對量子世界與經典世界之間模糊界限的持續探索，促進了量子科學和技術的重大發展。開放性量子理論中，系統容易與環境耦合而逐漸失去量子特性，純移相動力學就是其一代表性的行為，過程中系統環境間的交互作用中是否存在非古典性我們可以透過一新興理論CHER得到答案，並且量化過程中的非古典性，在這項研究中，我們以鑽石空缺做為我們的物理系統，鑽石空缺是一主流且歷史悠久的量子材料，其極長的退相干時間和能在室溫下能正常運作的特性使其成為CHER理論良好的實驗平台，並且我們建立一系列的數值模擬來搭建這個平台。

這項研究提供了在極化橫向方向狀態下，鑽石空缺的FID訊號會受到碳13核子環境以及磁場的影響在CHER圖像中會產生負值，負值的大小與非古典性呈正比，反過來可以得知，透過操縱外部環境可以控制量子特性的出現，我們把CHER理論運用在實際的物理系統中，CHER理論使我們不須動用過多測量資源即見證了純移相過程中非古典性的出現。我們的結果建造了連接理論與實驗之間的橋梁，給實驗學家提供見證非古典性的新方式與新方向。

The continuing exploration of the blurred boundary between the quantum and
classical worlds has led to significant developments in quantum science and tech-
nology. In open quantum theory, systems are prone to coupling with their envi-
ronment and gradually lose their quantum properties, pure dephasing dynamics
being a representative behavior. Whether there is non-classicality in the interac-
tion between the system environment in the process can be answered by the novel
theory maned Canonical Hamiltonian ensemble representation(CHER) and quan-
tifying the non-classicality, in this study we use the diamond vacancy(NV-center)
as our physical system. NV-center is a mainstream and long-established quantum
material with extremely long decoherence times and the ability to operate at room
temperature, which makes it a good experimental platform for CHER theory, and
we have built a series of numerical simulations to develop this platform.

This study provides evidence that the Free induction decay signal of the NV-
center is affected by the polarized transverse direction of the Carbon 13 nucleon
environment and the external magnetic field, resulting in negative values in the
CHER image. We apply the CHER theory to real physical systems, where CHER
theory allows us to witness the emergence of non-classicality in the process of
pure dephasing without the need for excessive measurement resources. Our results provide a bridge between theory and experiment, giving experimentalists new ways and directions to witness non-classicality.

[1] T. Young, “Experiments and calculations relative to physical optics, the philosophical transaction, 1803,” Young, T.(Ed.), A Course of Lectures on Natural Philosophy and the Mechanical Arts II , 639 (1803).
[2] M. Schlosshauer, “Quantum decoherence,” Physics Reports 831, 1 (2019).
[3] A. Streltsov, G. Adesso, and M. B. Plenio, “Colloquium: Quantum coherence as a
resource,” Reviews of Modern Physics 89, 041003 (2017).
[4] H.-P. Breuer, F. Petruccione, et al., The theory of open quantum systems (Oxford
University Press on Demand, 2002).
[5] M. A. Eriksson, M. Friesen, S. N. Coppersmith, R. Joynt, L. J. Klein, K. Slinker, C. Tahan, P. Mooney, J. Chu, and S. Koester, “Spin-based quantum dot quantum
computing in silicon,” Quantum Information Processing 3, 133 (2004).
[6] K. Bader, D. Dengler, S. Lenz, B. Endeward, S.-D. Jiang, P. Neugebauer, and J. Van Slageren, “Room temperature quantum coherence in a potential molecular qubit,” Nature communications 5, 1 (2014).
[7] H.-B. Chen and Y.-N. Chen, “Canonical hamiltonian ensemble representation of
dephasing dynamics and the impact of thermal fluctuations on quantum-to classical transition,” Scientific reports 11, 1 (2021).
[8] H.-B. Chen, P.-Y. Lo, C. Gneiting, J. Bae, Y.-N. Chen, and F. Nori, “Quantifying
the nonclassicality of pure dephasing,” Nature communications 10, 1 (2019).
[9] K. Hornberger, “Introduction to decoherence theory,” in Entanglement and decoherence (Springer, 2009) pp. 221–276.
[10] K. Roszak and Ł. Cywiński, “Characterization and measurement of qubit-
environment-entanglement generation during pure dephasing,” Physical Review A 92, 032310 (2015).
[11] B. Gu and I. Franco, “When can quantum decoherence be mimicked by classical noise?” The Journal of chemical physics 151, 014109 (2019).
[12] M. Planck, The theory of heat radiation (Blakiston, 1914).
[13] A. Einstein, “On a heuristic point of view concerning the production and transformation of light,” Annalen der Physik , 1 (1905).
[14] A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Physical review 47, 777 (1935).
[15] J. S. Bell, “On the einstein podolsky rosen paradox,” Physics Physique Fizika 1, 195(1964).
[16] A. Aspect, P. Grangier, and G. Roger, “Experimental tests of realistic local theories via bell’s theorem,” Physical review letters 47, 460 (1981).
[17] B. Hensen, H. Bernien, A. E. Dréau, A. Reiserer, N. Kalb, M. S. Blok, J. Ruitenberg,
R. F. L. Vermeulen, R. N. Schouten, C. Abellán, W. Amaya, V. Pruneri, M. W. Mitchell, M. Markham, D. J. Twitchen, D. Elkouss, S. Wehner, T. H. Taminiau, and R. Hanson, “Loophole-free bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682 (2015).
[18] M. Giustina, M. A. Versteegh, S. Wengerowsky, J. Handsteiner, A. Hochrainer,
K. Phelan, F. Steinlechner, J. Kofler, J.-Å. Larsson, C. Abellán, et al., “Significant-
loophole-free test of bell’s theorem with entangled photons,” Physical review letters 115, 250401 (2015).
[19] C. Emary, N. Lambert, and F. Nori, “Leggett–garg inequalities,” Reports on
Progress in Physics 77, 016001 (2013).
[20] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed experiment to
test local hidden-variable theories,” Physical review letters 23, 880 (1969).
[21] L. Cohen, “Generalized phase-space distribution functions,” Journal of Mathematical Physics 7, 781 (1966).
[22] S. Rahimi-Keshari, T. Kiesel, W. Vogel, S. Grandi, A. Zavatta, and M. Bellini, “Quantum process nonclassicality,” Physical Review Letters 110, 160401 (2013).
[23] J.-H. Hsieh, S.-H. Chen, and C.-M. Li, “Quantifying quantum-mechanical processes,” Scientific reports 7, 1 (2017).
[24] C. M. Kropf, C. Gneiting, and A. Buchleitner, “Effective dynamics of disordered
quantum systems,” Physical Review X 6, 031023 (2016).
[25] C. Gneiting, F. R. Anger, and A. Buchleitner, “Incoherent ensemble dynamics in
disordered systems,” Physical Review A 93, 032139 (2016).
[26] H.-B. Chen, C. Gneiting, P.-Y. Lo, Y.-N. Chen, and F. Nori, “Simulating open quantum systems with hamiltonian ensembles and the nonclassicality of the dynamics,”Physical review letters 120, 030403 (2018).
[27] H.-B. Chen, “Effects of symmetry breaking of the structurally-disordered hamiltonian ensembles on the anisotropic decoherence of qubits,” Scientific reports 12, 1(2022).
[28] M. Palenberg, R. Silbey, C. Warns, and P. Reineker, “Local and nonlocal approximation for a simple quantum system,” The Journal of Chemical Physics 114, 4386(2001).
[29] V. Acosta and P. Hemmer, “Nitrogen-vacancy centers: Physics and applications,”MRS bulletin 38, 127 (2013).
[30] M. W. Doherty, N. B. Manson, P. Delaney, F. Jelezko, J. Wrachtrup, and L. C.
Hollenberg, “The nitrogen-vacancy colour centre in diamond,” Physics Reports 528,1 (2013).
[31] 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).
[32] J. F. Barry, J. M. Schloss, E. Bauch, M. J. Turner, C. A. Hart, L. M. Pham, and
R. L. Walsworth, “Sensitivity optimization for nv-diamond magnetometry, Reviewsof Modern Physics 92, 015004 (2020).
[33] M. G. Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. Zibrov,
P. Hemmer, and M. Lukin, “Quantum register based on individual electronic and
nuclear spin qubits in diamond,” Science 316, 1312 (2007).
[34] E. L. Hahn, “Nuclear induction due to free larmor precession,” Physical Review 77,297 (1950).
[35] D. Redman, S. Brown, R. Sands, and S. Rand, “Spin dynamics and electronic
states of n-v centers in diamond by epr and four-wave-mixing spectroscopy,” Physical review letters 67, 3420 (1991).
[36] J. R. Maze, A. Dréau, V. Waselowski, H. Duarte, J.-F. Roch, and V. Jacques, “Free
induction decay of single spins in diamond,” New Journal of Physics 14, 103041
(2012).
[37] G.-Q. Liu, X.-Y. Pan, Z.-F. Jiang, N. Zhao, and R.-B. Liu, “Controllable effects of
quantum fluctuations on spin free-induction decay at room temperature,” Scientific reports 2, 1 (2012).
[38] K. Li, G. Xu, and D. Tong, “Coherence-protected nonadiabatic geometric quantum computation,” Physical Review Research 3, 023104 (2021).
[39] L. Childress, M. Gurudev Dutt, J. Taylor, A. Zibrov, F. Jelezko, J. Wrachtrup,
P. Hemmer, and M. Lukin, “Coherent dynamics of coupled electron and nuclear
spin qubits in diamond,” Science 314, 281 (2006).
[40] E. L. Hahn, “Spin echoes,” Physical review 80, 580 (1950).
[41] R. Hanson, O. Gywat, and D. Awschalom, “Room-temperature manipulation and decoherence of a single spin in diamond,” Physical Review B 74, 161203 (2006).
[42] E. Skorokhodov and B. V. Fine, “Electronic spin-echo envelope of nv-centers in
diamond,” (2020).
[43] D. Kwiatkowski, Ł. Cywiński, and J. K. Korbicz, “Appearance of objectivity for nv
centers interacting with dynamically polarized nuclear environment,” New Journal
of Physics 23, 043036 (2021).
[44] B. Smeltzer, L. Childress, and A. Gali, “13c hyperfine interactions in the nitrogen-vacancy centre in diamond,” New Journal of Physics 13, 025021 (2011).
[45] S. Ajisaka and Y. Band, “Decoherence of nitrogen vacancy centers in diamond,”(2015).
[46] H.-B. Chen, P.-Y. Lo, C. Gneiting, J. Bae, Y.-N. Chen, and F. Nori, “Quantifying
the nonclassicality of pure dephasing,” Nat. Commun. 10, 3794 (2019).
[47] S. Takahashi, R. Hanson, J. Van Tol, M. S. Sherwin, and D. D. Awschalom,
“Quenching spin decoherence in diamond through spin bath polarization,” Physi-cal review letters 101, 047601 (2008).
[48] V. Jacques, P. Neumann, J. Beck, M. Markham, D. Twitchen, J. Meijer, F. Kaiser,
G. Balasubramanian, F. Jelezko, and J. Wrachtrup, “Dynamic polarization of single
nuclear spins by optical pumping of nitrogen-vacancy color centers in diamond at
room temperature,” Physical review letters 102, 057403 (2009).
[49] V. Atsarkin, “Dynamic nuclear polarization: Yesterday, today, and tomorrow,” in Journal of Physics: Conference Series, Vol. 324 (IOP Publishing, 2011) p. 012003.
[50] G.-Q. Liu, Q.-Q. Jiang, Y.-C. Chang, D.-Q. Liu, W.-X. Li, C.-Z. Gu, H. C. Po, W.-X.
Zhang, N. Zhao, and X.-Y. Pan, “Protection of center-spin coherence by dynamically polarizing nuclear spin core in diamond,” arXiv preprint arXiv:1305.6424 (2013).
[51] P. Yang, M. B. Plenio, and J. Cai, “Dynamical nuclear polarization using multi-
colour control of color centers in diamond,” EPJ Quantum Technology 3, 1 (2016).
[52] J. Zopes, K. Herb, K. Cujia, and C. L. Degen, “Three-dimensional nuclear spin
positioning using coherent radio-frequency control,” Physical Review Letters 121,
170801 (2018).
[53] D. Kwiatkowski, P. Szańkowski, and Ł. Cywiński, “Influence of nuclear spin po-
larization on the spin-echo signal of an nv-center qubit,” Physical Review B 101,
155412 (2020).
[54] K. Sasaki, E. E. Kleinsasser, Z. Zhu, W.-D. Li, H. Watanabe, K.-M. C. Fu, K. M.
Itoh, and E. Abe, “Dynamic nuclear polarization enhanced magnetic field sensitiv-
ity and decoherence spectroscopy of an ensemble of near-surface nitrogen-vacancy centers in diamond,” Applied Physics Letters 110, 192407 (2017).
[55] S. Takahashi, R. Hanson, J. van Tol, M. S. Sherwin, and D. D. Awschalom, “Quenching spin decoherence in diamond through spin bath polarization,” Phys. Rev. Lett.101, 047601 (2008).
[56] P. London, J. Scheuer, J.-M. Cai, I. Schwarz, A. Retzker, M. B. Plenio, M. Katagiri,
T. Teraji, S. Koizumi, J. Isoya, R. Fischer, L. P. McGuinness, B. Naydenov, and
F. Jelezko, “Detecting and polarizing nuclear spins with double resonance on a singleelectron spin,” Phys. Rev. Lett. 111, 067601 (2013).