vestifmИзвестия Национальной академии наук Беларуси. Серия физико-математических наукProceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series1561-24302524-2415The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"vestifm-236Research ArticleФИЗИКАPHYSICSСТАБИЛЬНЫЕ ЭЛЕКТРОННО-ЯДЕРНЫЕ СПИНОВЫЕ СИСТЕМЫ NV–13C В АЛМАЗЕ ДЛЯ КВАНТОВЫХ ТЕХНОЛОГИЙROBUST ELECTRONIC-NUCLEAR NV–13C SPIN SYSTEMS IN THE DIAMOND FOR QUANTUM TECHNOLOGIESНизовцевА. П.NizovtsevA. P.

доктор физико- математических наук, ведущий научный сотрудник центра квантовой оптики и квантовой информатики

D. Sc. (Physics and Mathematics), Leading Researcher, Center of Quantum Optics and Quantum Informatics

apniz@ifanbel.bas-net.byПушкарчукА. Л.PushkarchukA. L.

кандидат физико-математических наук, старший научный сотрудник лаборатории ионного обмена и сорбции

Ph. D. (Physics and Mathematics), Senior Researcher, Laboratory of Adsorption and Ion Exchange

alexp51@bk.ruКутеньС. А.KutenS. A.

кандидат физико-математических наук, заведующий лабораторией теоретической физики и моделирования ядерных процессов

Ph. D. (Physics and Mathematics), Head of the Laboratory of the Theoretical Physics and Simulation of Nuclear Processes

kut@inp.bsu.byПушкарчукВ. А.PushkarchukV. A.

кандидат физико-математических наук, старший научный сотрудник центра 4.11 научно-исследовательской части

Ph. D. (Physics and Mathematics), Senior Researcher, Center 4.11 of the Research Department

vadim@nv-center.comКилинС. Я.KilinS. Ya.

академик, доктор физико-математических наук, профессор, заведующий Центром квантовой оптики и квантовой информатики Института физики им. Б. И. Степанова, Национальная академия наук Беларуси; Заместитель Председателя Президиума Национальной академии наук Беларуси

Academician, D. Sc. (Physics and Mathematics), Professor, Head of the Center of Quantum Optics and Quantum Informatics, B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus; Deputy Chairman of the Presidium of the National Academy of Sciences of Belarus

kilin@ifanbel.bas-net.byЛузановА. В.LuzanovA. V.

доктор физико- математических наук, ведущий научный сотрудник отдела рентгеноструктурных исследований и квантовой химии

D. Sc. (Physics and Mathematics), Professor, Leading Researcher, Department of X-ray Diffraction Studies and Quantum Chemistry

avluzanov@xray.isc.kharkov.comЖиколО. А.ZhikolO. A.

кандидат химических наук, научный сотрудник отдела рентгеноструктурных исследований и квантовой химии

Ph. D. (Chemistry), Researcher, Department of X-ray Diffraction Studies and Quantum Chemistry

zhikol@xray.isc.kharkov.comИнститут физики им. Б. И. Степанова Национальной академии наук Беларуси, МинскB. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus, MinskИнститут физико-органической химии Национальной академии наук Беларуси, Минск Институт ядерных проблем Белорусского государственного университета, МинскInstituteof Physical-Organic Chemistry of the National Academy of Sciences of Belarus, Minsk Institute for Nuclear Problems of the Belarusian State University, MinskИнститут ядерных проблем Белорусского государственного университета, МинскInstitute for Nuclear Problems of the Belarusian State University, MinskБелорусский государственный университет информатики и радиоэлектроники, МинскBelarusian State University of Informatics and Radioelectronics, MinskНаучно-технологический комплекс «Институт монокристаллов» Национальной академии наук Украины, ХарьковSSI Institute of Single Crystals of the National Academy of Sciences of Ukraine, Kharkiv2017300420170198110Copyright © Низовцев А.П., Пушкарчук А.Л., Кутень С.А., Пушкарчук В.А., Килин С.Я., Лузанов А.В., Жикол О.А., 20172017Низовцев А.П., Пушкарчук А.Л., Кутень С.А., Пушкарчук В.А., Килин С.Я., Лузанов А.В., Жикол О.А.Nizovtsev A.P., Pushkarchuk A.L., Kuten S.A., Pushkarchuk V.A., Kilin S.Y., Luzanov A.V., Zhikol O.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestifm.belnauka.by/jour/article/view/236

Методами компьютерной химии рассчитаны матрицы AKL, описывающие сверхтонкое взаимодействие (СТВ) электронного спина центра окраски «азот-вакансия» (NV-центра) в алмазе с ядерным спином атома 13С, который расположен в одном из возможных узлов решетки в пассивированном водородом углеродном кластере С510[NV]H252. Выполнен систематический анализ скоростей W0 переворотов ядерных спинов 13С, индуцируемых их анизотропным СТВ с электронным спином NV-центра. Показано, что в кластере имеются специфические позиции ядерного спина 13С, в которых он практически не испытывает таких переворотов вследствие малости недиагональных элементов в соответствующих матрицах AKL. Определено пространственное расположение найденных позиций стабильности в кластере относительно NV-центра и рассчитаны величины характерных расщеплений в спектрах оптически детектируемого магнитного резонанса (ОДМР) для стабильных систем NV–13C, по которым их можно идентифицировать в процессе их экспериментального поиска для использования в разрабатываемых квантовых технологиях. Показано, что полностью стабильными (W0 = 0) являются позиции ядерного спина, расположенные на оси симметрии NV-центра. Найдены характеристики восьми таких «осевых» систем NV–13C. Впервые обнаружено наличие в кластере дополнительных «неосевых» квазистабильных систем NV–13C, имеющих малые скорости переворотов (W0 .→0) спина 13С вследствие высокой локальной симметрии распределения спиновой плотности, обусловливающей малость недиагональных элементов матриц СТВ для таких систем. Пространственно «не осевые» стабильные системы NV–13C расположены в плоскости, проходящей через вакансию NV-центра перпендикулярно его оси. Выполненный анализ имеющихся литературных данных показал, что, по-видимому, некоторые из предсказанных стабильных систем NV–13C уже наблюдались экспериментально.

 

Using the methods of computational chemistry, we calculated matrices AKL describing hyperfine interactions (HFI) between the electron spin of the color ‘nitrogen-vacancy’ center (NV center) in a diamond and a 13C nuclear spin located somewhere in the Н-terminated carbon cluster C510[NV]H252 hosting the NV center. The rates W0 of the 13C spin flip-flops induced by anisotropic HFI are calculated systematically for all possible locations of 13C in the cluster. It is shown that in the cluster, there are specific positions of nuclear 13C spin, in which it almost does not undergo such flip-flops due to small off-diagonal elements in corresponding matrices AKL. Spatial locations of the 13C stability positions in the cluster are discovered and characteristic splitting values in the spectra of optically detected magnetic resonance (ODMR) for the stable NV–13C systems are calculated, which can be utilized to identify them during their experimental search for use in emerging quantum technologies. It is shown that the positions of the 13C nuclear spin located on the NV center symmetry axis are completely stable (W0 = 0). The characteristics of eight ‘axial’ NV–13C systems are elucidated. The presence of additional ‘non-axial’ near-stable NV–13C spin systems also exhibiting very low flip-flop rates (W0 → 0) due to a high local symmetry of the spin density distribution resulting in vanishing the off-diagonal HFI matrix AKL elements for such systems is revealed for the first time. Spatially, these ‘non-axial’ stable NV–13C systems are located near the plane passing through the vacancy of the NV center and being perpendicular to the NV axis. Analysis of the available publications showed that apparently, some of the predicted stable NV–13C systems have already been observed experimentally.

 

квантовые технологиикубитыNV-центр в алмазеспинысверхтонкое взаимодействиеквантово-химическое моделированиеquantum technologiesqubitsNV center in diamondspinshyperfine interactionquantum-chemical simulationReferencesDowling, J. P. Quantum technology: the second quantum revolution / J. P. Dowling, G. L. Milburn // Philos. Trans. R. Soc. A: Math., Phys. and Engineering Sci. – 2003. – Vol. 361, № 1809. – P. 1655–1674.Dowling J.P., Milburn G.L. Quantum technology: the second quantum revolution. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003, vol. 361, no. 1890, pp. 1655–1674. Doi: 10.1098/ rsta.2003.1227Quantum technology: from research to application / W. P. Schleich [et al.] // Appl. Phys. B. – 2016. – Vol. 122. – P. 130.Schleich W.P., Ranade K.S., Anton Ch., Arndt M., Aspelmeyer M., Bayer M., Berg G., Calarco T., Fuchs H., Giacobino E., Grassl M., Hänggi P., Heckl W.M., Hertel I.-V., Huelga S., Jelezko F., Keimer B., Kotthaus J.P., Leuchs G., Lütkenhaus N., Maurer U., Pfau T., Plenio M.B., Rasel E.M., Renn O., Silberhorn Ch., Schiedmayer J., Schmitt Landsiedel D., Schönhammer K., Ustinov A., Walther P., Weinfurter H., Welzl E., Wiesendanger R., Wolf S., Zeilinger A., Zoller P. Quantum technology: from research to application. Applied Physics B, 2016, vol. 122, p. 130. Doi: 10.1007/s00340-016-6353-8Morton, J. J. L. Hybrid Solid-State Qubits: The Powerful Role of Electron Spins / J. J .L. Morton, B. W. Lovett // Annu. Rev. Condens. Matter Phys. – 2011. Vol. 2, № 1. – P. 189–212.Morton J.J.L., Lovett B.W. Hybrid Solid-State Qubits: The Powerful Role of Electron Spins. Annual Review of Condensed Matter Physics, 2011, vol. 2, no. 1, pp. 189–212. Doi: 10.1146/annurev-conmatphys-062910-140514Ardavan, A. Quantum control in spintronics / A. Ardavan, G. A. D. Briggs // Philos. Trans. R. Soc. A: Math., Phys. and Engineering Sci. –2011. – Vol. 369, № 1948. – P. 3229–3248.Ardavan A., Briggs G.A.D. Quantum control in spintronics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011, vol. 369, no. 1948, pp. 3229–3248. Doi: 10.1098/rsta.2011.0009Quantum computing with defects / J. R. Weber [et al.] // Proc. Nat. Acad. Sci. USA. – 2010. – Vol. 107, № 1948. – P. 8513–8518.Weber J.R., Koehl W.F., Varley J.B., Janotti A., Buckley B.B., Van de Walle C.G., Awschalom D.D. Quantum computing with defects. Proceedings of the National Academy of Sciences of the United States of America, 2010, vol. 107, no. 19, pp. 8513–8518. Doi: 10.1073/pnas.1003052107Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors / D. D. Awschalom [et al.] // Science. – 2013. – Vol. 339, № 6124. – P. 1174–1179.Awschalom D.D., Bassett L.C., Dzurak A.S., Hu E.L., Petta J.R. Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors. Science, 2013, vol. 339, no. 6124, pp. 1174–1179. Doi: 10.1126/science.1231364Wrachtrup, J. Read-out of single spins by optical spectroscopy / J. Wrachtrup, F. Jelezko // J. Phys.: Condens. Matter. – 2004. – Vol. 16, № 30. – P. R1089–R1104.Jelezko F., Wrachtrup J. Read-out of single spins by optical spectroscopy. Journal of Physics: Condensed Matter, 2004, vol. 16, no. 30, pp. R1089–R1104. Doi: 10.1088/0953-8984/16/30/r03Wrachtrup, J. Processing quantum information in diamond / J. Wrachtrup, F. Jelezko // J. Phys.: Condens. Matter. – 2006. – Vol. 18, № 21. – P. S807–S824.Wrachtrup J., Jelezko F. Processing quantum information in diamond. Journal of Physics: Condensed Matter, 2006, vol. 18, no. 21, pp. S807–S824. Doi: 10.1088/0953-8984/18/21/s08Wrachtrup, J. Single defect centres in diamond: A review / J. Wrachtrup, F. Jelezko // Phys. Status Solidi (a). – 2006. – Vol. 203, № 13. – P. 3207–3225.Wrachtrup J., Jelezko F. Single defect centres in diamond: A review. Physica Status Solidi (a), 2006, vol. 203, no. 13, pp. 3207–3225. Doi: 10.1002/pssa.200671403The nitrogen-vacancy color centre in diamond / M. W. Doherty [et al.] // Physics Reports. – 2013. – Vol. 528, № 1. – P. 1–45.Doherty M.W., Manson N.B., Delaney P., Jelezko F., Wrachtrup J., Hollenberg L.C.L. The nitrogen-vacancy color centre in diamond. Physics Reports, 2013, vol. 528, no. 1, pp. 1–45. Doi: 1016/j.physrep.2013.02.001Quantum control over Single Spins in Diamond / V. V. Dobrovitski [et al.] // Annu. Rev. Condens. Matter Phys. – 2013. – Vol. 4, № 1. – P. 23–50.Dobrovitski V.V., Fuchs G.D., Falk A.L., Santori C., Awschalom D.D. Quantum control over Single Spins in Diamond. Annual Review of Condensed Matter Physics, 2013, vol. 4, no. 1, pp. 23–50. Doi: 10.1146/annurev-conmatphys-030212-184238Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate / F. Jelezko [et al.] // Phys. Rev. Lett. – 2004. – Vol. 93, № 13. –P. 130501.Jelezko F., Gaebel T., Popa I., Domhan M., Gruber A., Wrachtrup J. Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate. Physical Review Letters, 2004, vol. 93, no.13, p.130501. Doi: 10.1103/physrevlett.93.130501CVD diamond for spintronics / M. L. Markham [et al.] // Diamond Relat. Mater. – 2011. –Vol. 20, № 2. –P. 134–139.Markham M.L., Dodson J.M., Scarsbrook G.A., Twitchen D.J., Balasubramanian G., Jelezko F., Wrachtrup J. CVD diamond for spintronics. Diamond and Related Materials, 2011, vol. 20, no. 2, pp. 134–139. Doi: 10.1016/j.diamond.2010.11.016Fabrication of single optical centres in diamond – a review/ J.O. Orwa [et al.] // J. Lumin. – 2010. –Vol. 130, № 9. – P. 1646–1654.Orwa J.O., Greentree A.D., Aharonovich I., Alves A.D.C., VanDonkelaar J., Stacey A., Prawer S. Fabrication of single optical centres in diamond – a review. Journal of Luminescence, 2010, vol. 130, no. 9, pp. 1646–1654. Doi: 10.1016/j.jlumin.2009.12.028Aharonovich, I. Diamond Nanophotonics / I. Aharonovich, E. Neu // Adv. Opt. Mater. – 2014. –Vol. 2, № 10. – P. 911–928.Aharonovich I., Neu E. Diamond Nanophotonics. Advanced Optical Materials, 2014, vol. 2, no. 10, pp. 911–928. Doi: 10.1002/adom.201400189Souza, A. M. Robust dynamical decoupling / A. M. Souza, G. A. Álvarez, D. Suter // Phil. Trans. R. Soc. A: Math., Phys. and Engineering Sci. – 2012. – Vol. 370, № 1976. –P. 4748–4769.Souza A.M., Álvarez G.A., Suter D. Robust dynamical decoupling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012, vol. 370, no. 1976, pp. 4748–4769. Doi: 10.1098/rsta.2011.0355Smeltzer, B. 13C hyperfine interactions in the nitrogen-vacancy centre in diamond / B. Smeltzer, L. Childress, A. Gali // New J. Phys. – 2011. – Vol. 13, № 2. – P. 025021.Smeltzer B., Childress L., Gali A.13C hyperfine interactions in the nitrogen-vacancy centre in diamond. New Journal of Physics, 2011, vol. 13, no. 2, p. 025021. Doi: 10.1088/1367-2630/13/2/025021High-resolution spectroscopy of single NV defects coupled with nearby 13C nuclear spins in diamond / A. Dréau [et al.] // Phys. Rev. B. – 2012. – Vol. 85, № 13. – P. 134107.Dréau A., Maze J.-R., Lesik M., Roch J.-F., Jacques V. High-resolution spectroscopy of single NV defects coupled with nearby 13C nuclear spins in diamond. Physical Review B, 2012, vol. 85, no. 13, p. 134107. Doi: 10.1103/physrevb.85.134107Sensing single remote nuclear spins / N. Zhao [et al.] // Nat. Nanotech. – 2012. – Vol. 7, № 10. – P. 657–662.Zhao N., Honert J., Schmid B., Klas M., Isoya J., Markham M., Twitchen D., Jelezko F., Liu R.-B., Fedder H., Wrachtrup J. Sensing single remote nuclear spins. Nature Nanotechnology, 2012, vol. 7, no. 10, pp. 657–662. Doi: 10.1038/nnano.2012.152Kolkowitz, S. Sensing distant nuclear spins with a single electron spin / S. Kolkowitz, Q. P. Unterreithmeier, S. D. Bennett, M. D. Lukin/ / Phys. Rev. Lett. – 2012. – Vol. 109, № 13. – P. 13760.Kolkowitz S., Unterreithmeier Q.P., Bennett S.D., Lukin M.D. Sensing distant nuclear spins with a single electron spin. Physical Review Letters, 2012, vol. 109, no. 13, p. 13760. Doi: 10.1103/physrevlett.109.137601Magnetometry with nitrogen-vacancy defects in diamond / L. Rondin [et al.] // Rep. Prog. Phys. – 2014. – Vol. 77, № 5. – P. 056503.Rondin L.L., Tetienne J.-P., Hingant T., Roch J.-F., Maletinsky P., Jacques V. Magnetometry with nitrogen-vacancy defects in diamond. Repors on Progress in Physics, 2014, vol. 77, no. 5, p. 056503. Doi: 10.1088/0034-4885/77/5/056503Wrachtrup, J. Single spin magnetic resonance / J. Wrachtrup, A. Finkler // J. Magn. Reson. – 2016. – Vol. 269. – P. 225–236.Wrachtrup J., Finkler A. Single spin magnetic resonance. Journal of Magnetic Resonance, 2016, vol. 269, pp. 225– 236. Doi: 10.1016/j.jmr.2016.06.017Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology / R. Schirhagl [et al.] // Annu. Rev. Phys. Chem. – 2014. – Vol. 65, № 1. – P. 83–105.Schirhagl R., Chang K., Loretz M., Degen Ch.L. Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology. Annual Review of Physical Chemistry, 2014, vol. 65, no. 1, pp. 83–105. Doi: 10.1146/annurev-physchem-040513-103659Nagl, A. Improving surface and defect center chemistry of fluorescent nanodiamonds for imaging purposes – a review / A. Nagl, S. R. Hemelaar, R. Schirhagl // Anal. Bioanal. Chem. – 2015. – Vol. 407, № 25. – P. 7521–7536.Nagl A., Hemelaar S.R., Schirhagl R. Improving surface and defect center chemistry of fluorescent nanodiamonds for imaging purposes – a review. Analytical and Bioanalytical Chemistry, 2015, vol. 407, no. 25, pр. 7521–7536. Doi: 10.1007/ s00216-015-8849-1Diamond integrated quantum photonics / A. D. Greentree [et al.] // Mater. Today. – 2008. – Vol. 11, № 9. – P. 22–31.Greentree A.D., Fairchild B.A., Hossain F.M., Prawer S. Diamond integrated quantum photonics. Materials Today, 2008, vol. 11, no. 9, pр. 22–31. Doi: 10.1016/s1369-7021(08)70176-7Castelletto, S. Quantum Effects in Silicon Carbide Hold Promise for Novel Integrated Devices and Sensors / S. Castelletto, B. C. Johnson, A. Boretti // Adv. Opt. Mater. – 2013. – Vol. 1, № 9. – P. 609–625.Castelletto S., Johnson B.C., Boretti A. Quantum Effects in Silicon Carbide Hold Promise for Novel Integrated Devices and Sensors. Advanced Optical Materials, 2013, vol. 1, no. 9, pp. 609–625. Doi: 10.1002/adom.201300246Spin Centres in SiC for Quantum Technologies / G. V. Astakhov [et al.]// Appl. Magn. Reson. – 2016. – Vol. 47, № 1. – P. 793–812.Astakhov G.V., Simin D., Dyakonov V., Yavkin B.V., Orlinskii S.B., Proskuryakov I.I., Anisimov A.N., Soltamov V.A., Baranov P.G. Spin Centres in SiC for Quantum Technologies. Applied Magnetic Resonance, 2016, vol. 47, no. 7, pp. 793–812. Doi: 10.1007/s00723-016-0800-xAb Initio modeling of the electronic and spin properties of the [NV] –centers in diamond nanocrystals / V. A. Pushkarchuk [et al.] // Opt. Spectrosc. – 2005. – Vol. 99, № 2. – P. 245–256.Pushkarchuk V.A., Kilin S.Ya., Nizovtsev A.P., Pushkarchuk A.L., Borisenko V.E., von Borzyskowski C., Filonov A.B. Ab Initio modeling of the electronic and spin properties of the [NV]-centers in diamond nanocrystals. Optics and Spectroscopy, 2005, vol. 99, no. 2, pp. 245–256. Doi: 10.1134/1.2034611Modeling of atomic and electronic structure of diamond nanocrystals containing [NV]- centers by the density functional method / V. A. Pushkarchuk [et al.] // J. Appl. Spectrosc. – 2007. – Vol. 74, № 1. – P. 95–101.Pushkarchuk V.A. Kilin S.Ya., Nizovtsev A.P., Pushkarchuk A.L., Filonov A.B., Borisenko V.E. Modeling of atomic and electronic structure of diamond nanocrystals containing [NV]-centers by the density functional method. Journal Applied Spectroscopy, 2007, vol. 74, no. 1, pp. 95–101. Doi: 10.1007/s10812-007-0015-xQuantum Chemical Modeling of Structural, Electronic, and Spin Characteristics of NV Centers in Nanostructured Diamond: Surface Effect / V. A. Pushkarchuk [et. al]. // Opt. Spectrosc. – 2010. – Vol. 108, № 2. – P. 254–260.Pushkarchuk V.A., Kilin S.Ya., Nizovtsev A.P., Borisenko V.E., Filonov A.B., Pushkarchuk A.L., Kuten S.A. Quantum Chemical Modeling of Structural, Electronic, and Spin Characteristics of NV Centers in Nanostructured Diamond: Surface Effect. Optics and Spectroscopy, 2010, vol. 108, no. 2, pp. 254–260. Doi: 10.1134/s0030400x10020141Квантовые регистры на одиночных NV+n13С центрах в алмазе: I. Метод спин-гамильтониана / А. П. Низовцев [и др.] // Оптика и спектроскопия. – 2010. – Т. 108, № 2. – С. 260–269.Nizovtsev A.P., Kilin S.Ya., Pushkarchuk V.A., Pushkarchuk A.L., Kuten S.A. Quantum registers based on single NV + n13C centers in diamond: I. The spin Hamiltonian method. Optics and Spectroscopy, 2010, vol. 108, no. 2, pp. 230–238. Doi: 10.1134/s0030400x10020128Spin-Hamiltonian analysis of quantum registers on single NV center and proximal13Cnuclei in diamond / Alexander P. Nizovtsev [et al.] // Quantum cryptography and computing: Theory and Implementation / eds. by R. Horodecki, S. Kilin, J. Kowalik/ – IOS Press, 2010. – Vol. 26. – P. 148–157.Nizovtsev A.P., Kilin S.Ya., Pushkarchuk A.L., Pushkarchuk V.A., Kuten S.A. Spin-Hamiltonian analysis of quantum registers on single NV center and proximal 13Cnuclei in diamond. Horodecki R., Kilin S., Kowalik J. (eds.) Quantum cryptography and computing: Theory and Implementation. IOS Press, 2010, vol. 26, pp. 148–157. Doi: 10.3233/978-1-60750-547-1-148Kramers Degenerated Spin Systems “NV Center + Few Proximal 13C Nuclei” in Diamond for Single-Spin Magnetometry / Alexander P. Nizovtsev [et al.] // Nonlinear Phenomena in Complex Systems. – 2011. – Vol. 14, № 4. – P. 319–334.Nizovtsev A.P., Kilin S.Ya., Pushkarchuk A.L., Pushkarchuk V.L., Kuten S.A. Kramers Degenerated Spin Systems “NV Center + Few Proximal 13C Nuclei” in Diamond for Single-Spin Magnetometry. Nonlinear Phenomena in Complex Systems, 2011, vol. 14, no. 4, pp. 319–334.Gali, A. Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors / A. Gali, M. Fyta, E. Kaxiras // Phys. Rev. B. – 2008. – Vol. 77, № 15. – P. 155206.Gali A.A., Fyta M., Kaxiras E. Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors. Physal Review B, 2008, vol. 77, no. 15, p. 155206. Doi: 10.1103/physrevb.77.155206Smeltzer, B. 13C hyperfine interactions in the nitrogen-vacancy centre in diamond / B. Smeltzer, L. Childress, A. Gali // New J. Phys. – 2011. – Vol. 13, № 2. – P. 025021.Smeltzer B, Childress L, Gali A. 13C hyperfine interactions in the nitrogen-vacancy centre in diamond. New Journal of Physics, 2011, vol. 13, no. 2, p. 025021. Doi: 10.1088/1367-2630/13/2/025021Theoretical study of hyperfine interactions and optically detected magnetic resonance spectra by simulation of the C291[NV]–H172 diamond cluster hosting NV center / A. P. Nizovtsev [et al.] // New J. Phys. – 2014. – Vol. 16, № 8. – P. 083014.Nizovtsev A.P., Kilin S.Ya., Pushkarchuk A.L., Pushkarchuk V.A., Jelezko F. Theoretical study of hyperfine interactions and optically detected magnetic resonance spectra by simulation of the C291[NV]- H172 diamond cluster hosting NV center. New Journal of Physics, 2014, vol. 16, no. 8, p. 083014. Doi: 10.1088/1367-2630/16/8/083014Luzanov, A. V. About theoretical peculiarities of lowest excitations in modified nanodiamond color centers / A. V. Luzanov // Funct. Mater. – 2017. – Vol. 24.Luzanov A.V. About theoretical peculiarities of lowest excitations in modified nanodiamond color centers. Functional Materials, 2017, vol. 24.Probing the Dynamics of a Nuclear Spin Bath in Diamond through Time-Resolved Central Spin Magnetometry / A. Dréau [et al.] // Phys. Rev. Lett. – 2014. – Vol. 113, № 13. – P. 137601.Dréau A., Jamonneau P., Gazzano O., Kosen S., Roch J.-F., Maze J.R., Jacques V. Probing the Dynamics of a Nuclear Spin Bath in Diamond through Time-Resolved Central Spin Magnetometry. Physical Review Letters, 2014, vol. 113, no. 13, p. 137601. Doi: 10.1103/physrevlett.113.137601Quantum error correction in a solid-state hybrid spin register / G. Waldherr [et al.] // Nature. – 2014. – Vol. 506, № 7487. – P. 204–207.Waldherr G., Wang Y., Zaiser S., Jamali M., Schulte-Herbrüggen T., Abe H., Ohshima T., Isoya J., Du J.F., Neumann P., Wrachtrup J. Quantum error correction in a solid-state hybrid spin register. Nature, 2014, vol. 506, no. 7487, pp. 204–207. Doi: 10.1038/nature12919Enhancing quantum sensing sensitivity by a quantum memory / S. Zaiser [et al.] // Nat. Commun. – 2016. – Vol. 7. – P. 12279.Zaiser S., Rendler T., Jakobi I., Wolf Th., Lee S.-Y., Wagner S., Bergholm V., Schulte-Herbrüggen Th., Neumann Ph., Wrachtrup J. Enhancing quantum sensing sensitivity by a quantum memory. Nature Communications, 2016, vol. 7, p. 12279. Doi: 10.1038/ncomms12279Quantum metrology enhanced by repetitive quantum error correction / Th. Unden [et al.] // Phys. Rev. Lett. – 2016. – Vol. 116, № 23. – P. 230502.Unden Th., Balasubramanian P., Louzon D., Vinkler Y., Plenio M.B., Markham M., Twitchen D., Lovchinsky I., Sushkov A.O., Lukin M.D., Retzker A., Naydenov B., McGuinness L.P., Jelezko F. Quantum metrology enhanced by repetitive quantum error correction. Physical Review .Letters, 2016, vol. 116, no. 23, p. 230502. Doi: 10.1103/physrevlett.116.230502

The authors declare that there are no conflicts of interest present.