本論文首先簡要介紹近幾十年來光子回波技術的發展以及γ-ray量子光學的興起。之後利用量子力學中的密度矩陣方法探討M. Afzelius等人在2009年提出的原子頻率梳量子記憶理論，並且驗證光單子脈衝通過不均勻展寬原子團所形成的光子回波，其向前讀取效率有54%的上限。有了原子頻率梳量子記憶的概念後，我們結合了γ-ray量子光學的方法將頻率梳運用在原子核系統上，來探討高能量光子與原子核的作用。本論文主要研究的物理系統為γ-ray光子和鐵57靶材組的交互作用，透過外加磁場的操控來產生有效率的光子回波。在這個系統的理論分析上，我們給出第一光子回波的解並和數值模擬計算作比較，其結果大致上吻合。在效率最佳化方面，我們探討各個物理參數的最佳範圍讓第一光子回波有好的效率表現。另外，我們也討論了變化各個物理參數對光子回波的影響，包含改變靶材組的厚度分佈、翻轉外加磁場方向、選擇特定的靶材數目與靶材排列的順序等。;In this thesis, we firstly give the brief introduction to the development of photon echo techniques in the last decades and the emergency for γ-ray quantum optics. Then we use the density matrix method in quantum mechanics to investigate the atomic frequency comb (AFC) quantum memory theory proposed by M. Afzelius et al. in 2009 and verify that the forward photon echo has the upper limit efficiency about 54% when single photon pulse propagates through the inhomogeneously broadening atomic ensemble. With the concept of the atomic frequency comb (AFC) quantum memory, we move to the nuclear system and explore the interaction between γ-ray and nuclear ensembles by combining the frequency comb method with γ-ray quantum optics. The mainly physical system we study in this thesis is the interaction between γ-ray photon and 57Fe nuclear targets. In order to generate the nuclear frequency comb, there are also external magnetic fields applied on these targets. Based on the theoretical analysis, we give first echo solution and compare it with the numerical calculations. Both analytical and numerical results show the consistency. For efficiency optimization, we discuss the best ranges for different physical parameters so that the first echo has a good performance. In addition, we also study the effect on photon echo by variating the physical parameters including changing thickness distribution of targets, inverting the external magnetic field direction, choosing the specific number and arrangement of targets.
