為了想要了解在半導體奈米元件中量子相位應用的可行性，退相干過程是一個重要的研究課題。本論文中的實驗是利用GaAs/AlGaAs異質結構的材料來製備 Aharonov–Bohm(AB)與自旋版本的Mach–Zehnder干涉計來探討一系列有關相位同調長度和退相干機制的問題
在第一章裡，我們介紹本篇論文的實驗動機以及背景知識。在第二章，我們將探討溫度、電流和量測形態在彈道式AB量子環中對退相干率的影響。首先我們想要了解不同的訊號量測形態如何影響電導以及退相干率，實際量測中，發現由熱激發電子或者增加電流，皆使得傳輸相位被均化而造成退相干的現象。透過實驗結果的分析計算，找到一個能量視窗可由電子的漂移速度和路徑不對稱所表示。此能量視窗能表示量子相位元件對外界環境的容忍度。第三章中，我們用路徑傳輸率可調式的AB干涉元件來探討傳輸不對稱性對不同的量測形態所造成的影響。原本在路徑上傳輸率對稱的情況下，我們觀察到退相干率在不同的量測形態近似相同；相反地，當透過金屬閘來造成路徑上的傳輸率不對稱時，我們觀察到直接透過AB環所量測的退相干率會大於間接量測到的結果。透過分析，我們發現到這部份的影響可以在定性上估算出經由量測電路傳導至元件的電壓擾動對退相干率造的影響。而此部份的理論，早期也被M. Büttiker教授的團隊所提出[56]。在第四章我們介紹一種新穎的SMZI的量子干涉元件，此元件是利用在量子霍爾區域中的自旋解析邊緣態來設計。除此之外，我們也對此新形態量子干涉元件的電子的同調長度亦有高度的興趣，因此透過不過大小的元件設計和變溫的實驗中，我們發現在此SMZI元件中的同調長度比一般電子式MZI來的長[75, 83]。
在最後第五章中，我們總結一系列的實驗結果，並提出一些未來能建立在此基礎上可行之工作。

To realize the probability of nanodevices application using quantum phase information, dephasing processes are one of the most crucial essential issues regarding semiconducting mesoscopic systems. This thesis presents a series of experiments that study the phase coherence and dephasing mechanisms by using Aharonov–Bohm (AB) and spin-type Mach–Zehnder interferometers (SMZIs) fabricated in GaAs/AlGaAs heterostructured crystals.
In chapter 1, we introduce the motivation and context for the experimental works described in the following chapters.
In chapter 2, we investigate the dependence of the dephasing rate in a ballistic AB ring on the temperature, bias current, and probe configuration. First, we would like to study how the probe configuration influences the conductance and the dephasing rate. In fact, averaging of the transmission phase, in which current is carried by thermally excited or current-induced electrons, results in dephasing. We find that the appropriate energy window for dephasing is set by the drift velocity of the interfering electrons and the asymmetry of the ring path.
In chapter 3, we investigate the dephasing rates in ballistic AB rings with local and nonlocal probe configurations by tuning the transmission through one arm of the ring. The dephasing rates are independent of the probe configuration, whereas the transmission through the ring paths is equal. In contrast, because AB interferometers are tuned to be strongly asymmetric, the dephasing rate of the local configuration becomes larger than that of the nonlocal configuration. We find that our observations can be explained qualitatively by voltage fluctuations from the measurement circuit, as proposed by G. Seelig, S. Pilgram, A. N. Jordan, and M. Büttiker [56].
In chapter 4, we first introduce a novel SMZI by using spin-resolved edge states in the integer quantum Hall regime. Furthermore, to investigate the phase coherence length in this interferometer, we determined the finite temperature coherence length of the spin-resolved edge states by designing interferometers of various sizes and attempted to explain the dephasing mechanism in this novel system. The phase coherence length in the present experiment, surprisingly, is noticeable larger than the charge coherence length found in an electronic MZI[75, 83].
Finally, in chapter 5, we summarize our finding from the experimental works and discuss future work based on our presented results.

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