Quantum criticality at high temperature revealed by spin echo.

• Other Authors: Chen, Shaowen
• Format: Others
• Language: English; Chinese
• Published: 2013
• Subjects: Quantum theory
• Online Access: http://library.cuhk.edu.hk/record=b5549791; http://repository.lib.cuhk.edu.hk/en/item/cuhk-328295

當一個宏觀量子系統的基態因為一個參數的變動產生劇烈的變化時，量子臨界現象會伴隨出現。量子臨界現像是指示新物理產生的重要標誌。在傳統觀測方法裡，量子臨界現像只有在零溫或者低溫下才能被觀測到(這裡低溫是相對於系統中相互作用強度而言的)。我們發現，一個量子探針，如果它的相干時間足夠長，在高溫下依然可以探測到量子臨界現象。特別是，自旋回波可以移除熱漲落效應，從而揭示量子漲落中的臨界現象，而無需把系統冷卻到極低溫度。我們先採用一個嚴格可解模型，即一維橫場伊辛模型演示了在高溫下通過自旋回波揭示量子臨界現象的可能性。臨界行為可以通過嚴格解計算來研究，並可用噪音譜高斯近似法加以理解。通過對噪音譜的分析，我們發現，為觀測到量子臨界現象，傳統方法中所需的溫度(TQc )和探針退相干測量中所需的相干時間( tQc)存在對應關係， 即TQc~ l/tQc 並遠小於系統的相互作用強度。例如，有毫秒或者秒量級相干時間的探針可以用來探測到原本在10 ⁻⁹ K或者1O⁻¹² K溫度下才能看到的量子臨界現象而無需降低系統的溫度。這個發現提供了一種新的研究量子物質的方法。 === 我們還發明了一個用法拉第旋轉回波譜(FRES) 研究透明材料中的自旋噪音的方案，是一種關於測量法拉第旋轉魚漲落的方法。FRES通過抑制熱漲落展現高溫下的量子漲落。它使用的原理和核磁共振中的自旋回波類似。我們用一種稀土化合物LiHoF₄測試了我們的理論。FRES得到的量子漲落在相界上有一個增強的效應。FRES可以被推廣到更複雜的配置，對應核磁共振以及電子自旋共振中的更複雜的動力學去耦操控。以此，我們可以得到更多磁性材料的結構和動力學性質方面的信息。 === Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly with tuning a system parameter. It is an important indicator of new quantum matters emerging. In conventional methods, quantum criticality is observable only at zero or low temperature (as compared with the interaction strength in the system). We find that a quantum probe, if its coherence time is long, can detect quantum criticality of a system at high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveal the critical quantum fluctuation without requiring low temperature. We first use the exact solution of the one-dimensional transverse-field Ising model to demonstrate the possibility of detecting the quantum criticality at high temperature by spin echo. The critical behaviors have been calculated using the exact solution and understood with the noise spectrum analysis in the Gaussian noise approximation. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature (TQC) in conventional methods and the necessary long coherence time (tQC) in probe decoherence measurement to observe the quantum criticality, that is, TQC ~ 1/tQC and much less than the interaction strength of the system. For example, probes with quantum coherence time of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that is previously known only observable at extremely low temperatures of nano- or pico-Kelvin. This finding provides a new possibility to study quantum matters. === We also designed a scheme of Faraday rotation echo spectroscopy (FRES) that can be used to study spin noise dynamics in transparent materials by measuring the fluctuation of Faraday rotation angles. The FRES suppresses the static part of the noise and reveal the quantum fluctuations at relatively high temperature, which shares the same idea of the spin echo technique in nuclear magnetic resonance (NMR). We tested our theory on a rare-earth compound LiHoF₄.The quantum fluctuation obtained by FRES gives an enhanced feature at the phase boundary. The FRES can be straightforwardly generalized to more complicated configurations that correspond to more complex dynamical decoupling sequences in NMR and electron spin resonance, which may give us more extensive information on the structural and dynamical properties of magnetic materials. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Chen, Shaowen = 自旋回波中的高溫量子臨界現象 / 陳少文. === Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. === Includes bibliographical references (leaves 73-80). === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstracts also in Chinese. === Chen, Shaowen = Zi xuan hui bo zhong de gao wen liang zi lin jie xian xiang / Chen Shaowen. === Abstract --- p.1 === 摘要 --- p.3 === Acknowledgment --- p.4 === Chapter 1 --- Introduction --- p.5 === Chapter 1.1 --- Motivation --- p.5 === Chapter 1.2 --- Thesis outline --- p.9 === Chapter 2 --- Central Spin Decoherence Problem --- p.11 === Chapter 2.1 --- Introduction --- p.11 === Chapter 2.2 --- Spin Echo --- p.14 === Chapter 2.3 --- Noise spectrumapproach --- p.14 === Chapter 3 --- Criticality in One-dimensional Transverse Field Ising Model --- p.17 === Chapter 3.1 --- Introduction --- p.17 === Chapter 3.2 --- TheModel and the Exact Solution --- p.19 === Chapter 3.3 --- Results fromexact solution --- p.22 === Chapter 3.4 --- Noise spectrumapproach --- p.23 === Chapter 3.5 --- Time-inverse temperature correspondence --- p.24 === Chapter 3.6 --- Critical exponents --- p.26 === Chapter 3.7 --- More Discussions --- p.30 === Chapter 3.7.1 --- Noise spectra --- p.30 === Chapter 3.7.2 --- Finite probe-bath coupling effect --- p.30 === Chapter 3.7.3 --- Revivals in FID --- p.31 === Chapter 3.8 --- Perspectives for experimental observation --- p.32 === Chapter 3.9 --- Summary --- p.33 === Chapter 4 --- Faraday Roation Echo Spectroscopy --- p.39 === Chapter 4.1 --- Introduction --- p.39 === Chapter 4.2 --- Faraday rotation --- p.41 === Chapter 4.3 --- Faraday rotation echo --- p.44 === Chapter 5 --- Faraday rotation echo of lithium holmium tetrafluoride --- p.47 === Chapter 5.1 --- Introduction --- p.47 === Chapter 5.2 --- Lithium Holmium tetrafluoride: LiHoF₄ --- p.48 === Chapter 5.3 --- Faraday rotation echo spectroscopy --- p.52 === Chapter 5.4 --- Summary --- p.54 === Chapter 6 --- Conclusion and Future work --- p.55 === Chapter Appendix --- p.57 === Chapter A. --- Exact solution of 1D Transverse-field Isingmodel --- p.57 === Chapter B. --- Calculation of the magnetic susceptibility --- p.64 === Chapter C. --- Faraday Rotation --- p.66 === Bibliography --- p.73