (2014).

    CAS  Google Scholar 

  51. Sangtawesin, S. et al. Origins of diamond surface noise probed by correlating single-spin measurements with surface spectroscopy. Phys. Rev. X 9, 031052 (2019).

    CAS  Google Scholar 

  52. Tetienne, J.-P. et al. Spin relaxometry of single nitrogen-vacancy defects in diamond nanocrystals for magnetic noise sensing. Phys. Rev. B 87, 235436 (2013).

    Google Scholar 

  53. Ariyaratne, A., Bluvstein, D., Myers, B. A. & Jayich, A. C. B. Nanoscale electrical conductivity imaging using a nitrogen-vacancy center in diamond. Nat. Commun. 9, 2406 (2018).

    Google Scholar 

  54. Morton, J. J. L. et al. Solid-state quantum memory using the 31P nuclear spin. Nature 455, 1085–1088 (2008).

    CAS  Google Scholar 

  55. Maurer, P. C. et al. Room-temperature quantum bit memory exceeding one second. Science 336, 1283–1286 (2012).

    CAS  Google Scholar 

  56. Bienfait, A. et al. Controlling spin relaxation with a cavity. Nature 531, 74–77 (2016).

    CAS  Google Scholar 

  57. Schweiger, A. & Jeschke, G. Principles of Pulse Electron Paramagnetic Resonance Vol. 4 (Oxford Univ. Press, 2001).

  58. Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nat. Mater. 11, 143–147 (2011).

    Google Scholar 

  59. Wolfowicz, G. et al. Atomic clock transitions in silicon-based spin qubits. Nat. Nanotechnol. 8, 881–881 (2013).

    CAS  Google Scholar 

  60. Miao, K. C. et al. Universal coherence protection in a solid-state spin qubit. Science 369, 1493–1497 (2020).

    CAS  Google Scholar 

  61. Yang, W. & Liu, R. Quantum many-body theory of qubit decoherence in a finite-size spin bath. II. Ensemble dynamics. Phys. Rev. B 79, 115320 (2009).

    Google Scholar 

  62. Witzel, W. M. & Das Sarma, S. Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment. Phys. Rev. B 74, 035322 (2006).

    Google Scholar 

  63. Bar-Gill, N. et al. Suppression of spin-bath dynamics for improved coherence of multi-spin-qubit systems. Nat. Commun. 3, 858 (2012).

    CAS  Google Scholar 

  64. Seo, H. et al. Quantum decoherence dynamics of divacancy spins in silicon carbide. Nat. Commun. 7, 12935 (2016).

    CAS  Google Scholar 

  65. Balian, S. J., Wolfowicz, G., Morton, J. J. L. & Monteiro, T. S. Quantum-bath-driven decoherence of mixed spin systems. Phys. Rev. B 89, 045403 (2014).

    Google Scholar 

  66. Kanai, S. et al. Generalized scaling of spin qubit coherence in over 12,000 host materials. Preprint at arXiv https://arxiv.org/abs/2102.02986 (2021).

  67. Salikhov, K. M., Dzuba, S. A. & Raitsimring, A. M. The theory of electron spin-echo signal decay resulting from dipole-dipole interactions between paramagnetic centers in solids. J. Magn. Reson. 42, 255–276 (1981).

    CAS  Google Scholar 

  68. Mims, W. B. Phase memory in electron spin echoes, lattice relaxation effects in CaWO4: Er, Ce, Mn. Phys. Rev. 168, 370–389 (1968).

    CAS  Google Scholar 

  69. Kukharchyk, N. et al. Optical coherence of 166Er:7LiYF4 crystal below 1 K. New J. Phys. 20, 023044 (2018).

    Google Scholar 

  70. Car, B., Veissier, L., Louchet-Chauvet, A., Le Gouët, J. L. & Chanelière, T. Optical study of the anisotropic erbium spin flip-flop dynamics. Phys. Rev. B 100, 165107 (2019).

    CAS  Google Scholar 

  71. Tosi, G. et al. Silicon quantum processor with robust long-distance qubit couplings. Nat. Commun. 8, 450 (2017).

    Google Scholar 

  72. Ferrón, A., Rodríguez, S. A., Gómez, S. S., Lado, J. L. & Fernández-Rossier, J. Single spin resonance driven by electric modulation of the g-factor anisotropy. Phys. Rev. Res. 1, 033185 (2019).

    Google Scholar 

  73. Park, D. K., Park, S., Jee, H. & Lee, S. Electron spin relaxations of phosphorus donors in bulk silicon under large electric field. Sci. Rep. 9, 2951 (2019).

    Google Scholar 

  74. Kim, M. et al. Decoherence of near-surface nitrogen-vacancy centers due to electric field noise. Phys. Rev. Lett. 115, 087602 (2015).

    CAS  Google Scholar 

  75. Rogers, L. J. et al. All-optical initialization, readout, and coherent preparation of single silicon-vacancy spins in diamond. Phys. Rev. Lett. 113, 263602 (2014).

    Google Scholar 

  76. Witzel, W. M., Carroll, M. S., Morello, A., Cywiński, Ł. & Das Sarma, S. Electron spin decoherence in isotope-enriched silicon. Phys. Rev. Lett. 105, 187602 (2010).

    Google Scholar 

  77. Bourassa, A. et al. Entanglement and control of single nuclear spins in isotopically engineered silicon carbide. Nat. Mater. 19, 1319–1325 (2020).

    CAS  Google Scholar 

  78. Balasubramanian, G. et al. Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8, 383–387 (2009).

    CAS  Google Scholar 

  79. Ye, M., Seo, H. & Galli, G. Spin coherence in two-dimensional materials. NPJ Comput. Mater. 5, 44 (2019).

    Google Scholar 

  80. Abe, E., Itoh, K. M., Isoya, J. & Yamasaki, S. Electron-spin phase relaxation of phosphorus donors in nuclear-spin-enriched silicon. Phys. Rev. B 70, 033204 (2004).

    Google Scholar 

  81. Longdell, J. J., Alexander, A. L. & Sellars, M. J. Characterization of the hyperfine interaction in europium-doped yttrium orthosilicate and europium chloride hexahydrate. Phys. Rev. B 74, 195101 (2006).

    Google Scholar 

  82. McAuslan, D. L., Bartholomew, J. G., Sellars, M. J. & Longdell, J. J. Reducing decoherence in optical and spin transitions in rare-earth-metal-ion–doped materials. Phys. Rev. A 85, 032339 (2012).

    Google Scholar 

  83. Onizhuk, M. et al. Probing the coherence of solid-state qubits at avoided crossings. PRX Quantum 2, 010311 (2021).

    Google Scholar 

  84. Parker, A. J., Wang, H.-J., Li, Y., Pines, A. & King, J. P. Decoherence-protected transitions of nitrogen vacancy centers in 99% 13C-enriched diamond. Preprint at arXiv https://arxiv.org/abs/1506.05484 (2015).

  85. Barfuss, A., Teissier, J., Neu, E., Nunnenkamp, A. & Maletinsky, P. Strong mechanical driving of a single electron spin. Nat. Phys. 11, 820–824 (2015).

    CAS  Google Scholar 

  86. Stark, A. et al. Clock transition by continuous dynamical decoupling of a three-level system. Sci. Rep. 8, 14807 (2018).

    Google Scholar 

  87. Viola, L., Knill, E. & Lloyd, S. Dynamical decoupling of open quantum systems. Phys. Rev. Lett. 82, 2417–2421 (1999).

    CAS  Google Scholar 

  88. Bylander, J. et al. Noise spectroscopy through dynamical decoupling with a superconducting flux qubit. Nat. Phys. 7, 565–570 (2011).

    CAS  Google Scholar 

  89. Wang, Z.-H., de Lange, G., Ristè, D., Hanson, R. & Dobrovitski, V. V. Comparison of dynamical decoupling protocols for a nitrogen-vacancy center in diamond. Phys. Rev. B 85, 155204 (2012).

    Google Scholar 

  90. Pickard, C. J. & Mauri, F. First-principles theory of the EPR g tensor in solids: defects in quartz. Phys. Rev. Lett. 88, 086403 (2002).

    Google Scholar 

  91. Pfanner, G., Freysoldt, C., Neugebauer, J. & Gerstmann, U. Ab initio EPR parameters for dangling-bond defect complexes in silicon: Effect of Jahn-Teller distortion. Phys. Rev. B 85, 195202 (2012).

    Google Scholar 

  92. Gali, A., Fyta, M. & Kaxiras, E. Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors. Phys. Rev. B 77, 155206 (2008).

    Google Scholar 

  93. Seo, H., Ma, H., Govoni, M. & Galli, G. Designing defect-based qubit candidates in wide-gap binary semiconductors for solid-state quantum technologies. Phys. Rev. Mater. 1, 075002 (2017).

    Google Scholar 

  94. Ghosh, K., Ma, H., Gavini, V. & Galli, G. All-electron density functional calculations for electron and nuclear spin interactions in molecules and solids. Phys. Rev. Mater. 3, 043801 (2019).

    CAS  Google Scholar 

  95. Bodrog, Z. & Gali, A. The spin–spin zero-field splitting tensor in the projector-augmented-wave method. J. Phys. Condens. Matter 26, 015305 (2014).

    CAS  Google Scholar 

  96. Pica, G. et al. Hyperfine Stark effect of shallow donors in silicon. Phys. Rev. B 90, 195204 (2014).

    Google Scholar 

  97. Whiteley, S. J. et al. Spin–phonon interactions in silicon carbide addressed by Gaussian acoustics. Nat. Phys. 15, 490–495 (2019).

    CAS  Google Scholar 

  98. Kramers, H. A. Théorie générale de la rotation paramagnetique dans les cristaux. Proc. Acad. Amst. 33, 959–972 (1930).

    CAS  Google Scholar 

  99. Udvarhelyi, P., Shkolnikov, V. O., Gali, A., Burkard, G. & Pályi, A. Spin-strain interaction in nitrogen-vacancy centers in diamond. Phys. Rev. B 98, 075201 (2018).

    CAS  Google Scholar 

  100. Rao, K. R. K. & Suter, D. Nonlinear dynamics of a two-level system of a single spin driven beyond the rotating-wave approximation. Phys. Rev. A 95, 053804 (2017).

    Google Scholar 

  101. Laucht, A. et al. Electrically controlling single-spin qubits in a continuous microwave field. Sci. Adv. 1, e1500022 (2015).

    Google Scholar 

  102. Dreher, L. et al. Electroelastic hyperfine tuning of phosphorus donors in silicon. Phys. Rev. Lett. 106, 037601 (2011).

    CAS  Google Scholar 

  103. Klimov, P. V., Falk, A. L., Buckley, B. B. & Awschalom, D. D. Electrically driven spin resonance in silicon carbide color centers. Phys. Rev. Lett. 112, 087601 (2014).

    Google Scholar 

  104. Asaad, S. et al. Coherent electrical control of a single high-spin nucleus in silicon. Nature 579, 205–209 (2020).

    CAS  Google Scholar 

  105. Maity, S. et al. Coherent acoustic control of a single silicon vacancy spin in diamond. Nat. Commun. 11, 193 (2020).

    CAS  Google Scholar 

  106. Neuman, T. et al. A phononic bus for coherent interfaces between a superconducting quantum processor, spin memory, and photonic quantum networks. Preprint at arXiv https://arxiv.org/abs/2003.08383 (2020).

  107. Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrüggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: Design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005).

    CAS  Google Scholar 

  108. Tannús, A. & Garwood, M. Adiabatic pulses. NMR Biomed. 10, 423–434 (1997).

    Google Scholar 

  109. Wimperis, S. Broadband, narrowband, and passband composite pulses for use in advanced NMR experiments. J. Magn. Reson. A 109, 221–231 (1994).

    CAS  Google Scholar 

  110. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003).

    CAS  Google Scholar 

  111. Bergmann, K., Theuer, H. & Shore, B. W. Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 70, 1003–1025 (1998).

    CAS  Google Scholar 

  112. Baldit, E. et al. Identification of Λ-like systems in Er3+:Y2SiO5 and observation of electromagnetically induced transparency. Phys. Rev. B 81, 144303 (2010).

    Google Scholar 

  113. Yale, C. G. et al. Optical manipulation of the Berry phase in a solid-state spin qubit. Nat. Photonics 10, 184–189 (2016).

    CAS  Google Scholar 

  114. Yale, C. G. et al. All-optical control of a solid-state spin using coherent dark states. Proc. Natl Acad. Sci. USA 110, 7595–7600 (2013).

    CAS  Google Scholar 

  115. Zwier, O. V., O’Shea, D., Onur, A. R. & van der Wal, C. H. All-optical coherent population trapping with defect spin ensembles in silicon carbide. Sci. Rep. 5, 10931 (2015).

    CAS  Google Scholar 

  116. Evans, R. E. et al. Photon-mediated interactions between quantum emitters in a diamond nanocavity. Science 362, 662–665 (2018).

    CAS  Google Scholar 

  117. Zhou, B. B. et al. Holonomic quantum control by coherent optical excitation in diamond. Phys. Rev. Lett. 119, 140503 (2017).

    Google Scholar 

  118. Sekiguchi, Y., Niikura, N., Kuroiwa, R., Kano, H. & Kosaka, H. Optical holonomic single quantum gates with a geometric spin under a zero field. Nat. Photonics 11, 309–314 (2017).

    CAS  Google Scholar 

  119. Zhou, B. B. et al. Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system. Nat. Phys. 13, 330–334 (2017).

    CAS  Google Scholar 

  120. Bersin, E. et al. Individual control and readout of qubits in a sub-diffraction volume. NPJ Quantum Inf. 5, 39 (2019).

    Google Scholar 

  121. Chen, S., Raha, M., Phenicie, C. M., Ourari, S. & Thompson, J. D. Parallel single-shot measurement and coherent control of solid-state spins below the diffraction limit. Science 370, 592–595 (2020).

    CAS  Google Scholar 

  122. Reiserer, A. et al. Robust quantum-network memory using decoherence-protected subspaces of nuclear spins. Phys. Rev. X 6, 021040 (2016).

    Google Scholar 

  123. Kalb, N. et al. Entanglement distillation between solid-state quantum network nodes. Science 356, 928–932 (2017).

    CAS  Google Scholar 

  124. Waldherr, G. et al. Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014).

    CAS  Google Scholar 

  125. Taminiau, T. H., Cramer, J., Van Der Sar, T., Dobrovitski, V. V. & Hanson, R. Universal control and error correction in multi-qubit spin registers in diamond. Nat. Nanotechnol. 9, 171–176 (2014).

    CAS  Google Scholar 

  126. Zaiser, S. et al. Enhancing quantum sensing sensitivity by a quantum memory. Nat. Commun. 7, 12279 (2016).

    CAS  Google Scholar 

  127. Saeedi, K. et al. Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28. Science 342, 830–833 (2013).

    CAS  Google Scholar 

  128. Hartman, J. S. et al. NMR studies of nitrogen doping in the 4H polytype of silicon carbide: Site assignments and spin–lattice relaxation. J. Phys. Chem. C 113, 15024–15036 (2009).

    CAS  Google Scholar 

  129. Bergeron, L. et al. Characterization of the T center in 28Si. Preprint at arxiv https://arxiv.org/abs/2006.08794 (2020).

  130. Ohno, K. et al. Engineering shallow spins in diamond with nitrogen delta-doping. Appl. Phys. Lett. 101, 082413 (2012).

    Google Scholar 

  131. Rabeau, J. R. et al. Implantation of labelled single nitrogen vacancy centers in diamond using 15N. Appl. Phys. Lett. 88, 023113 (2006).

    Google Scholar 

  132. Wolfowicz, G. et al. Decoherence mechanisms of 209Bi donor electron spins in isotopically pure 28Si. Phys. Rev. B 86, 245301 (2012).

    Google Scholar 

  133. Taminiau, T. H. et al. Detection and control of individual nuclear spins using a weakly coupled electron spin. Phys. Rev. Lett. 109, 137602 (2012).

    CAS  Google Scholar 

  134. Kolkowitz, S., Unterreithmeier, Q. P., Bennett, S. D. & Lukin, M. D. Sensing distant nuclear spins with a single electron spin. Phys. Rev. Lett. 109, 137601 (2012).

    Google Scholar 

  135. Abobeih, M. H. et al. Atomic-scale imaging of a 27-nuclear-spin cluster using a quantum sensor. Nature 576, 411–415 (2019).

    CAS  Google Scholar 

  136. Zhao, N. et al. Sensing single remote nuclear spins. Nat. Nanotechnol. 7, 657–662 (2012).

    CAS  Google Scholar 

  137. Guichard, R., Balian, S. J., Wolfowicz, G., Mortemousque, P. A. & Monteiro, T. S. Decoherence of nuclear spins in the frozen core of an electron spin. Phys. Rev. B 91, 214303 (2015).

    Google Scholar 

  138. Kalb, N., Humphreys, P. C., Slim, J. J. & Hanson, R. Dephasing mechanisms of diamond-based nuclear-spin memories for quantum networks. Phys. Rev. A 97, 062330 (2018).

    CAS  Google Scholar 

  139. Blok, M. S., Kalb, N., Reiserer, A., Taminiau, T. H. & Hanson, R. Towards quantum networks of single spins: analysis of a quantum memory with an optical interface in diamond. Faraday Discuss. 184, 173–182 (2015).

    CAS  Google Scholar 

  140. Mądzik, M. T. et al. Controllable freezing of the nuclear spin bath in a single-atom spin qubit. Sci. Adv. 6, eaba3442 (2020).

    Google Scholar 

  141. Itoh, K. M. & Watanabe, H. Isotope engineering of silicon and diamond for quantum computing and sensing applications. MRS Commun. 4, 143–157 (2014).

    CAS  Google Scholar 

  142. Dibos, A. M., Raha, M., Phenicie, C. M. & Thompson, J. D. Atomic source of single photons in the telecom band. Phys. Rev. Lett. 120, 243601 (2018).

    CAS  Google Scholar 

  143. Spindlberger, L. et al. Optical properties of vanadium in 4H silicon carbide for quantum technology. Phys. Rev. Appl. 12, 014015 (2019).

    CAS  Google Scholar 

  144. Smith, A. M., Mancini, M. C. & Nie, S. Bioimaging: Second window for in vivo imaging. Nat. Nanotechnol. 4, 710–711 (2009).

    CAS  Google Scholar 

  145. Dréau, A. et al. Quantum frequency conversion of single photons from a nitrogen-vacancy center in diamond to telecommunication wavelengths. Phys. Rev. Appl. 9, 064031 (2018).

    Google Scholar 

  146. Pelc, J. S., Langrock, C., Zhang, Q. & Fejer, M. M. Influence of domain disorder on parametric noise in quasi-phase-matched quantum frequency converters. Opt. Lett. 35, 2804 (2010).

    CAS  Google Scholar 

  147. Kumar, P. Quantum frequency conversion. Opt. Lett. 15, 1476 (1990).

    CAS  Google Scholar 

  148. Siyushev, P. et al. Monolithic diamond optics for single photon detection. Appl. Phys. Lett. 97, 241902 (2010).

    CAS  Google Scholar 

  149. Huang, T. Y. et al. A monolithic immersion metalens for imaging solid-state quantum emitters. Nat. Commun. 10, 2392 (2019).

    Google Scholar 

  150. Butcher, A. et al. High-Q nanophotonic resonators on diamond membranes using templated atomic layer deposition of TiO2. Nano Lett. 20, 4603–4609 (2020).

    CAS  Google Scholar 

  151. Norman, V. A. et al. Novel color center platforms enabling fundamental scientific discovery. InfoMat https://doi.org/10.1002/inf2.12128 (2020).

    Article  Google Scholar 

  152. Kim, J.-H., Aghaeimeibodi, S., Carolan, J., Englund, D. & Waks, E. Hybrid integration methods for on-chip quantum photonics. Optica 7, 291–308 (2020).

    CAS  Google Scholar 

  153. Crook, A. L. et al. Purcell enhancement of a single silicon carbide color center with coherent spin control. Nano Lett. 20, 3427–3434 (2020).

    CAS  Google Scholar 

  154. Huang, K. & Rhys, A. Theory of light absorption and non-radiative transitions in F-centres. Proc. R. Soc. Lond. A Math. Phys. Sci. 204, 406–423 (1950).

    CAS  Google Scholar 

  155. Udvarhelyi, P. et al. Vibronic states and their effect on the temperature and strain dependence of silicon-vacancy qubits in 4H-SiC. Phys. Rev. Appl. 13, 054017 (2020).

    CAS  Google Scholar 

  156. Alkauskas, A., Buckley, B. B., Awschalom, D. D. & Van de Walle, C. G. First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centres. New J. Phys. 16, 073026 (2014).

    CAS  Google Scholar 

  157. Gali, A., Simon, T. & Lowther, J. E. An ab initio study of local vibration modes of the nitrogen-vacancy center in diamond. New J. Phys. 13, 025016 (2011).

    Google Scholar 

  158. Kindem, J. M. et al. Control and single-shot readout of an ion embedded in a nanophotonic cavity. Nature 580, 201–204 (2020).

    CAS  Google Scholar 

  159. Raha, M. et al. Optical quantum nondemolition measurement of a single rare earth ion qubit. Nat. Commun. 11, 1605 (2020).

    CAS  Google Scholar 

  160. Bockstedte, M., Schütz, F., Garratt, T., Ivády, V. & Gali, A. Ab initio description of highly correlated states in defects for realizing quantum bits. NPJ Quantum Mater. 3, 31 (2018).

    Google Scholar 

  161. Christle, D. J. et al. Isolated spin qubits in SiC with a high-fidelity infrared spin-to-photon interface. Phys. Rev. X 7, 021046 (2017).

    Google Scholar 

  162. Radko, I. P. et al. Determining the internal quantum efficiency of shallow-implanted nitrogen-vacancy defects in bulk diamond. Opt. Express 24, 27715 (2016).

    CAS  Google Scholar 

  163. Gali, Á. Ab initio theory of the nitrogen-vacancy center in diamond. Nanophotonics 8, 1907–1943 (2019).

    CAS  Google Scholar 

  164. Lannoo, M. & Bourgoin, J. Point Defects in Semiconductors I. Springer Series in Solid-State Sciences Vol. 22 36–67 (Springer, 1981).

  165. Koehl, W. F. et al. Resonant optical spectroscopy and coherent control of Cr4+ spin ensembles in SiC and GaN. Phys. Rev. B 95, 035207 (2017).

    Google Scholar 

  166. Laporte, O. & Meggers, W. F. Some rules of spectral structure. J. Opt. Soc. Am. 11, 459–463 (1925).

    CAS  Google Scholar 

  167. Seo, H., Govoni, M. & Galli, G. Design of defect spins in piezoelectric aluminum nitride for solid-state hybrid quantum technologies. Sci. Rep. 6, 20803 (2016).

    CAS  Google Scholar 

  168. Ma, H., Govoni, M. & Galli, G. Quantum simulations of materials on near-term quantum computers. NPJ Comput. Mater. 6, 85 (2020).

    Google Scholar 

  169. Bosma, T. et al. Identification and tunable optical coherent control of transition-metal spins in silicon carbide. NPJ Quantum Inf. 4, 48 (2018).

    Google Scholar 

  170. Tanabe, Y. & Sugano, S. On the absorption spectra of complex ions II. J. Phys. Soc. Jpn. 9, 766–779 (1954).

    CAS  Google Scholar 

  171. Tanabe, Y. & Sugano, S. On the absorption spectra of complex ions. I. J. Phys. Soc. Jpn. 9, 753–766 (1954).

    CAS  Google Scholar 

  172. Togan, E. et al. Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466, 730–734 (2010).

    CAS  Google Scholar 

  173. Müller, T. et al. Optical signatures of silicon-vacancy spins in diamond. Nat. Commun. 5, 3328 (2014).

    Google Scholar 

  174. Nagy, R. et al. High-fidelity spin and optical control of single silicon-vacancy centres in silicon carbide. Nat. Commun. 10, 1954 (2019).

    Google Scholar 

  175. Diler, B. et al. Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide. NPJ Quantum Inf. 6, 11 (2020).

    Google Scholar 

  176. Acosta, V. M. et al. Dynamic stabilization of the optical resonances of single nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 108, 206401 (2012).

    CAS  Google Scholar 

  177. Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011).

    CAS  Google Scholar 

  178. Manson, N. B., Sellars, M. J., Fisk, P. T. H. & Meltzer, R. S. Hole burning of rare earth ions with kHz resolution. J. Lumin. 64, 19–23 (1995).

    CAS  Google Scholar 

  179. Zhong, T. et al. Nanophotonic rare-earth quantum memory with optically controlled retrieval. Science 357, 1392–1395 (2017).

    CAS  Google Scholar 

  180. Biktagirov, T. & Gerstmann, U. Spin-orbit driven electrical manipulation of the zero-field splitting in high-spin centers in solids. Phys. Rev. Res. 2, 023071 (2020).

    CAS  Google Scholar 

  181. Thiering, G. & Gali, A. Ab initio calculation of spin-orbit coupling for an NV center in diamond exhibiting dynamic Jahn-Teller effect. Phys. Rev. B 96, 081115 (2017).

    Google Scholar 

  182. Goldman, M. L. et al. Phonon-induced population dynamics and intersystem crossing in nitrogen-vacancy centers. Phys. Rev. Lett. 114, 145502 (2015).

    CAS  Google Scholar 

  183. Thiering, G. & Gali, A. Theory of the optical spin-polarization loop of the nitrogen-vacancy center in diamond. Phys. Rev. B 98, 085207 (2018).

    CAS  Google Scholar 

  184. Dong, W., Doherty, M. W. & Economou, S. E. Spin polarization through intersystem crossing in the silicon vacancy of silicon carbide. Phys. Rev. B 99, 184102 (2019).

    CAS  Google Scholar 

  185. Toyli, D. M. et al. Measurement and control of single nitrogen-vacancy center spins above 600 K. Phys. Rev. X 2, 031001 (2012).

    Google Scholar 

  186. Hopper, D., Shulevitz, H. & Bassett, L. Spin readout techniques of the nitrogen-vacancy center in diamond. Micromachines 9, 437 (2018).

    Google Scholar 

  187. Bonato, C. et al. Optimized quantum sensing with a single electron spin using real-time adaptive measurements. Nat. Nanotechnol. 11, 247–252 (2016).

    CAS  Google Scholar 

  188. Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013).

    CAS  Google Scholar 

  189. Kambs, B. & Becher, C. Limitations on the indistinguishability of photons from remote solid state sources. New J. Phys. 20, 115003 (2018).

    CAS  Google Scholar 

  190. Miao, K. C. et al. Electrically driven optical interferometry with spins in silicon carbide. Sci. Adv. 5, eaay0527 (2019).

    CAS  Google Scholar 

  191. Hong, C. K., Ou, Z. Y. & Mandel, L. Measurement of subpicosecond time intervals between two photons by interference. Phys. Rev. Lett. 59, 2044–2046 (1987).

    CAS  Google Scholar 

  192. Humphreys, P. C. et al. Deterministic delivery of remote entanglement on a quantum network. Nature 558, 268–273 (2018).

    CAS  Google Scholar 

  193. Jahnke, K. D. et al. Electron–phonon processes of the silicon-vacancy centre in diamond. New J. Phys. 17, 043011 (2015).

    Google Scholar 

  194. Fu, K.-M. C. et al. Observation of the dynamic Jahn-Teller effect in the excited states of nitrogen-vacancy centers in diamond. Phys. Rev. Lett. 103, 256404 (2009).

    Google Scholar 

  195. Böttger, T., Thiel, C. W., Sun, Y. & Cone, R. L. Optical decoherence and spectral diffusion at 1.5 μm in Er3+:Y2SiO5 versus magnetic field, temperature, and Er3+ concentration. Phys. Rev. B 73, 075101 (2006).

    Google Scholar 

  196. Cardona, M. & Thewalt, M. L. W. Isotope effects on the optical spectra of semiconductors. Rev. Mod. Phys. 77, 1173–1224 (2005).

    CAS  Google Scholar 

  197. Macfarlane, R. M., Cassanho, A. & Meltzer, R. S. Inhomogeneous broadening by nuclear spin fields: A new limit for optical transitions in solids. Phys. Rev. Lett. 69, 542–545 (1992).

    CAS  Google Scholar 

  198. Anderson, C. P. et al. Electrical and optical control of single spins integrated in scalable semiconductor devices. Science 366, 1225–1230 (2019).

    CAS  Google Scholar 

  199. Wolfowicz, G., Whiteley, S. J. & Awschalom, D. D. Electrometry by optical charge conversion of deep defects in 4H-SiC. Proc. Natl Acad. Sci. USA 115, 7879–7883 (2018).

    CAS  Google Scholar 

  200. Bassett, L. C., Heremans, F. J., Yale, C. G., Buckley, B. B. & Awschalom, D. D. Electrical tuning of single nitrogen-vacancy center optical transitions enhanced by photoinduced fields. Phys. Rev. Lett. 107, 266403 (2011).

    CAS  Google Scholar 

  201. Anderson, C. P. Spin Qubits in Silicon Carbide Electronic Devices. PhD thesis, Univ. Chicago (2020).

  202. Candido, D. R. & Flatté, M. E. Suppression of the optical linewidth and spin decoherence of a quantum spin center in a pn diode. Preprint at arXiv https://arxiv.org/abs/2008.13289 (2020).

  203. Sipahigil, A. et al. Indistinguishable photons from separated silicon-vacancy centers in diamond. Phys. Rev. Lett. 113, 113602 (2014).

    CAS  Google Scholar 

  204. Schmidgall, E. R. et al. Frequency control of single quantum emitters in integrated photonic circuits. Nano Lett. 18, 1175–1179 (2018).

    CAS  Google Scholar 

  205. Giri, R. et al. Coupled charge and spin dynamics in high-density ensembles of nitrogen-vacancy centers in diamond. Phys. Rev. B 98, 045401 (2018).

    CAS  Google Scholar 

  206. Scherpelz, P. & Galli, G. Optimizing surface defects for atomic-scale electronics: Si dangling bonds. Phys. Rev. Mater. 1, 021602 (2017).

    Google Scholar 

  207. Wickramaratne, D. et al. Defect identification based on first-principles calculations for deep level transient spectroscopy. Appl. Phys. Lett. 113, 192106 (2018).

    Google Scholar 

  208. Wolfowicz, G. et al. Optical charge state control of spin defects in 4H-SiC. Nat. Commun. 8, 1876 (2017).

    Google Scholar 

  209. Jayakumar, H. et al. Optical patterning of trapped charge in nitrogen-doped diamond. Nat. Commun. 7, 12660 (2016).

    CAS  Google Scholar 

  210. Isoya, J. et al. EPR identification of intrinsic defects in SiC. Phys. Status Solidi 245, 1298–1314 (2008).

    CAS  Google Scholar 

  211. Aslam, N., Waldherr, G., Neumann, P., Jelezko, F. & Wrachtrup, J. Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection. New J. Phys. 15, 013064 (2013).

    CAS  Google Scholar 

  212. Wong, D. et al. Characterization and manipulation of individual defects in insulating hexagonal boron nitride using scanning tunnelling microscopy. Nat. Nanotechnol. 10, 949–953 (2015).

    CAS  Google Scholar 

  213. Han, K. Y., Kim, S. K., Eggeling, C. & Hell, S. W. Metastable dark states enable ground state depletion microscopy of nitrogen vacancy centers in diamond with diffraction-unlimited resolution. Nano Lett. 10, 3199–3203 (2010).

    CAS  Google Scholar 

  214. Fávaro de Oliveira, F. et al. Tailoring spin defects in diamond by lattice charging. Nat. Commun. 8, 15409 (2017).

    Google Scholar 

  215. Lo, C. C. et al. Electrically detected magnetic resonance of neutral donors interacting with a two-dimensional electron gas. Phys. Rev. Lett. 106, 207601 (2011).

    CAS  Google Scholar 

  216. Irber, D. M. et al. Robust all-optical single-shot readout of NV centers in diamond. Preprint at arXiv https://arxiv.org/abs/2006.02938 (2020).

  217. Shields, B. J., Unterreithmeier, Q. P., De Leon, N. P., Park, H. & Lukin, M. D. Efficient readout of a single spin state in diamond via spin-to-charge conversion. Phys. Rev. Lett. 114, 136402 (2015).

    CAS  Google Scholar 

  218. Lo, C. C. et al. Hybrid optical–electrical detection of donor electron spins with bound excitons in silicon. Nat. Mater. 14, 490–494 (2015).

    CAS  Google Scholar 

  219. Hoehne, F., Huebl, H., Galler, B., Stutzmann, M. & Brandt, M. S. Spin-dependent recombination between phosphorus donors in silicon and Si/SiO2 interface states investigated with pulsed electrically detected electron double resonance. Phys. Rev. Lett. 104, 046402 (2010).

    Google Scholar 

  220. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004).

    CAS  Google Scholar 

  221. Siyushev, P. et al. Photoelectrical imaging and coherent spin-state readout of single nitrogen-vacancy centers in diamond. Science 363, 728–731 (2019).

    CAS  Google Scholar 

  222. Falk, A. L. et al. Polytype control of spin qubits in silicon carbide. Nat. Commun. 4, 1819 (2013).

    Google Scholar 

  223. Doherty, M. W. et al. Measuring the defect structure orientation of a single NV centre in diamond. New J. Phys. 16, 063067 (2014).

    CAS  Google Scholar 

  224. Westerhausen, M. T. et al. Controlled doping of GeV and SnV color centers in diamond using chemical vapor deposition. ACS Appl. Mater. Interfaces 12, 29700–29705 (2020).

    CAS  Google Scholar 

  225. Toyli, D. M., Weis, C. D., Fuchs, G. D., Schenkel, T. & Awschalom, D. D. Chip-scale nanofabrication of single spins and spin arrays in diamond. Nano Lett. 10, 3168–3172 (2010).

    CAS  Google Scholar 

  226. Rugar, A. E. et al. Generation of tin-vacancy centers in diamond via shallow ion implantation and subsequent diamond overgrowth. Nano Lett. 20, 1614–1619 (2020).

    CAS  Google Scholar 

  227. Scarabelli, D., Trusheim, M., Gaathon, O., Englund, D. & Wind, S. J. Nanoscale engineering of closely-spaced electronic spins in diamond. Nano Lett. 16, 4982–4990 (2016).

    CAS  Google Scholar 

  228. Wan, N. H. et al. Large-scale integration of artificial atoms in hybrid photonic circuits. Nature 583, 226–231 (2020).

    CAS  Google Scholar 

  229. Schröder, T. et al. Scalable focused ion beam creation of nearly lifetime-limited single quantum emitters in diamond nanostructures. Nat. Commun. 8, 15376 (2017).

    Google Scholar 

  230. Ziegler, J. F. & Biersack, J. P. in Treatise on Heavy-Ion Science (eds. Bromley, D. A.) 93–129 (Springer, 1985).

  231. Lebedev, A. A. Radiation Effects in Silicon Carbide (Materials Research Forum, 2017).

  232. McLellan, C. A. et al. Patterned formation of highly coherent nitrogen-vacancy centers using a focused electron irradiation technique. Nano Lett. 16, 2450–2454 (2016).

    CAS  Google Scholar 

  233. Singh, M. K. et al. Epitaxial Er-doped Y2O3 on silicon for quantum coherent devices. APL Mater. 8, 031111 (2020).

    CAS  Google Scholar 

  234. Jaffe, T. et al. Novel ultra localized and dense nitrogen delta-doping in diamond for advanced quantum sensing. Nano Lett. 20, 3192–3198 (2020).

    CAS  Google Scholar 

  235. Ohno, K. et al. Three-dimensional localization of spins in diamond using 12C implantation. Appl. Phys. Lett. 105, 052406 (2014).

    Google Scholar 

  236. Lesik, M. et al. Perfect preferential orientation of nitrogen-vacancy defects in a synthetic diamond sample. Appl. Phys. Lett. 104, 113107 (2014).

    Google Scholar 

  237. Michl, J. et al. Perfect alignment and preferential orientation of nitrogen-vacancy centers during chemical vapor deposition diamond growth on (111) surfaces. Appl. Phys. Lett. 104, 102407 (2014).

    Google Scholar 

  238. Chakravarthi, S. et al. Window into NV center kinetics via repeated annealing and spatial tracking of thousands of individual NV centers. Phys. Rev. Mater. 4, 023402 (2020).

    CAS  Google Scholar 

  239. Hruszkewycz, S. O. et al. Strain annealing of SiC nanoparticles revealed through Bragg coherent diffraction imaging for quantum technologies. Phys. Rev. Mater. 2, 086001 (2018).

    CAS  Google Scholar 

  240. Lee, D. & Gupta, J. A. Perspectives on deterministic control of quantum point defects by scanned probes. Nanophotonics 8, 2033–2040 (2019).

    CAS  Google Scholar 

  241. Schofield, S. R. et al. Atomically precise placement of single dopants in Si. Phys. Rev. Lett. 91, 136104 (2003).

    CAS  Google Scholar 

  242. Stock, T. J. Z. et al. Atomic-scale patterning of arsenic in silicon by scanning tunneling microscopy. ACS Nano 14, 3316–3327 (2020).

    CAS  Google Scholar 

  243. Schuler, B. et al. How substitutional point defects in two-dimensional WS2 induce charge localization, spin–orbit splitting, and strain. ACS Nano 13, 10520–10534 (2019).

    CAS  Google Scholar 

  244. Mitterreiter, E. et al. Atomistic positioning of defects in helium ion treated single-layer MoS2. Nano Lett. 20, 4437–4444 (2020).

    CAS  Google Scholar 

  245. Kurita, T. et al. Efficient generation of nitrogen-vacancy center inside diamond with shortening of laser pulse duration. Appl. Phys. Lett. 113, 211102 (2018).

    Google Scholar 

  246. Chen, Y.-C. et al. Laser writing of individual nitrogen-vacancy defects in diamond with near-unity yield. Optica 6, 662–667 (2019).

    CAS  Google Scholar 

  247. Smith, J. M., Meynell, S. A., Jayich, A. C. B. & Meijer, J. Colour centre generation in diamond for quantum technologies. Nanophotonics 8, 1889–1906 (2019).

    CAS  Google Scholar 

  248. Jakob, A. M. et al. Deterministic single ion implantation with 99.87% confidence for scalable donor-qubit arrays in silicon. Preprint at arXiv https://arxiv.org/abs/2009.02892 (2020).

  249. Andrich, P. et al. Engineered micro- and nanoscale diamonds as mobile probes for high-resolution sensing in fluid. Nano Lett. 14, 4959–4964 (2014).

    CAS  Google Scholar 

  250. Momenzadeh, S. A. et al. Nanoengineered diamond waveguide as a robust bright platform for nanomagnetometry using shallow nitrogen vacancy centers. Nano Lett. 15, 165–169 (2015).

    CAS  Google Scholar 

  251. Widmann, C. J. et al. Fabrication and characterization of single crystalline diamond nanopillars with NV-centers. Diam. Relat. Mater. 54, 2–8 (2015).

    CAS  Google Scholar 

  252. Andrich, P. et al. Microscale-resolution thermal mapping using a flexible platform of patterned quantum sensors. Nano Lett. 18, 4684–4690 (2018).

    CAS  Google Scholar 

  253. von Kugelgen, S. & Freedman, D. E. A chemical path to quantum information. Science 366, 1070–1071 (2019).

    Google Scholar 

  254. Bayliss, S. L. et al. Optically addressable molecular spins for quantum information processing. Science 370, 1309–1312 (2020).

    CAS  Google Scholar 

  255. George, R. E., Edwards, J. P. & Ardavan, A. Coherent spin control by electrical manipulation of the magnetic anisotropy. Phys. Rev. Lett. 110, 027601 (2013).

    Google Scholar 

  256. Trusheim, M. E. et al. Transform-limited photons from a coherent tin-vacancy spin in diamond. Phys. Rev. Lett. 124, 023602 (2020).

    CAS  Google Scholar 

  257. Rose, B. C. et al. Strongly anisotropic spin relaxation in the neutral silicon vacancy center in diamond. Phys. Rev. B 98, 235140 (2018).

    CAS  Google Scholar 

  258. Lo Nardo, R. et al. Spin relaxation and donor-acceptor recombination of Se+ in 28-silicon. Phys. Rev. B 92, 165201 (2015).

    Google Scholar 

  259. Lim, H.-J., Welinski, S., Ferrier, A., Goldner, P. & Morton, J. J. L. Coherent spin dynamics of ytterbium ions in yttrium orthosilicate. Phys. Rev. B 97, 064409 (2018).

    CAS  Google Scholar 

  260. Mrózek, M. et al. Longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond. EPJ Quantum Technol. 2, 22 (2015).

    Google Scholar 

  261. Simin, D. et al. Locking of electron spin coherence above 20 ms in natural silicon carbide. Phys. Rev. B 95, 161201 (2017).

    Google Scholar 

  262. Chaim, R. Relations between flash onset-, Debye-, and glass transition temperature in flash sintering of oxide nanoparticles. Scr. Mater. 169, 6–8 (2019).

    CAS  Google Scholar 

  263. Agne, M. T., Hanus, R. & Snyder, G. J. Minimum thermal conductivity in the context of diffuson-mediated thermal transport. Energy Environ. Sci. 11, 609–616 (2018).

    Google Scholar 

  264. Sun, Z., Li, M. & Zhou, Y. Thermal properties of single-phase Y2SiO5. J. Eur. Ceram. Soc. 29, 551–557 (2009).

    CAS  Google Scholar 

  265. Cline, C. F., Dunegan, H. L. & Henderson, G. W. Elastic constants of hexagonal BeO, ZnS, and CdSe. J. Appl. Phys. 38, 1944–1948 (1967).

    CAS  Google Scholar 

  266. Jones, G. H. S. & Hallett, A. C. H. The specific heat of crystalline quartz between 2 °K and 4 °K. Can. J. Phys. 38, 696–700 (1960).

    CAS  Google Scholar 

  267. Wolfowicz, G. Quantum Control of Donor Spins in Silicon and Their Environment. PhD thesis, Oxford Univ. (2015).

  268. Wandel, M. E. Attenuation in Silica-based Optical Fibers. Thesis, Tech. Univ. Denmark (2006).

  269. Strehlow, W. H. & Cook, E. L. Compilation of energy band gaps in elemental and binary compound semiconductors and insulators. J. Phys. Chem. Ref. Data 2, 163–200 (1973).

    CAS  Google Scholar 

  270. Ching, W. Y., Ouyang, L. & Xu, Y.-N. Electronic and optical properties of Y2SiO5 and Y2Si2O7 with comparisons to α-SiO2 and Y2O3. Phys. Rev. B 67, 245108 (2003).

    Google Scholar 

  271. Brenneis, A. et al. Ultrafast electronic readout of diamond nitrogen–vacancy centres coupled to graphene. Nat. Nanotechnol. 10, 135–139 (2014).

    Google Scholar 

  272. Ohno, K. Nanometer-scale Engineering of Shallow Spins in Diamond. PhD thesis, Univ. California, Santa Barbara (2014).

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Acknowledgements

We thank Jaewook Lee and Huijin Park for their help in cross-checking the CCE predictions, Hideo Ohno, Tomasz Dietl, Fumihiro Matsukura and Shunsuke Fukami for fruitful discussion, and Michael Solomon and Grant Smith for reviewing the manuscript. This work was primarily supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (G.W., F.J.H., C.P.A. and D.D.A.). H.S. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (nos. 2018R1C1B6008980, 2018R1A4A1024157 and 2019M3E4A1078666). G.G. was supported by AFOSR FA9550-19-1-0358. S.K. was supported by Marubun Research Promotion Foundation, RIEC through Overseas Training Program for Young Profession and Cooperative Research Projects, MEXT through the Program for Promoting the Enhancement of Research Universities and JSPS Kakenhi nos. 19KK0130 and 20H02178. A.G. was supported by the Hungarian NKFIH grant no. KKP129866 of the National Excellence Program of Quantum-coherent materials project, no. 2017-1.2.1-NKP-2017-00001 of the National Quantum Technology Program, no. 127902 of the EU QuantERA Nanospin project, no. 127889 of the EU QuantERA Q_magine project and by the European Commission of EU H2020 Quantum Technology Flagship project ASTERIQS (grant no. 820394), as well as the EU H2020 FETOPEN project QuanTELCO (grant no. 862721).

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Wolfowicz, G., Heremans, F.J., Anderson, C.P. et al. Quantum guidelines for solid-state spin defects. Nat Rev Mater 6, 906–925 (2021). https://doi.org/10.1038/s41578-021-00306-y

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