臺灣博碩士論文加值系統

本文主要探討的「交互作用暗共振（IDR）」是一個四能階原子系統，其主要的結構是由一Λ型之「電磁波導致透明（EIT）」的三能階系統外加第四個能階，並由一台微波源來驅動；微波所驅動的另一個能階是EIT中與驅動雷射（coupling laser）作用的基態能階。由於微波的驅動，此交互作用暗共振的典型光譜是有兩個來自黑暗能態的透明點，並且於EIT透明窗口中會出現一窄線寬且對比強烈之吸收峰，這吸收峰是來自前面所提之黑暗能態交互作用的結果。本篇論文對於這個四能階系統，交替地使用了三種物理觀點去解釋，其一是密度矩陣的運動方程，其二是Dressed-state 圖象, 最後是利用雙邊費曼圖（Double-sided Feynman Diagram）。在量子光學的範疇內，適切地運用這三種方法可以帶給我們豐富的資訊，去理解當中的量子干涉現象並且簡化計算。
本文第二個主要部分是去探討EIT和IDR系統中的靜態增益機制，此增益機制並不需要在原子能階上具有分佈反轉（population inversion）的情形產生。利用外加一「不同調幫浦（incoherence pump）」於探測雷射（probe laser）之躍遷上，利用此幫浦可以造成密度矩陣在零階解上有所變化，使得探特雷射有增益的可能。因此從中去探討激發態「自發輻射率（spontaneous emission）」到不同的基態能階間的比例，會影響探測雷射靜態增益機制。當中使用數值分析方法，依照所提出的假設驗證在不同的自發輻射率下所預測的現象，可以解釋EIT和IDR之靜態增益機制與自發輻射率的關係。

The quantum interference phenomenon of a narrow and high-contrast absorption
peak arising in the middle of the transparent window of a standard electromagnetically
induced transparency (EIT) spectrum has been attributed to the interference of
interacting dark resonances (IDR) in a four-level system. This phenomenon have been
predicted in Phys. Rev. A 60,3225[2]. Because this quantum interference involves
a three-level electromagnetically induced transparency (EIT) scheme coupled with an
extra atomic state driven by an external coherent electromagnetic field, in order to
get more physics insight and simple calculation, I using three alternative methods to
explain the IDR system, the first one is the optical Bloch equation, the second one is
using dressed-state picture, and the last but not least one is the double-sided Feynman
diagram. These three methods can provide complete information of atomic system in
the quantum optics field.
The other main part of this thesis is the steady-state gain mechanism of EIT and
IDR , this gain mechanism is not from population inversion, but the quantum coherence.
Adding an incoherence pump into above systems as same as the probe transitions,
this incoherence pump will change the magnitudes of the zero-order density matrix elements
and to enhance the gain. I discuss the relation between the gain mechanism of
above systems and the fraction of spontaneous emission rate to specific ground state.
By systematically varying the spontaneous decay rate, the numerical calculations have
been performed in EIT and IDR systems.

Contents
1 Introduction to the quantum interference phenomenon 4
1.1 Coherence population trapping(CPT)−dark states . . . . . . . . . . . . . . . 4
1.2 Electromagnetically Induced Transparency(EIT) . . . . . . . . . . . . . . . . 5
1.3 Interacting of Dark Resonances(IDR) . . . . . . . . . . . . . . . . . . . . . . 6
2 Study of IDR 9
2.1 Equation of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Optical Bloch Equation . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Dressed-state Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3 Double-sided Feynman Diagram (DFD) . . . . . . . . . . . . . . . . . 18
3 Experimental setup and results 25
4 Applications 27
4.1 The Steady-state Gain Mechanism and Lasing Without Population Inversion(
LWI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.1 Introduction to the Gain Mechanism . . . . . . . . . . . . . . . . . . 27
4.1.2 The Rabi oscillation and the coherence in two-level system . . . . . . 28
4.1.3 Gain of EIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1.4 Gain of IDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.2 Refractive index enhancement without absorption . . . . . . . . . . . . . . . 48
5 Conclusion 49

[1] For a review of coherent population trapping, see E. Arimondo, in Progress in Optics
XXXV, edited by A. Wolf (Elsevier, Amsterdam, 1996), p. 258
[2] M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, Phys. Rev. A 60,
3225(1999)
[3] Jung-Jung Su, Thesis of National Tsing Hua University(2001)
[4] Ying-Cheng Chen, Yean-An Liao, Hsin-Ying Chiu, Jung-Jung Su, and Ite A. Yu, Phys.
Rev. A 64, 053806(2001)