本篇論文包含二個理論研究分別探討：一、單光子層級的原子系統的量子同調性；二、以損耗調制單光子波包達到單週期之單光子。
第一個部分，以單光子超輻射態描述單光子激發的原子系統並分析它的幾何特性，從分析發現單光子超輻射態具有幾個特性：模態的態密度函數具有羅倫茲布分、頻譜具有拉比分裂的二個峰值。這些特性與等效共振腔模型有良好的對應，並以等效共振腔模型描述這個系統的時間演化，最後利用推廣的Leggett-Garg不等式和量子同調見證檢驗系統是否具有量子同調性，結果都顯示違反古典行為的預測，和具有量子同調性。
第二個部分，以降頻轉換(PDC)產生雙光子對為基礎理論，加入量子朗之萬理論探討具有損耗的降頻轉換。接著，計算和分析雙光子對的格勞勃相關函數和單邊光子的光子生成率，得知格勞勃相關函數的FWHM會隨著損耗越大而越窄。 最後，利用FWHM隨損耗變化的特性，可以預測單週期之單光子需要的損耗大小。

This thesis contains two theoretical studies: 1. The quantum coherence of the system at the single-photon level. 2. Single-cycle single photon wave packet of the parametric down conversion (PDC) with the inherent loss.
In the first part, we study the quantum coherence in the atomic ensemble ex-cited by a single photon. This ensemble can be described by the single-photon su-perradiant state (SPSS). We treat SPSS in the 3D cylindrical coordinate, and discus the geometry effect from the cylinder to the disc by tuning the Fresnel number. Then, the Rabi splitting is observed in the spectrum of SPSS. The density of state of SPSS is shown in the shape of the Lorentzian distribution. Based on these features, SPSS can be mapped to the effective cavity model which couples to a two-level emitter. Finally, to test quantum coherence, the effective cavity model is applied to the extended Leggett-Garg inequality and the quantum coherence witness. The violations of these tests are observed and indicate the system are non-classical, and supposed to be quantum.
In the second part, we study the inherent loss PDC with the quantum Langevin theory. Then, the count rates of each photons and the Glauber correlation function of the biphotons are derived and analyzed. As a result, the FWHM of the Glauber correlation function is inverse proportional to the strength of the inherent loss. Fi-nally, the single-cycle single photon can be predicted by comparing the single cycle period to the FWHM affected by the inherent loss.

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[31]資料來源國立中央大學陳彥宏教授的非線性積體雷射元件實驗室。