實驗上我們成功做出高轉換效率(84%)的類單光子波長轉換，以及預計使用
四波混頻機制打破Hong-Ou-Mandel Interference 的輸入光子必須為不可區分性的
必要條件，並且為未來嘗試演示頻率域的Hong-Ou-Mandel Interference 的實驗做
理論鋪陳。
章節二主要為理論討論EIT(Electromagnetically induced transparency)、慢光
(Slow light)以及四波混頻(Four-wave mixing)的轉換機制，並且分別給出簡單的物
理圖像來幫助理解此三種的物理現象。
章節三重點則是探討四波混頻的系統參數的選定及量測，並且數值探討實驗
上的最佳效率之參數設定。接著討論系統的動量不守恆之缺陷(Ldk)，並且給予
該破壞效應的簡單物理圖像，以及簡單且直覺的推測Ldk 與系統最佳參數設定
的關係式。
第四章節主要是古典光的共振與非共振型之四波混頻的實驗演示，以及實驗
掃動系統參數量測不同四波混頻的輸出結果。接著第五章節將入射光減弱至類單
光子等級且量測最佳四波混頻的轉換效率(84%)，並且實驗性研究該機制下的輸
出光子間之相關性(𝑔2)。第六章節，我們在實驗上同時輸入兩種波長之古典入射
光，因此在實驗上看到四波混頻的干涉現象，並且發現該干涉頻率與實驗參數有
特定之關係。
第七章節，簡單介紹單光子干涉(Michelson interferometer)以及雙光子干涉
(Hong-Ou-Mandel Interference)的差別，並且完整推導出Coherence state 的HOMI
輸出完整解，以及實驗上利用Coherence 以及BS 演示基本的HOMI，並實驗分
析經過HOMI 的光源量子特性。

We experimentally demonstrate a high efficiency wavelength conversion via fourwave-
mixing process with coherent state in single photon level. We also discuss the
posibility of using a four-wave-mixing (FWM) process for Hong-Ou-Mandel
interference (HOMI) in the future experiment.
Chapter 2 is about the theoretical derivation of the electromagnetically induce
transparency (EIT), slow light and four-wave-mixing process. The physical picture to
help understanding these phenomena is also presented.
In chapter 3, we first discuss the measurement and determination of the optical
depth we used in a FWM process. Then we talk about the defect of phase mismatch
(Ldk) and give a simple picture to predict the relation between Ldk and the highest
conversion efficiency condition. Finally, the numerical calculation of the highest
conversion efficiency condition with the defect is performed.
In chapter 4, we conduct the on-resonance and off-resonance FWM experiments,
and also optimized the conversion efficiency by scan the One and Two-photon detuning.
Then we attenuate the input light source from classical to single-photon level to perform
the wavelength conversion, which efficiency achieves 84%, as shown in chapter 5. In
chapter 6, we send two light source with different wavelengths in the FWM process and
observe the interference between two output channels. We discover that the beat note
frequency is a function of two-photon detuning difference of two inputs light source.
In chapter 7, we introduce the difference between one-photon interference
(Michelson interferometer) and two-photon interference (Hong-Ou-Mandel
interference). We also derive the 𝑔2 formula of HOMI with coherence states input and
experimentally demonstrate the typical beam-splitter-based HOMI. The output
quantum feature after this interference is measured.

1. J.G. Rarity, P.R. Tapster, and R. Loudon，“Non-classical interference between
independent sources”，Journal of Optics B: Quantum and Semiclassical Optics, 7
(2005) S171.
2. C. Hua, A. Xue-Bi, W. Juan, Y. Zhen-Qiang, W. Shuang, C. Wei, and H. Zhen-
Fu，“Hong-Ou-Mandel interference with two independent weak coherent
states”，Chinese Physics B, 25 (2016) 020305.
3. Agata M. Bra ́nczyk，“Hong-Ou-Mandel Interference”，(2017)
4. 1. C. Y. Lee, B. H. Wu, G. Wang, Y. F. Chen, Y. C. Chen, and I. A. Yu，“High
conversion efficiency in resonant four-wave mixing processes”，Opt. Express 24,
1008 (2016)
5. 2. Chang-Kai Chiu, Yi-Hsin Chen, Yen-Chun Chen, Ite A. Yu, Ying-Cheng Chen,
and Yong-Fan Chen，“Low-light-level four-wave mixing by quantum
interference”，Phys. Rev. A 89, 023839 (2014)
6. Zi-Yu Liu, Jian-Ting Xiao, Jia-Kang Lin, Jun-Jie Wu, Jz-Yuan Juo, Chin-Yao
Cheng & Yong-Fan Chen，“High-efciency backward four-wave mixing by
quantum interference”，Sci. Rep. 7:15796 (2017)
7. Gang Wang, Yan Xue, Jin-Hui Wu, Zhi-Hui Kang, Yun Jiang, Si-Sheng Liu, and
Jin-Yue Gao，“Efficient frequency conversion induced by quantum constructive
interference”，Opt. Lett. 35, 3778 (2010)
8. Zi-Yu Liu, Yi-Hsin Chen, Yen-Chun Chen, Hsiang-Yu Lo, Pin-Ju Tsai, Ite A. Yu,
Ying-Cheng Chen, and Yong-Fan Chen，“Large Cross-Phase Modulations at the
Few-Photon Level”，Phys. Rev. Lett. 117, 203601 (2016)
9. Meng-Jung Lee, Yi-Hsin Chen, I-Chung Wang, and Ite A. Yu，“EIT-based alloptical
switching and cross-phase modulation under the influence of four-wave
mixing”，Opt. Express 20, 11057 (2012)
10. Ya-Fen Hsiao, Hung-Shiue Chen, Pin-Ju Tsai, and Ying-Cheng Chen，“Cold
atomic media with ultrahigh optical depths”，Phys. Rev. A 90, 055401 (2014)
11. 洪舜昶，“高光學密度的冷原子雲製備”，國立清華大學，碩士論文，民國
104 年
12. 陳俊毅，“高效率的單光子同調波長轉換”，國立清華大學，碩士論文，民國
106 年
13. 洪偉倫，“載入與儲存冷原子至光偶極陷阱之研究”，國立清華大學，博士論
文，民國102 年
14. 廖文德，“電磁誘發透明介質中靜止光脈衝的理論研究”，國立清華大學，碩
士論文，民國97 年
15. 管培辰，“塞曼簡併態對慢光及光儲存之影響”，國立清華大學，碩士論文，
民國96 年