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金刚石氮-空位(nitrogen-vacancy, NV)色心量子体系因在室温条件下具有可实现单自旋寻址与操控、长量子相干时间等独特优势, 在固态量子计算、量子精密测量等领域展现了巨大的应用潜力, 其中单自旋的精确操控技术对于NV色心应用的发展尤为关键. NV色心量子体系中常用的自旋操控方法都是通过共振的交变磁场来驱动和操控NV色心电子自旋. 本文开展了利用交变电场对NV色心电子自旋进行调控的技术研究. 通过电极所产生的交变电场成功驱动了NV色心自旋在
$|m_{\rm{s}}=-1\rangle$ 与$|m_{\rm{s}}=+1\rangle$ 两个$\Delta m_{\rm{s}} =\pm2$ 的磁禁戒能级间的跃迁, 并观测到受控自旋在相关能级的布居度周期性变化而展现出的Rabi振荡现象. 进一步的研究表明, 电场驱动Rabi振荡的频率受驱动电场功率的调控, 与驱动电场的共振频率无直接关系. 将自旋电控制技术与磁控制技术方法相结合, 能够实现对NV色心3个自旋能级间直接跃迁的全操控. 自旋电控制技术的发展将进一步推动NV色心量子体系在量子模拟、量子计算、电磁场的精密测量等领域研究和应用的发展.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
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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Fig. 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 2 (a)电极和微波线的结构设计简图; (b) 激光共聚焦扫描NV色心的荧光图
Fig. 2. (a) Structural design diagram of electrode and microwave line; (b) fluorescence diagram of NV centers scanned by a laser scanning confocal microscope.
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$1.6\ {\rm{ms}}$ Fig. 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).
图 4 (a) EODMR脉冲序列及自旋跃迁示意图; (b) EODMR的共振峰谱图
Fig. 4. (a) EODMR pulse sequence and spin transition diagram; (b) the resonance peak spectrum of EODMR.
图 5 (a) ERabi脉冲序列; (b) 在不同电场驱动功率的作用下, NV色心电子自旋的ERabi振荡谱
Fig. 5. (a) ERabi pulse sequence; (b) ERabi oscillatory spectrum of electron spin in NV center under the action of different electric field driving power.
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[1] Gruber A, Drabenstedt A, Tietz C, Fleury L, Wrachtrup J, vonBorczyskowski C 1997 Science 276 2012
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
[3] 刘刚钦, 邢健, 潘新宇 2018 物理学报 67 120302
Google Scholar
Liu G Q, Xing J, Pan X Y 2018 Acta Phys. Sin. 67 120302
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
[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
[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
[7] Liu G Q, Pan X Y 2018 Chin. Phys. B 27 020304
Google Scholar
[8] 董杨, 杜博, 张少春, 陈向东, 孙方稳 2018 物理学报 67 160301
Google Scholar
Dong Y, Du B, Zhang S C, Chen X D, Sun F W 2018 Acta Phys. Sin. 67 160301
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
[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
[11] 彭世杰, 刘颖, 马文超, 石发展, 杜江峰 2018 物理学报 67 167601
Google Scholar
Peng S J, Liu Y, Ma W C, Shi F Z, Du J F 2018 Acta Phys. Sin. 67 167601
Google Scholar
[12] 王成杰, 石发展, 王鹏飞, 段昌奎, 杜江峰 2018 物理学报 67 130701
Google Scholar
Wang C J, Shi F Z, Wang P F, Duan C K, Du J F 2018 Acta Phys. Sin. 67 130701
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
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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
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Google Scholar
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Google Scholar
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Google Scholar
[19] Zhao P J, Kong F, Li R, Shi F Z, Du J F 2021 Acta Phys. Sin. 70 213301
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
[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
[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
[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
[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
[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
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Google Scholar
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Google Scholar
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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
[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
[32] Vanoort E, Glasbeek M 1990 Chemical Physics Letters 168 529
Google Scholar
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Google Scholar
[34] Liu P, Yen R, Bloembergen N 1978 IEEE J. Quantum Elect. 14 574
Google Scholar
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