在這項研究中，我們深入探討了鑽石中的氮空位（NV）中心的自旋回波動力學，特別關注其與核自旋極化的相互作用。我們的調查利用IBM量子計算機平台上的量子電 路，使我們能夠模擬電子自旋、核自旋和輔助量子比特之間的複雜互動。這項研究不僅突出了自旋回波過程的傳統特徵，還展示了附近核自旋的極化如何顯著影響這些過程的結果。通過檢查核自旋極化的效果，我們評估了它們的存在和行為如何影響自旋回波方法的有效性和細微差別。
我們的發現為NV中心的複雜動力學提供了更深入的洞見，增強了我們對其在受核自旋影響的量子系統中角色的理解。通過詳細檢查這些互動，我們的工作有助於改進量子測量和控制技術，這對於提高利用NV中心的量子系統的穩定性和功能至關重要。這項研究探索了如何附近核自旋的極化影響自旋回波過程的結果等關鍵方面，這對於在量子計算、計量學和感測中開發更有效、更可靠的協議至關重要。
此外，這項研究推進了我們對量子退相干的知識，提供了在量子設備中減輕其影響的新視角。通過改善我們對影響NV中心量子相干的基礎機制的理解，我們可以指導更強大的量子技術的發展。這種全面的方法不僅完善了基本的量子測量和控制技術，還突出了NV中心在各個領域的潛在應用，對推動量子技術的進步做出了重大貢獻。

In this study, we delve into the spin-echo dynamics of a nitrogen-vacancy (NV) center in diamond, focusing particularly on how it interacts with nuclear spin polarization. Our investigation employs quantum circuits on the IBM Quantum Computer platform, enabling us to simulate the intricate interactions between electron spins, nuclear spins, and auxiliary qubits. This research not only highlights traditional features of the spin-echo process but also demonstrates how the polarization of nearby nuclear spins significantly influences the outcomes of these processes. By examining the effects of nuclear spin polarization, we assess how their presence and behavior impact the effectiveness and nuances of the spin-echo method.
Our research offers more profound understanding of the intricate dynamics within the NV center, deepening our grasp of its function in quantum systems affected by nuclear spins.
By thoroughly analyzing these interactions, our efforts aid in honing methods for quantum measurement and control, pivotal for enhancing the robustness and effectiveness of quantum systems that employ NV centers. This investigation delves into vital elements like the influence of nearby nuclear spins’ polarization on the outcomes of spin-echo processes, which is vital for crafting more efficient and dependable protocols in quantum computing, metrology, and sensing.
Additionally, this research advances our knowledge of quantum decoherence, offering new perspectives on mitigating its effects in quantum devices. By improving our understanding of the underlying mechanisms that affect quantum coherence in NV centers, we can guide the development of more robust quantum technologies. This comprehensive approach not only refines the fundamental quantum measurement and control techniques but also highlights the potential applications of NV centers in various fields, contributing significantly to the advancement of quantum technologies.

[1] M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C. Hollenberg, arXiv:1302.3288 (2013).
[2] M. Pfender, N. Aslam, G. Waldherr, P. Neumann, and J. Wrachtrup, Proc. Natl. Acad. Sci. U.S.A. 111, 14669 (2014).
[3] G.-Q. Liu, Y.-R. Zhang, Y.-C. Chang, J.-D. Yue, H. Fan, and X.-Y. Pan, Nat. Commun. 6, 6726 (2015).
[4] F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, Phys. Rev. Lett. 92, 076401 (2004).
[5] F. A. Hahl, L. Lindner, X. Vidal, T. Luo, T. Ohshima, S. Onoda, S. Ishii, A. M. Zaitsev, M. Capelli, B. C. Gibson, et al., Sci. Adv. 8, eabn7192 (2022).
[6] C. L. Degen, F. Reinhard, and P. Cappellaro, Rev. Mod. Phys. 89, 035002 (2017).
[7] M. Gulka, D. Wirtitsch, V. Ivády, J. Vodnik, J. Hruby, G. Magchiels, E. Bourgeois, A. Gali, M. Trupke, and M. Nesladek, Nat. Commun. 12, 4421 (2021).
[8] H. Morishita, S. Kobayashi, M. Fujiwara, H. Kato, T. Makino, S. Yamasaki, and N. Mizuochi, Sci. Rep. 10, 792 (2020).
[9] D. B. Bucher, D. P. Aude Craik, M. P. Backlund, M. J. Turner, O. Ben Dor, D. R. Glenn, and R. L. Walsworth, Nat. Protoc. 14, 2707 (2019).
[10] G.-Q. Liu and X.-Y. Pan, Chin. Phys. B 27, 020304 (2018).
[11] Z. Xu, Z.-q. Yin, Q. Han, and T. Li, Opt. Mater. Express 9, 4654 (2019).
[12] K. Nemoto, M. Trupke, S. J. Devitt, B. Scharfenberger, K. Buczak, J. chmiedmayer, and W. J. Munro, Sci. Rep. 6, 26284 (2016).
[13] D. B. Rao, S. Yang, and J. Wrachtrup, Phys. Rev. B 92, 081301 (2015).
[14] V. K. Sewani, H. H. Vallabhapurapu, Y. Yang, H. R. Firgau, C. Adambukulam, B. C. Johnson, J. J. Pla, and A. Laucht, Am. J. Phys. 88, 1156 (2020).
[15] K. Takeda, A. Noiri, T. Nakajima, T. Kobayashi, and S. Tarucha, Nature 608, 682 (2022).
[16] J. L. Lancaster and D. B. Allen, arXiv:2207.10567 (2022).
[17] F. Kleißler, Towards Solid-State Spin Based, High-Fidelity Quantum Computation, Ph.D. thesis, Georg-August-Universität Göttingen (2018).
[18] B. Fauseweh, Nat. Commun. 15, 2123 (2024).
[19] J. A. Jones, Prog. Nucl. Magn. Reson. Spectrosc. 59, 91 (2011).
[20] I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014).
[21] C. E. Avalos, Detection and polarization of nuclear and electron spins using nitrogen-vacancy centers (University of California, Berkeley, 2014).
[22] H. Mamin, M. Kim, M. Sherwood, C. T. Rettner, K. Ohno, D. Awschalom, and D. Rugar, Science 339, 557 (2013).
[23] R. Ghassemizadeh, W. Körner, D. F. Urban, and C. Elsässer, arXiv:2404.08388 (2024).
[24] P. V. Klimov, A. L. Falk, D. J. Christle, V. V. Dobrovitski, and D. D. Awschalom, Sci. Adv. 1, e1501015 (2015).
[25] K. Khazen and H. J. von Bardeleben, Front. Quantum Sci. Technol. 2, 1115039 (2023).
[26] P. Rembold, N. Oshnik, M. M. Müller, S. Montangero, T. Calarco, and E. Neu, AVS Quantum Sci. 2 (2020).
[27] A. Bermudez, F. Jelezko, M. B. Plenio, and A. Retzker, Phys. Rev. Lett. 107, 150503 (2011).
[28] J. M. Rios, Quantum manipulation of nitrogen-vacancy centers in diamond: from basic properties to appli (Harvard University, 2010).
[29] J. Jiang and Q. Chen, Phys. Rev. A 105, 042426 (2022).
[30] B. Smeltzer, L. Childress, and A. Gali, New J. Phys. 13, 025021 (2011).
[31] C. S. Shin, M. C. Butler, H.-J. Wang, C. E. Avalos, S. J. Seltzer, R.-B. Liu, A. Pines, and V. S. Bajaj, Phys. Rev. B 89, 205202 (2014).
[32] D. A. Barskiy, A. M. Coffey, P. Nikolaou, D. M. Mikhaylov, B. M. Goodson, R. T. Branca, G. J. Lu, M. G. Shapiro, V.-V. Telkki, V. V. Zhivonitko, et al., Chem. Eur. J. 23, 725 (2017).
[33] J. Eills, D. Budker, S. Cavagnero, E. Y. Chekmenev, S. J. Elliott, S. Jannin, A. Lesage, J. Matysik, T. Meersmann, T. Prisner, et al., Chem. Rev. 123, 1417 (2023).
[34] K. R. Thurber and R. Tycko, J. Chem. Phys. 140 (2014).
[35] X. Gao, S. Vaidya, K. Li, P. Ju, B. Jiang, Z. Xu, A. E. L. Allcca, K. Shen, T. Taniguchi, K. Watanabe, et al., Nat. Mater. 21, 1024 (2022).
[36] S. Ru, Z. Jiang, H. Liang, J. Kenny, H. Cai, X. Lyu, R. Cernansky, F. Zhou, Y. Yang, K. Watanabe, et al., arXiv:2306.15960 (2023).
[37] J. Scheuer, I. Schwartz, S. Müller, Q. Chen, I. Dhand, M. B. Plenio, B. Naydenov, and F. Jelezko, Phys. Rev. B 96, 174436 (2017).
[38] K. H. Sze, Q. Wu, H. S. Tse, and G. Zhu, NMR of Proteins and Small Biomolecules , 215 (2012).
[39] M. D. Lingwood and S. Han, Annu. Rep. NMR Spectrosc. 73, 83 (2011).
[40] H. Andrä, H. Plöhn, A. Gaupp, and R. Fröhling, Z. Phys. A Atoms Nucl. 281, 15 (1977).
[41] V. M. Acosta, Optical magnetometry with nitrogen-vacancy centers in diamond (University of California, Berkeley, 2011).
[42] P. Kaye, R. Laflamme, and M. Mosca, An introduction to quantum computing (OUP Oxford, 2006).
[43] Y.-H. Kuo and H.-B. Chen, Physical Review Research 5, 043139 (2023).
[44] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Physical Review A 98, 032309 (2018).
[45] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Reviews of modern physics 81, 865 (2009).
[46] R. Orús, S. Mugel, and E. Lizaso, Rev. Phys. 4, 100028 (2019).
[47] I. G. Karafyllidis, IEEE Trans. Circuits Syst. I Regul. Pap. 52, 1590 (2005).
[48] P. I. Hagouel and I. G. Karafyllidis, in 2012 28th International Conference on Microelectronics Proceedings (IEEE, 2012) pp. 15–21.
[49] F. Stallmach and P. Galvosas, Annual reports on NMR spectroscopy 61, 51 (2007).
[50] R. Gallay and J. Van der Klink, Journal of Physics E: Scientific Instruments 19, 226 (1986).
[51] E. Ostroff and J. Waugh, Physical Review Letters 16, 1097 (1966).
[52] J. Butterworth, Proceedings of the Physical Society 86, 297 (1965).
[53] M. Kofu, M. Nagao, T. Ueki, Y. Kitazawa, Y. Nakamura, S. Sawamura, M. Watanabe, and O. Yamamuro, The Journal of Physical Chemistry B 117, 2773 (2013).
[54] L. Garrido and J. Guzman, Macromolecules 51, 8681 (2018).
[55] M.-C. Lin, P.-Y. Lo, F. Nori, and H.-B. Chen, Journal of Physics: Condensed Matter 34, 505701 (2022).
[56] J. R. Maze, A. Dréau, V. Waselowski, H. Duarte, J.-F. Roch, and V. Jacques, New Journal of Physics 14, 103041 (2012).
[57] L. Childress, M. Gurudev Dutt, J. Taylor, A. Zibrov, F. Jelezko, J. Wrachtrup, P. Hemmer, and M. Lukin, Science 314, 281 (2006).
[58] D. Kwiatkowski, P. Szańkowski, and Ł. Cywiński, Phys. Rev. B 101, 155412 (2020).
[59] K. Roszak and Ł. Cywiński, Physical Review A 103, 032208 (2021).