本文主要探討在單晶奈米鑽石中的氮聯袂空缺有色中心電子自旋弛豫的動力學機制。首先我們以光學探測磁共振技術(ODMR)，在固定的外磁場下探測單晶奈米鑽石，得出亮度與微波頻率的頻譜關係圖，磁場中所量測到的尖峰為賽曼效應(Zeeman split)所產生，其峰值為相對應的躍遷頻率。藉由頻譜圖的數據分析所擬合出的結果，可以得出該單晶奈米鑽石空間中的相對位置與方向，擁有該鑽石的空間資訊，則可用做測量未知磁場的奈米探針。
接著我們研究在不同的磁場以及不同的外加微波場下氮聯袂空缺有色中心的縱向弛豫時間。我們發現了單粒子模型下的指數衰減擬合曲線，無法很好的貼合實驗數據。為了更好的了解其動力學機制，因此我們引入拉伸指數函數擬合，且更好的貼合實驗數據。擬合結果顯示了帶有氮聯袂空缺有色中心的單晶奈米鑽石電子自旋弛豫現象其弛豫機制，更接近多個簡單指數函數綜合的表現，反應出帶有氮聯袂空缺有色中心的單晶奈米鑽石的綜合複雜機制。
關鍵字：氮聯袂空缺有色中心，單晶奈米鑽石，光學探測磁共振技術，賽曼效應，奈米探針，弛豫時間，拉伸指數函數。

This thesis studies the relaxation dynamics of an ensemble of ground-state spins of negatively charged nitrogen-vacancy color (NV- or simply NV) centers in a single-crystalline nanodiamond. The spin resonance spectrum of the NV centers was first determined by the optically detected magnetic resonance (ODMR) technique. The spectrum peaks mark the spin transition frequencies and are Zeeman split in a static magnetic field. By fitting the transition frequencies given by a known field to the spin Hamiltonian, we can determine the crystal orientation of the nanodiamond. With this information, the single-crystalline nanodiamond can then be utilized as a nanoprobe, and we can use the nanodiamond to detect an unknown magnetic field.
The longitudinal relaxation time of the ground spins of NV- centers was studied under conditions of different static magnetic fields and with or without resonant microwaves. Non-exponential spin relaxation was observed, and the spin-1 model of a single NV- center can not adequately explain the spin relaxation, which gives an exponential decay. The relaxation curve fitted to a so-called stretched exponential decay. To better understand the underlying dynamics of the spin relaxation, simulation of an ensemble of coupled NV- center spins was performed. Simulation results pointed out that coupling between NV spins seems to initiate collective spin relaxation, which can be responsible for the stretched exponential decay.
Keywords: negatively charged nitrogen-vacancy color (NV- center), single-crystalline nanodiamond, optically detected magnetic resonance (ODMR), Zeeman split, nanoprobe, relaxation time, stretched exponential decay.

[1] Nobelprize.org. All nobel prizes in physics. http://www.nobelprize.org/nobel_prizes/physics/laureates/. Accessed in July, 2013.
[2] S. Siddique, J.C.L Chow. Application of Nanomaterials in Biomedical Imaging and Cancer Therapy. Nanomaterials (Basel, Switzerland), 10(9), 1700 (2020).
[3] R. A. Shimkunas, E. Robinson, R. Lam, S. Lu, X. Xu, X. Q. Zhang, H. Huang, E. Osawa, and D. Ho. Nanodiamond-insulin complexes as pH-dependent protein delivery vehicles. Biomaterials 30(29), 5720 (2009).
[4] Y. R. Chang, H. Y. Lee, K. Chen, et al. Mass production and dynamic imaging of fluorescent nanodiamonds. Nature Nanotech 3, 284 (2008).
[5] Y. Chu, M. Markham, D. J. Twitchen, and M. D. Lukin. All-optical control of a single electron spin in diamond. Phys. Rev. A 91, 021801 (2015).
[6] R. S. Schoenfeld and W. Harneit. Real Time Magnetic Field Sensing and Imaging Using a Single Spin in Diamond. Phys. Rev. Lett. 106, 030802 (2011).
[7] V. M. Acosta, E. Bauch, M. P. Ledbetter, A. Waxman, L. S. Bouchard, and D. Budker. Temperature Dependence of the Nitrogen-Vacancy Magnetic Resonance in Diamond. Phys. Rev. Lett. 104, 070801 (2010).
[8] C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter. Stable Solid-State Source of Single Photons. Phys. Rev. Lett. 85, 290 (2000).
[9] P. Neumann, J. Beck, M. Steiner, F. Rempp, H. Fedder, P. R Hemmer, J. Wrachtrup, and F. Jelezko. Single-shot readout of a single nuclear spin. Science (New York, N.Y.) 329, 542 (2010).
[10] V. M. Acosta, Ph.D. thesis, UC Berkeley (2011).
[11] V. M. Acosta, A. Jarmola, E. Bauch and D. Budker. Optical properties of the nitrogen-vacancy singlet levels in diamond. Phys. Rev. B 82, 201202(R) (2010).
[12] A. Gali, M. Fyta, and E. Kaxiras. Ab initio supercell calculations on nitrogen-vacancy center in diamond: Electronic structure and hyperfine tensors. Phys. Rev. B 77, 155206 (2008).
[13] M.W. Doherty, N.B. Manson, P. Delaney and L.C.L. Hollenberg. The negatively charged nitrogen-vacancy centre in diamond: the electronic solution. New Journal of Physics 13, 025019 (2011).
[14] R. Schirhagl, K. Chang, M. Loretz, and C. L. Degen. Nitrogen-Vacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology. Annu. Rev. Phys. Chem. 65, 83 (2014).
[15] A.M. Zaitsev. Optical Properties of Diamond: A Data Handbook. (Springer, 2001).
[16] A. Gali. Time-dependent density functional study on the excitation spectrum of point defects in semiconductors. Physica status solidi (b), 248(6):1337 (2011).
[17] J.Choi, S. Choi, G. Kucsko, P. C. Maurer, B. J. Shields, H. Sumiya, S. Onoda, J. Isoya, E. Demler, F. Jelezko, N. Y. Yao, and M. D. Lukin. Depolarization Dynamics in a Strongly Interacting Solid-State Spin Ensemble. Phys. Rev. Lett. 118, 093601 (2017).
[18] K. Procházka, Z. Limpouchová, F. Uhlík, P. Košovan, P. Matějíček, M. Štěpánek, M. Uchman, J Kuldová, R. Šachl, J. Humpolíčková, and M. Hof. Fluorescence spectroscopy as a tool for investigating the self-organized polyelectrolyte systems. In Self Organized Nanostructures of Amphiphilic Block Copolymers I, (Springer Berlin Heidelberg, 2011) volume 241 of Advances in Polymer Science, pages 187-249.
[19] A. Angerer, K. Streltsov, T. Astner, S. Putz, H. Sumiya, S. Onoda, J. Isoya, W. J. Munro, K. Nemoto, J. Schmiedmayer and J. Majer. Superradiant emission from colour centres in diamond. Nature Phys 14, 1168–1172 (2018).
[20] C. Belthangady, N. Bar-Gill, L. M. Pham, K. Arai, D. Le Sage, P. Cappellaro, and R. L. Walsworth. Dressed-State Resonant Coupling between Bright and Dark Spins in Diamond. Phys. Rev. Lett. 110, 157601 (2013).
[21] G. Kucsko, S. Choi, J. Choi, P. C. Maurer, H. Zhou, R. Landig, H. Sumiya, S. Onoda, J. Isoya, F. Jelezko, E. Demler, N. Y. Yao, and M. D. Lukin. Critical Thermalization of a Disordered Dipolar Spin System in Diamond. Phys. Rev. Lett. 121, 023601 (2018).
[22] N. Zhao, Z. Y. Wang, R. B. Liu. Anomalous decoherence effect in a quantum bath. Phys. Rev. Lett. 106, 217205 (2011).
[23] M. Capelli, P. Reineck, D. W. M. Lau, A. Orth, J. Jeske, M. W. Doherty, T. Ohshima, A. D. Greentree and B. C. Gibson. Magnetic field-induced enhancement of the nitrogen-vacancy fluorescence quantum yield. Nanoscale, 2017, 9, 9299 (2017).
[24] N. B. Manson, J. P. Harrison, and M. J. Sellars. Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics. Phys. Rev. B 74, 104303 (2006).
[25] M. Luszczek, R. Laskowski, and P. Horodecki. The ab initio calculations of single nitrogen-vacancy defect center in diamond. Physica B Condensed Matter, 348:292 (2004).
[26] J. P. Goss, R. Jones, P. R. Briddon, G. Davies, A. T. Collins, A. Mainwood, J. A. van Wyk, J. M. Baker, M. E. Newton, A. M. Stoneham, and S. C. Lawson. Comment on “Electronic structure of the N-V center in diamond: Theory”. Phys. Rev. B 56, 16031 (1997).
[27] J. R. Lakowicz. Principles of Fluorescence Spectroscopy. (Springer London, Limited, 2006).
[28] N. Bar-Gill, L.M. Pham, A. Jarmola, D. Budker, and R.L. Walsworth. Solid-state electronic spin coherence time approaching one second. Nature Communications volume 4, Article number: 1743 (2013).