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研究生： 莊又霖
Chuang, You-Lin
論文名稱： 電磁引發透明介質系統下的量子光學
Quantum Optics in Electromagnetically Induced Transparency-Based Systems
指導教授： 李瑞光
Lee, Ray-Kuang
口試委員: 余怡德
Yu, Ite A.
賴暎杰
Lai, Yinchieh
陳泳帆
Chen, Yong-Fan
褚志崧
Chuu, Chih-Sung
學位類別： 博士
Doctor
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2012
畢業學年度： 101
語文別： 英文
論文頁數： 98
中文關鍵詞： 電磁引發透明 、量子光學 、量子糾纏 、量子壓縮
外文關鍵詞： Electromagnetically induced transparency, quantum optics, quantum entanglement, quantum squeezing
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    • 本論文主要是在以電磁引發透明為基礎的系統下, 研究場的量子特性- 壓縮與糾
    纏。在弱光近似的條件下, 我們研究兩道光場在通過單一Lambda型態的EIT介質之
    後的量子糾纏特性, 並且找出在特別的條件之下滿足不可分離之限制。將單
    一Lambda的EIT系統推廣到多重的EIT系統, 將有更多的自由度去研究光場的量子性質。於是我們發現若是入射光為非古典光時, 藉由調變耦合場之間的相對強度,
    從多重-Lambda EIT介質傳播出來的光的量子特性會被改變。除此之外, 場自身的量子性質可被徹底地改變經由交差相位調變的非線性交互作用, 此非線性項可由一些可控制的物理變量來做調變。

    EIT 是一種由場與原子能階交互作用下引發的量子干涉現象; 由於場所引發的原
    子同調性, 造成許多新奇的特性被產生, 如吸收率降低與慢光現象。也因此利
    用在多重- (雙重-Lambda與三重-Lambda EIT) EIT系統中, 具有共同的原子同調性的特性, 一些場的非古典的效應能被產生, 並且以古典的方式加以操控。

    藉由EIT的慢光特性, 兩個光脈衝之間的交互作用時間可被大幅地增加, 因此交
    差相位調變的非線性交互作用可以被加強, 以至於個別場的量子性質以及場與場
    之間的量子性質可從原先古典入射光中產生。

    藉由從理論上研究這些以EIT為基礎的系統下的交互作用場之量子特性, 我們得
    出定量的結果, 提供了原子與場交互作用過程中更進一步的瞭解。再者, 我們
    更期望此論文的結果能有助於量子資訊科學的研究。

    The thesis is to study the quantum properties of optical fields, squeezing and entanglement, based on the electromagnetically induced transparency (EIT) schemes. Under the low-intensity approximation,
    we study the quantum entanglement between two fields after travelling through a Lambda-type EIT medium,
    and find that some particular conditions satisfies non-separable criterion.
    Extending the single-Lambda EIT system to multi-Lambda EIT system,
    one has more degree freedom to study quantum properties of light.
    By controlling the relative strengths among coupling fields, we find that the quantum properties of output fields
    can be changed if the input fields are non-classical light.
    Besides, the quantum nature of interacting fields can be thoroughly changed via cross phase modulation (XPM) nonlinear interactions, which depends on some controllable physical quantities.

    EIT is a quantum interference phenomenon that is caused by the interaction between light field and atomic levels.
    Some novel effects such as reduction of absorption and slow light can be arisen due to the atomic coherence induced by the interacting fields.
    Accordingly, based on the common atomic coherence in multi-Lambda EIT systems (double- and triple-Lambda EIT system), the non-classical effects of fields can be generated and manipulated by means of some classical manners.

    The interacting time between two light pulses can be greatly increased by the slow light effect in EIT system, and therefore the nonlinear interaction by the XPM term could be enhanced so that the quantum properties of individual fields or that between two fields can be generated from initial input classical fields.

    By investigating the quantum properties of interacting fields in these EIT-based systems theoretically,
    we obtain some results quantitatively, providing a further understanding about atom-field interaction processes.
    Furthermore, we expect that the results of the thesis can contribute to the field of quantum information science.

    1 Introduction and Overview 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Theory of Electromagnetically Induced Transparency 4 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Slow Light, Light Storage and Retrieval . . . . . . . . . . . . . . . . 11 2.2.1 Slow Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Light Storage and Retrieval . . . . . . . . . . . . . . . . . . 14 3 Squeezing and Entanglement in Electromagnetically Induced Trans- parency System 16 3.1 Quantum Description of Electromagnetically Induced Transparency 17 3.2 Spectral Method Approach . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Full Quantum Mechanically Description of Electromagnetically Induced Transparency . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Conditions to preserve quantum entanglement in EIT Media . . . . 29 4 Multi- Electromagnetically Induced Transparency System 33 4.1 Double- electromagnetically induced transparency system . . . . . 34 4.2 Quantum Beam Splitter . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3 Quantum Entanglement between output elds . . . . . . . . . . . . 42 4.4 Comparisons of Double- EIT and Quantum Beam Splitter . . . . 43 4.4.1 Quantum Squeezing of Output Fields . . . . . . . . . . . . . 43 4.4.2 Quantum Entanglement of Output Fields . . . . . . . . . . . 49 4.5 Physical Interpretation for the Two Systems . . . . . . . . . . . . . 52 4.6 Triple- electromagnetically induced transparency system . . . . . 56 5 N-type Electromagnetically Induced Transparency 59 5.1 Field Equations of the EIT-based system . . . . . . . . . . . . . . . 60 5.2 Back-Propagation Method Approach . . . . . . . . . . . . . . . . . 62 5.3 Squeezing Ratio of the vector mode in EIT-based scheme . . . . . . 66 5.4 Quantum Squeezing in the EIT-based scheme . . . . . . . . . . . . 68 5.5 Quantum Entanglement in the EIT-based scheme . . . . . . . . . . 70 6 Conclusion 72 A Maxwell Schrodinger Equation 74 B Pulse Propagating in EIT Medium 78 C Dark-State Polariton in EIT 81 D Generalized Einstein Relations 84 E Field Equation in Time Domain 87 F Back-Propagation Method 90 Bibliography 94

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