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				The nitrogen-vacancy (NV) color center quantum system in diamond has shown great application potential in the fields of solid-state quantum computing and quantum precision measurement because of its unique advantages such as single-spin addressing and manipulation and long quantum coherence time at room temperature. The precise manipulation technology of single spin is particularly important for the development of the application of NV center. The common spin manipulation methods used in NV center quantum system are to drive and manipulate the electron spin by resonant alternating magnetic field. In recent years, the electrical control of quantum spin has attracted extensive attention. In this paper, using the alternating electric field to control the electron spin of NV center is studied. The alternating electric field generated by the electrode successfully drives the Rabi oscillation of the NV center spin between the$\Delta m_{\rm{s}}=\pm2$ magnetic-dipole forbidden energy levels of$|m_{\rm{s}}=-1\rangle$ and$|m_{\rm{s}}=+1\rangle$ . Further studies show that the frequency of the electrically driven Rabi oscillation is controlled by the power of the driven electric field but independent of the resonant frequency of the electric field. The combination of spin electric control and magnetic control technology can realize the full manipulation of the direct transition among the three spin energy levels of NV center, thus promoting the development of the researches and applications of NV quantum system in the fields of quantum simulation, quantum computing, precision measurement of electromagnetic field, etc.- 
										Keywords:
										
- quantum coherent control /
- nitrogen-vacancy color center /
- diamond /
- electric field
 [1] Gruber A, Drabenstedt A, Tietz C, Fleury L, Wrachtrup J, vonBorczyskowski C 1997 Science 276 2012  Google Scholar Google Scholar[2] Neumann P, Beck J, Steiner M, Rempp F, Fedder H, Hemmer P R, Wrachtrup J, Jelezko F 2010 Science 329 542  Google Scholar Google Scholar[3] 刘刚钦, 邢健, 潘新宇 2018 67 120302  Google Scholar Google ScholarLiu G Q, Xing J, Pan X Y 2018 Acta Phys. Sin. 67 120302  Google Scholar Google Scholar[4] Balasubramanian G, Neumann P, Twitchen D, Markham M, Kolesov R, Mizuochi N, Isoya J, Achard J, Beck J, Tissler J, Jacques V, Hemmer P R, Jelezko F, Wrachtrup J 2009 Nat. Mater. 8 383  Google Scholar Google Scholar[5] Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y, Du J F 2015 Nat. Commun. 25 8748  Google Scholar Google Scholar[6] Waldherr G, Wang Y, Zaiser S, Jamali M, Schulte-Herbruggen T, Abe H, Ohshima T, Isoya J, Du J F, Neumann P, Wrachtrup J 2014 Nature 506 204  Google Scholar Google Scholar[7] Liu G Q, Pan X Y 2018 Chin. Phys. B 27 020304  Google Scholar Google Scholar[8] 董杨, 杜博, 张少春, 陈向东, 孙方稳 2018 67 160301  Google Scholar Google ScholarDong Y, Du B, Zhang S C, Chen X D, Sun F W 2018 Acta Phys. Sin. 67 160301  Google Scholar Google Scholar[9] Taylor J M, Cappellaro P, Childress L, Jiang L, Budker D, Hemmer P R, Yacoby A, Walsworth R, Lukin M D 2008 Nat. Phys. 4 810  Google Scholar Google Scholar[10] Wang P F, Yuan Z H, Huang P, Rong X, Wang M Q, Xu X, Duan C K, Ju C Y, Shi F Z, Du J F 2015 Nat. Commun. 6 6631  Google Scholar Google Scholar[11] 彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 67 167601  Google Scholar Google ScholarPeng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601  Google Scholar Google Scholar[12] 王成杰, 石发展, 王鹏飞, 段昌奎, 杜江峰 2018 67 130701  Google Scholar Google ScholarWang C J, Shi F Z, Wang P F, Duan C K, Du J F 2018 Acta Phys. Sin. 67 130701  Google Scholar Google Scholar[13] Dolde F, Fedder H, Doherty M W, Nobauer T, Rempp F, Balasubramanian G, Wolf T, Reinhard F, Hollenberg L C L, Jelezko F, Wrachtrup J 2011 Nat. Phys. 7 459  Google Scholar Google Scholar[14] Dolde F, Doherty M W, Michl J, Jakobi I, Naydenov B, Pezzagna S, Meijer J, Neumann P, Jelezko F, Manson N B, Wrachtrup J 2014 Phys. Rev. Lett. 112 097603  Google Scholar Google Scholar[15] Michl J, Steiner J, Denisenko A, Bulau A, Zimmermann A, Nakamura K, Sumiya H, Onoda S, Neumann P, Isoya J, Wrachtrup J 2019 Nano Lett. 19 4904  Google Scholar Google Scholar[16] Li R, Kong F, Zhao P J, Cheng Z, Qin Z Y, Wang M Q, Zhang Q, Wang P f, Wang Y, Shi F Z, Du J F 2020 Phys. Rev. Lett. 124 247701  Google Scholar Google Scholar[17] Barson M S J, Oberg L M, McGuinness L P, Denisenko A, Manson N B, Wrachtrup J, Doherty M W 2021 Nano Lett. 21 2962  Google Scholar Google Scholar[18] Bian K, Zheng W T, Zeng X Z, Chen X K, Stoehr R, Denisenko A, Yang S, Wrachtrup J, Jiang Y 2021 Nat. Commun. 12 2457  Google Scholar Google Scholar[19] Zhao P J, Kong F, Li R, Shi F Z, Du J F 2021 Acta Phys. Sin. 70 213301  Google Scholar Google Scholar[20] Doherty M W, Struzhkin V V, Simpson D A, McGuinness L P, Meng Y, Stacey A, Karle T J, Hemley R J, Manson N B, Hollenberg L C L, Prawer S 2014 Phys. Rev. Lett. 112 047601  Google Scholar Google Scholar[21] Neumann P, Jakobi I, Dolde F, Burk C, Reuter R, Waldherr G, Honert J, Wolf T, Brunner A, Shim J H, Suter D, Sumiya H, Isoya J, Wrachtrup J 2013 Nano Lett. 13 2738  Google Scholar Google Scholar[22] Kucsko G, Maurer P C, Yao N Y, Kubo M, Noh H J, Lo P K, Park H, Lukin M D 2013 Nature 500 54  Google Scholar Google Scholar[23] Choi J, Zhou H, Landig R, Wu H-Y, Yu X, Von Stetina S E, Kucsko G, Mango S, Needleman D J, Samuel A D T, Maurer P C, Park H, Lukin M D 2020 P. Nat. Acad. Sci. USA 117 14636  Google Scholar Google Scholar[24] Fujiwara M, Sun S, Dohms A, Nishimura Y, Suto K, Takezawa Y, Oshimi K, Zhao L, Sadzak N, Umehara Y, Teki Y, Komatsu N, Benson O, Shikano Y, Kage-Nakadai E 2020 Science Advances 6 37  Google Scholar Google Scholar[25] Mueller C, Kong X, Cai J M, Melentijevic K, Stacey A, Markham M, Twitchen D, Isoya J, Pezzagna S, Meijer J, Du J F, Plenio M B, Naydenov B, McGuinness L P, Jelezko F 2014 Nat. Commun. 5 4703  Google Scholar Google Scholar[26] Nowack K C, Koppens F H L, Nazarov Y V, Vandersypen L M K 2007 Science 318 1430  Google Scholar Google Scholar[27] Klimov P V, Falk A L, Buckley B B, Awschalom D D 2014 Phys. Rev. Lett. 112 187601  Google Scholar Google Scholar[28] Asaad S, Mourik V, Joecker B, Johnson M A I, Baczewski A D, Firgau H R, Madzik M T, Schmitt V, Pla J J, Hudson F E, Itoh K M, McCallum J C, Dzurak A S, Laucht A, Morello A 2020 Nature 579 205  Google Scholar Google Scholar[29] Yang B, Murooka T, Mizuno K, Kim K, Kato H, Makino T, Ogura M, Yamasaki S, Schmidt M E, Mizuta H, Yacoby A, Hatano M, Iwasaki T 2020 Phys. Rev. Appl. 14 044049  Google Scholar Google Scholar[30] Loubser J, van Wyk J 1977 Diamond Research 9 11 [31] MacQuarrie E R, Gosavi T A, Jungwirth N R, Bhave S A, Fuchs G D 2013 Phys. Rev. Lett. 111 227602  Google Scholar Google Scholar[32] Vanoort E, Glasbeek M 1990 Chemical Physics Letters 168 529  Google Scholar Google Scholar[33] Rabeau J R, Reichart P, Tamanyan G, Jamieson D N, Prawer S, Jelezko F, Gaebel T, Popa I, Domhan M, Wrachtrup J 2006 Appl. Phys. Lett. 88 023113  Google Scholar Google Scholar[34] Liu P, Yen R, Bloembergen N 1978 IEEE J. Quantum Elect. 14 574  Google Scholar Google Scholar
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图 1 (a) NV色心结构图; (b) 存在轴向磁场 $B_{z}$ 下NV色心的基态能级图,$|\uparrow \rangle$ 和$|\downarrow \rangle$ 代表$^{15}{\rm{N}}$ 核自旋朝向; 黄色和蓝色箭头分别代表$\Delta m_{{\rm{s}}}=\pm 1$ 跃迁和$\Delta m_{{\rm{s}}}=\pm 2$ 跃迁Figure 1. (a) Structure diagram of the NV center; (b) energy level diagram for the NV ground-state spin in the presence of an axial magnetic field $B_{z}$ ,$|\uparrow \rangle$ and$|\downarrow \rangle$ represent the spin orientation of$^{15}{\rm{N}}$ ;$\Delta m_{{\rm{s}}} = \pm 1$ transitions (yellow arrows) and the$\Delta m_{{\rm{s}}} = \pm 2$ transition (blue arrows) are indicated.图 3 (a) ODMR的频率谱; (b) NV色心电子自旋的相干时间测量. $ ^{12}{\rm{C}}$ 纯化延长了电子自旋的相干时间, 弛豫时间$T_{2}$ 经指数衰减函数${\rm{exp}}[-(2 \tau/T_{2})^2]$ (红线)拟合约为$1.6\ {\rm{ms}}$ Figure 3. (a) The frequency spectrum of ODMR; (b) coherent time measurement of electron spin in NV center. The purification of $ ^{12}{\rm{C}}$ prolongs the coherence time of electron spin, and the relaxation time$T_{2}$ is estimated to be$1.6\ {\rm{ms}}$ through the exponential attenuation function${\rm{exp}}[-(2 \tau/T_{2})^2]$ (red line).
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[1] Gruber A, Drabenstedt A, Tietz C, Fleury L, Wrachtrup J, vonBorczyskowski C 1997 Science 276 2012  Google Scholar Google Scholar[2] Neumann P, Beck J, Steiner M, Rempp F, Fedder H, Hemmer P R, Wrachtrup J, Jelezko F 2010 Science 329 542  Google Scholar Google Scholar[3] 刘刚钦, 邢健, 潘新宇 2018 67 120302  Google Scholar Google ScholarLiu G Q, Xing J, Pan X Y 2018 Acta Phys. Sin. 67 120302  Google Scholar Google Scholar[4] Balasubramanian G, Neumann P, Twitchen D, Markham M, Kolesov R, Mizuochi N, Isoya J, Achard J, Beck J, Tissler J, Jacques V, Hemmer P R, Jelezko F, Wrachtrup J 2009 Nat. Mater. 8 383  Google Scholar Google Scholar[5] Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y, Du J F 2015 Nat. Commun. 25 8748  Google Scholar Google Scholar[6] Waldherr G, Wang Y, Zaiser S, Jamali M, Schulte-Herbruggen T, Abe H, Ohshima T, Isoya J, Du J F, Neumann P, Wrachtrup J 2014 Nature 506 204  Google Scholar Google Scholar[7] Liu G Q, Pan X Y 2018 Chin. Phys. B 27 020304  Google Scholar Google Scholar[8] 董杨, 杜博, 张少春, 陈向东, 孙方稳 2018 67 160301  Google Scholar Google ScholarDong Y, Du B, Zhang S C, Chen X D, Sun F W 2018 Acta Phys. Sin. 67 160301  Google Scholar Google Scholar[9] Taylor J M, Cappellaro P, Childress L, Jiang L, Budker D, Hemmer P R, Yacoby A, Walsworth R, Lukin M D 2008 Nat. Phys. 4 810  Google Scholar Google Scholar[10] Wang P F, Yuan Z H, Huang P, Rong X, Wang M Q, Xu X, Duan C K, Ju C Y, Shi F Z, Du J F 2015 Nat. Commun. 6 6631  Google Scholar Google Scholar[11] 彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 67 167601  Google Scholar Google ScholarPeng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601  Google Scholar Google Scholar[12] 王成杰, 石发展, 王鹏飞, 段昌奎, 杜江峰 2018 67 130701  Google Scholar Google ScholarWang C J, Shi F Z, Wang P F, Duan C K, Du J F 2018 Acta Phys. Sin. 67 130701  Google Scholar Google Scholar[13] Dolde F, Fedder H, Doherty M W, Nobauer T, Rempp F, Balasubramanian G, Wolf T, Reinhard F, Hollenberg L C L, Jelezko F, Wrachtrup J 2011 Nat. Phys. 7 459  Google Scholar Google Scholar[14] Dolde F, Doherty M W, Michl J, Jakobi I, Naydenov B, Pezzagna S, Meijer J, Neumann P, Jelezko F, Manson N B, Wrachtrup J 2014 Phys. Rev. Lett. 112 097603  Google Scholar Google Scholar[15] Michl J, Steiner J, Denisenko A, Bulau A, Zimmermann A, Nakamura K, Sumiya H, Onoda S, Neumann P, Isoya J, Wrachtrup J 2019 Nano Lett. 19 4904  Google Scholar Google Scholar[16] Li R, Kong F, Zhao P J, Cheng Z, Qin Z Y, Wang M Q, Zhang Q, Wang P f, Wang Y, Shi F Z, Du J F 2020 Phys. Rev. Lett. 124 247701  Google Scholar Google Scholar[17] Barson M S J, Oberg L M, McGuinness L P, Denisenko A, Manson N B, Wrachtrup J, Doherty M W 2021 Nano Lett. 21 2962  Google Scholar Google Scholar[18] Bian K, Zheng W T, Zeng X Z, Chen X K, Stoehr R, Denisenko A, Yang S, Wrachtrup J, Jiang Y 2021 Nat. Commun. 12 2457  Google Scholar Google Scholar[19] Zhao P J, Kong F, Li R, Shi F Z, Du J F 2021 Acta Phys. Sin. 70 213301  Google Scholar Google Scholar[20] Doherty M W, Struzhkin V V, Simpson D A, McGuinness L P, Meng Y, Stacey A, Karle T J, Hemley R J, Manson N B, Hollenberg L C L, Prawer S 2014 Phys. Rev. Lett. 112 047601  Google Scholar Google Scholar[21] Neumann P, Jakobi I, Dolde F, Burk C, Reuter R, Waldherr G, Honert J, Wolf T, Brunner A, Shim J H, Suter D, Sumiya H, Isoya J, Wrachtrup J 2013 Nano Lett. 13 2738  Google Scholar Google Scholar[22] Kucsko G, Maurer P C, Yao N Y, Kubo M, Noh H J, Lo P K, Park H, Lukin M D 2013 Nature 500 54  Google Scholar Google Scholar[23] Choi J, Zhou H, Landig R, Wu H-Y, Yu X, Von Stetina S E, Kucsko G, Mango S, Needleman D J, Samuel A D T, Maurer P C, Park H, Lukin M D 2020 P. Nat. Acad. Sci. USA 117 14636  Google Scholar Google Scholar[24] Fujiwara M, Sun S, Dohms A, Nishimura Y, Suto K, Takezawa Y, Oshimi K, Zhao L, Sadzak N, Umehara Y, Teki Y, Komatsu N, Benson O, Shikano Y, Kage-Nakadai E 2020 Science Advances 6 37  Google Scholar Google Scholar[25] Mueller C, Kong X, Cai J M, Melentijevic K, Stacey A, Markham M, Twitchen D, Isoya J, Pezzagna S, Meijer J, Du J F, Plenio M B, Naydenov B, McGuinness L P, Jelezko F 2014 Nat. Commun. 5 4703  Google Scholar Google Scholar[26] Nowack K C, Koppens F H L, Nazarov Y V, Vandersypen L M K 2007 Science 318 1430  Google Scholar Google Scholar[27] Klimov P V, Falk A L, Buckley B B, Awschalom D D 2014 Phys. Rev. Lett. 112 187601  Google Scholar Google Scholar[28] Asaad S, Mourik V, Joecker B, Johnson M A I, Baczewski A D, Firgau H R, Madzik M T, Schmitt V, Pla J J, Hudson F E, Itoh K M, McCallum J C, Dzurak A S, Laucht A, Morello A 2020 Nature 579 205  Google Scholar Google Scholar[29] Yang B, Murooka T, Mizuno K, Kim K, Kato H, Makino T, Ogura M, Yamasaki S, Schmidt M E, Mizuta H, Yacoby A, Hatano M, Iwasaki T 2020 Phys. Rev. Appl. 14 044049  Google Scholar Google Scholar[30] Loubser J, van Wyk J 1977 Diamond Research 9 11 [31] MacQuarrie E R, Gosavi T A, Jungwirth N R, Bhave S A, Fuchs G D 2013 Phys. Rev. Lett. 111 227602  Google Scholar Google Scholar[32] Vanoort E, Glasbeek M 1990 Chemical Physics Letters 168 529  Google Scholar Google Scholar[33] Rabeau J R, Reichart P, Tamanyan G, Jamieson D N, Prawer S, Jelezko F, Gaebel T, Popa I, Domhan M, Wrachtrup J 2006 Appl. Phys. Lett. 88 023113  Google Scholar Google Scholar[34] Liu P, Yen R, Bloembergen N 1978 IEEE J. Quantum Elect. 14 574  Google Scholar Google Scholar
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