本論文研究如何以攝氏41.6度之單同位素銣原子（87Rb）產生單光子對。在每對單光子中，兩顆光子之間具有時間關聯性，其中第一顆光子被作為觸發光子，而第二顆光子則可作為單光子源使用，並應用至其他領域，如量子資訊。

在產生單光子對以前，電磁波引發透明（Electromagmeticallu-induced-transparency，EIT）及四波混頻（Four-wave-mixing，FWM）光譜被用以決定系統狀態。在本實驗系統之電磁波引發透明光譜中，其透明窗口峰值可達61%，而其半高全寬為1百萬赫茲，另外，該光譜在其透明窗口兩側50百萬赫茲之範圍內，穿透率皆很低，因此該電磁波引發透明系統可被視為一窄頻帶通濾波器，此特質對後端應用有很大助益。而藉由量測四波混頻光譜，不僅能夠確認系統所產生的光的確是由四波混頻機制所產生，也提供了一條有效收集成對光子的途徑。除此之外，在進行產生單光子對實驗時，如何去除欲收集之光子對之外的光子亦是研究的一大課題。此論文提供一種可能的濾波方式，可將這些光子濾除120分貝。最終，實驗系統每秒可產生約900對單光子對（已對系統收光效率校正）。

This thesis sheds light on single-photon pairs generation with single isotope 87Rb vapor that was heated to 41.6 degree Celsius. In each pair, there are two time-correlated photons with different frequencies. The first photon functions as the trigger photon and the second photon can then be utilized as a single-photon source and be applied to other study fields, such as quantum information.

In an attempt to investigate the conditions of the system, both of the eletromagnetically-induced-transparency (EIT) and the four-wave-mixing (FWM) spectra are examined. In the EIT spectrum, a peak with sub-natural linewidth and high transmission is performed. In addition, its baseline is low enough (1.0 ($2
i\times$MHz)) so that the EIT mechanism can be viewed as a narrowband frequency filter, which profits consequential work. As for the FWM experiment, it not only confirms that the generated beam is genuinely the sum-frequency of the other fields, but provides an approach to collect the paired photons efficiently. Besides those mentioned above, in an effort to execute the single-photon pairs generation, how to get rid of the undesired photons becomes a crucial issue. This work gives a probable arrangement of filtering that attenuates the unwanted fields by over 120 dB. In the end, a generation rate of approximately 900 photon pairs per second is reported (corrected by the collection efficiency).

1 Introduction 1

2 Theory 3
2.1 Electromagnetically Induced Transparency (EIT) 3
2.1.1 Hamiltonian .3
2.1.2 Unitary Transformation and Rotating-Wave Approximation of the Hamiltonian . 5
2.1.3 Optical Bloch Equation (OBE) 6
2.2 RubidiumAtoms in ExternalMagnetic Field 9

3 Electromagnetically-Induced-Transparency (EIT) Spectrum 12
3.1 Setup 12
3.1.1 The Lasers 13
3.1.2 TheMagnetic Field 14
3.2 EIT SpectrumProcessing 15
3.2.1 Constructing an EIT Spectrum 15
3.2.2 Fitting an EIT Spectrum 16
3.3 Optimization of the EIT Spectrum 17
3.3.1 Polarization of the Optical Pumping Beam 17
3.3.2 Beam Size and Power of the Coupling Beam 18
3.4 Discussion on the EIT Spectrum 19

4 Four-Wave-Mixing (FWM) Spectrum 21
4.1 Setup 21
4.2 FWMSpectrum 23
4.3 Phase-Matching Condition in FWMMechanism 24
4.4 AC Stark Shift 25

5 Biphoton Generation 29
5.1 Setup 29
5.2 Attenuation of the Strong Beams 29
5.3 Settings of theMultiple-Event Time Digitizer (TDC) 33
5.4 Biphoton Diagram 37
5.5 SpatialModes of the Signal and Probe Beams 38
5.5.1 SpatialMode of the Signal Beam (Experimental) 38
5.5.2 SpatialMode of the Triggered Probe Beam(Experimental) 39
5.5.3 Prediction of the Biphoton-Mode Beam Size (Theoretical) 39
5.6 Hyperfine Optical Pumping (HOP) Beam 41
5.6.1 Solid HOP Beam 42
5.6.2 Hollow HOP Beam 44

6 Outlook 49
6.1 Comparison with Other’s Result 49
6.2 FutureWork 50

7 Conclusion 52

Appendix A Rabi Frequency of the Pumping Field 55
Appendix B Efficiency of the SPCM 56
Appendix C Characteristics of the Etalons 57
C.1 Single Etalon 57
C.2 Two Etalons 58
C.3 Three Etalons 59
Appendix D Fitting Formula of the HOP Test 61

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