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Extending and measuring dephasing times of nuclear spins in NV centers of diamond

Jingfu Zhang1,2,*, Swathi S. Hegde1,†, Fedor Jelezko2,3, and Dieter Suter1

  • *Contact author: zhangjfu2000@yahoo.com.
  • †Present address: Qruise GmbH, Am Hoelzersbach 7, D-66113 Saarbruecken, Germany.
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Phys. Rev. B 114, 144411 – Published 9 September, 2026

DOI: https://doi.org/10.1103/c1ng-bsnr

Abstract

Long coherence times rank among the most important performance measures for many different types of quantum technology. In the electron-nuclear spin system of NV centers of diamond, the nuclear spins provide particularly long dephasing times. However, since initialization and readout require assistance from the electron spin, the apparent dephasing times can be reduced by the electron spin lifetime. Here we propose and implement schemes for measuring and extending the dephasing times of nuclear spins, resulting in dephasing times that are longer than the longitudinal relaxation time T1 of the electron spin.

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References (66)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, and J. Schmiedmayer, Quantum technologies with hybrid systems, Proc. Natl. Acad. Sci. USA 112, 3866 (2015).
  3. J. J. L. Morton and B. W. Lovett, Hybrid solid-state qubits: The powerful role of electron spins, Annu. Rev. Condens. Matter Phys. 2, 189 (2011).
  4. D. Suter and F. Jelezko, Single-spin magnetic resonance in the nitrogen-vacancy center of diamond, Prog. Nucl. Magn. Reson. Spectrosc. 98-99, 50 (2017).
  5. J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and R. L. Walsworth, Sensitivity optimization for NV-diamond magnetometry, Rev. Mod. Phys. 92, 015004 (2020).
  6. J. Zhang and D. Suter, Single NV centers as sensors for radio-frequency fields, Phys. Rev. Res. 5, L022026 (2023).
  7. R. Katsumi, K. Takada, F. Jelezko, and T. Yatsui, Recent progress in hybrid diamond photonics for quantum information processing and sensing, Commun. Eng. 4, 85 (2025).
  8. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
  9. J. Stolze and D. Suter, Quantum Computing: A Short Course from Theory to Experiment, 2nd ed. (Wiley-VCH, Berlin, 2008).
  10. T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O'Brien, Quantum computers, Nature (London) 464, 45 (2010).
  11. C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, A ten-qubit solid-state spin register with quantum memory up to one minute, Phys. Rev. X 9, 031045 (2019).
  12. T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, Decoherence-protected quantum gates for a hybrid solid-state spin register, Nature (London) 484, 82 (2012).
  13. J. H. Shim, I. Niemeyer, J. Zhang, and D. Suter, Room-temperature high-speed nuclear-spin quantum memory in diamond, Phys. Rev. A 87, 012301 (2013).
  14. N. Kalb, P. C. Humphreys, J. J. Slim, and R. Hanson, Dephasing mechanisms of diamond-based nuclear-spin memories for quantum networks, Phys. Rev. A 97, 062330 (2018).
  15. P. C. Maurer, G. Kucsko, C. Latta, L. Jiang, N. Y. Yao, S. D. Bennett, F. Pastawski, D. Hunger, N. Chisholm, M. Markham, et al., Room-temperature quantum bit memory exceeding one second, Science 336, 1283 (2012).
  16. A. Reiserer, N. Kalb, M. S. Blok, K. J. M. van Bemmelen, T. H. Taminiau, R. Hanson, D. J. Twitchen, and M. Markham, Robust quantum-network memory using decoherence-protected subspaces of nuclear spins, Phys. Rev. X 6, 021040 (2016).
  17. M. Pfender, N. Aslam, H. Sumiya, S. Onoda, P. Neumann, J. Isoya, C. A. Meriles, and J. Wrachtrup, Nonvolatile nuclear spin memory enables sensor-unlimited nanoscale spectroscopy of small spin clusters, Nat. Commun. 8, 834 (2017).
  18. M. S. Blok, N. Kalb, A. Reiserer, T. H. Taminiau, and R. Hanson, Towards quantum networks of single spins: Analysis of a quantum memory with an optical interface in diamond, Faraday Discuss. 184, 173 (2015).
  19. N. Grimm, K. Senkalla, P. J. Vetter, J. Frey, P. Gundlapalli, T. Calarco, G. Genov, M. M. Muller, and F. Jelezko, Coherent control of a long-lived nuclear memory spin in a germanium-vacancy multi-qubit node, Phys. Rev. Lett. 134, 043603 (2025).
  20. P. Gundlapalli, P. J. Vetter, G. Genov, M. Olney-Fraser, P. Wang, M. M. Mueller, K. Senkalla, and F. Jelezko, High-fidelity single-shot readout and selective nuclear spin control for a spin-1/2 quantum register in diamond, arXiv:2510.09164.
  21. J. Zhang, S. S. Hegde, and D. Suter, Improved indirect control of nuclear spins in diamond N-V centers, Phys. Rev. Appl. 12, 064047 (2019).
  22. S. S. Hegde, J. Zhang, and D. Suter, Efficient quantum gates for individual nuclear spin qubits by indirect control, Phys. Rev. Lett. 124, 220501 (2020).
  23. S. S. Hegde, J. Zhang, and D. Suter, Toward the speed limit of high-fidelity two-qubit gates, Phys. Rev. Lett. 128, 230502 (2022).
  24. H. P. Bartling, M. H. Abobeih, B. Pingault, M. J. Degen, S. J. H. Loenen, C. E. Bradley, J. Randall, M. Markham, D. J. Twitchen, and T. H. Taminiau, Entanglement of spin-pair qubits with intrinsic dephasing times exceeding a minute, Phys. Rev. X 12, 011048 (2022).
  25. M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. L. Hollenberg, The nitrogen-vacancy colour centre in diamond, Phys. Rep. 528, 1 (2013).
  26. M. C. Cambria, A. Norambuena, H. T. Dinani, G. Thiering, A. Gardill, I. Kemeny, Y. Li, V. Lordi, A. Gali, J. R. Maze, and S. Kolkowitz, Temperature-dependent spin-lattice relaxation of the nitrogen-vacancy spin triplet in diamond, Phys. Rev. Lett. 130, 256903 (2023).
  27. A. Asare, R. Lazda, F. Gahbauer, V. Cimalla, and M. Auzinsh, Theoretical analysis and experimental measurement of N14 nuclear spin polarization in nitrogen-vacancy centers in diamond, Phys. Rev. B 111, 064113 (2025).
  28. C. Zu, W.-B. Wang, L. He, W.-G. Zhang, C.-Y. Dai, F. Wang, and L.-M. Duan, Experimental realization of universal geometric quantum gates with solid-state spins, Nature (London) 514, 72 (2014).
  29. W.-B. Wang, C. Zu, L. He, W.-G. Zhang, and L.-M. Duan, Memory-built-in quantum cloning in a hybrid solid-state spin register, Sci. Rep. 5, 12203 (2015).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/c1ng-bsnr for more details on population relaxation of the electron spin, initialization and normalization of the qubits system, evolution of the C13 spin, parameters for the quantum gates, and the experimental setup, which includes Refs. [31, 32, 33, 34, 35, 36, 37, 38, 39, 40].
  31. M. Howard, J. Twamley, C. Wittmann, T. Gaebel, F. Jelezko, and J. Wrachtrup, Quantum process tomography and Linblad estimation of a solid-state qubit, New J. Phys. 8, 33 (2006).
  32. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Observation of coherent oscillations in a single electron spin, Phys. Rev. Lett. 92, 076401 (2004).
  33. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate, Phys. Rev. Lett. 93, 130501 (2004).
  34. G. Waldherr, J. Beck, M. Steiner, P. Neumann, A. Gali, T. Frauenheim, F. Jelezko, and J. Wrachtrup, Dark states of single nitrogen-vacancy centers in diamond unraveled by single shot NMR, Phys. Rev. Lett. 106, 157601 (2011).
  35. J. Harrison, M. Sellars, and N. Manson, Measurement of the optically induced spin polarisation of N-V centres in diamond, Diam. Relat. Mater. 15, 586 (2006).
  36. J. Zhang and D. Suter, Experimental protection of two-qubit quantum gates against environmental noise by dynamical decoupling, Phys. Rev. Lett. 115, 110502 (2015).
  37. J. Zhang, S. S. Hegde, and D. Suter, Pulse sequences for controlled two- and three-qubit gates in a hybrid quantum register, Phys. Rev. A 98, 042302 (2018).
  38. J. Wrachtrup and F. Jelezko, Processing quantum information in diamond, J. Phys.: Condens. Matter 18, S807 (2006).
  39. F. Jelezko and J. Wrachtrup, Single defect centres in diamond: A review, Phys. Status Solidi A 203, 3207 (2006).
  40. C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, Stable solid-state source of single photons, Phys. Rev. Lett. 85, 290 (2000).
  41. J. Zhang, J. H. Shim, I. Niemeyer, T. Taniguchi, T. Teraji, H. Abe, S. Onoda, T. Yamamoto, T. Ohshima, J. Isoya, et al., Experimental implementation of assisted quantum adiabatic passage in a single spin, Phys. Rev. Lett. 110, 240501 (2013).
  42. J. Zhang, S. S. Hegde, and D. Suter, Efficient implementation of a quantum algorithm in a single nitrogen-vacancy center of diamond, Phys. Rev. Lett. 125, 030501 (2020).
  43. V. Soshenko, I. Cojocaru, S. Bolshedvorskii, O. Rubinas, A. Smolyaninov, V. Vorobyov, V. Sorokin, and A. Akimov, Measurement of the longitudinal relaxation time for the nitrogen nuclear spin in a nitrogen-vacancy colour centre of diamond, Quantum Electron. 51, 1144 (2021).
  44. K. R. K. Rao and D. Suter, Characterization of hyperfine interaction between an NV electron spin and a first-shell C13 nuclear spin in diamond, Phys. Rev. B 94, 060101(R) (2016).
  45. A. Dreau, P. Spinicelli, J. R. Maze, J.-F. Roch, and V. Jacques, Single-shot readout of multiple nuclear spin qubits in diamond under ambient conditions, Phys. Rev. Lett. 110, 060502 (2013).
  46. A. Jarmola, V. M. Acosta, K. Jensen, S. Chemerisov, and D. Budker, Temperature- and magnetic-field-dependent longitudinal spin relaxation in nitrogen-vacancy ensembles in diamond, Phys. Rev. Lett. 108, 197601 (2012).
  47. N. Khaneja, Switched control of electron nuclear spin systems, Phys. Rev. A 76, 032326 (2007).
  48. J. S. Hodges, J. C. Yang, C. Ramanathan, and D. G. Cory, Universal control of nuclear spins via anisotropic hyperfine interactions, Phys. Rev. A 78, 010303(R) (2008).
  49. J. Zhang, S. S. Hegde, and D. Suter, Fast quantum state tomography in the nitrogen vacancy center of diamond, Phys. Rev. Lett. 130, 090801 (2023).
  50. K. D. Jahnke, B. Naydenov, T. Teraji, S. Koizumi, T. Umeda, J. Isoya, and F. Jelezko, Long coherence time of spin qubits in C12 enriched polycrystalline chemical vapor deposition diamond, Appl. Phys. Lett. 101, 012405 (2012).
  51. T. Teraji, T. Taniguchi, S. Koizumi, Y. Koide, and J. Isoya, Effective use of source gas for diamond growth with isotopic enrichment, Appl. Phys. Express 6, 055601 (2013).
  52. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, Ultralong spin coherence time in isotopically engineered diamond, Nat. Mater. 8, 383 (2009).
  53. D. N. Shykind, J. Baum, S.-B. Liu, A. Pines, and A. N. Garroway, Phase-incremented multiple-quantum NMR experiments, J. Magn. Reson. 76, 149 (1988).
  54. L. Childress, M. V. Gurudev Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer, and M. D. Lukin, Coherent dynamics of coupled electron and nuclear spin qubits in diamond, Science 314, 281 (2006).
  55. M. C. Cambria, A. Gardill, Y. Li, A. Norambuena, J. R. Maze, and S. Kolkowitz, State-dependent phonon-limited spin relaxation of nitrogen-vacancy centers, Phys. Rev. Res. 3, 013123 (2021).
  56. D. Suter and G. A. Alvarez, Protecting quantum information against environmental noise, Rev. Mod. Phys. 88, 041001 (2016).
  57. A. M. Souza, G. A. Alvarez, and D. Suter, Robust dynamical decoupling, Philos. Trans. R. Soc. A 370, 4748 (2012).
  58. M. Pfender, P. Wang, H. Sumiya, S. Onoda, W. Yang, D. B. R. Dasari, P. Neumann, X.-Y. Pan, J. Isoya, R.-B. Liu, and J. Wrachtrup, High-resolution spectroscopy of single nuclear spins via sequential weak measurements, Nat. Commun. 10, 594 (2019).
  59. A. Norambuena, E. Munoz, H. T. Dinani, A. Jarmola, P. Maletinsky, D. Budker, and J. R. Maze, Spin-lattice relaxation of individual solid-state spins, Phys. Rev. B 97, 094304 (2018).
  60. T. Unden, P. Balasubramanian, D. Louzon, Y. Vinkler, M. B. Plenio, M. Markham, D. Twitchen, A. Stacey, I. Lovchinsky, A. O. Sushkov, et al., Quantum metrology enhanced by repetitive quantum error correction, Phys. Rev. Lett. 116, 230502 (2016).
  61. S. Zaiser, T. Rendler, I. Jakobi, T. Wolf, S.-Y. Lee, S. Wagner, V. Bergholm, T. Schulte-Herbrueggen, P. Neumann, and J. Wrachtrup, Enhancing quantum sensing sensitivity by a quantum memory, Nat. Commun. 7, 12279 (2016).
  62. G. A. Alvarez and D. Suter, Measuring the spectrum of colored noise by dynamical decoupling, Phys. Rev. Lett. 107, 230501 (2011).
  63. J. Krzywda, P. Szankowski, and L. Cywinski, The dynamical-decoupling-based spatiotemporal noise spectroscopy, New J. Phys. 21, 043034 (2019).
  64. P. Szańkowski, G. Ramon, J. Krzywda, D. Kwiatkowski, and L. Cywiński, Environmental noise spectroscopy with qubits subjected to dynamical decoupling, J. Phys.: Condens. Matter 29, 333001 (2017).
  65. Y. Zhang, C. A. Ryan, R. Laflamme, and J. Baugh, Coherent control of two nuclear spins using the anisotropic hyperfine interaction, Phys. Rev. Lett. 107, 170503 (2011).
  66. K. Senkalla, G. Genov, M. H. Metsch, P. Siyushev, and F. Jelezko, Germanium vacancy in diamond quantum memory exceeding 20 ms, Phys. Rev. Lett. 132, 026901 (2024).

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Phys. Rev. B 114, 144411– Published 9 September, 2026
  • Received 30 May 2025
  • Revised 5 May 2026
  • Accepted 17 August 2026
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