窄頻糾纏的光子不論在基礎研究或是應用方面都十分有趣。本論文對於冷原子團中利用自發四波混頻產生的時間能量糾纏的光子(雙光子)的產生以及操作提供了詳細的研究。其中,我們在低光學深度的系統中,利用控制失諧的自發四波混頻中的量子干涉高效率的產生雙光子。利用這種方法,產生的雙光子會有小於(光頻率為原子躍遷頻時的)自然線寬的859 kHz線寬。此外,我們也展示了雙光子波包的電光振幅調變。這項實驗成果為原子晶片系統和以量子中繼器實現的量子通訊提供了一個產生次自然線寬的微型化雙光子光源之可行方法。在本論文中,我們也提出了利用五能階原子系統將窄頻雙光子源結合開關功能的方法。我們在實驗上展示了雙光子的開關,也為其中的物理機制提供了理論計算。此雙光子開關不但能應用於雙光子波包的波形操控,並且基於基礎研究的興趣,也提供了產生相關聯的光學前驅的方法。我們也討論了如何利用失諧的開關場來實現量子相位閘門的可能性。

Narrowband entangled photons provide intriguing features for both fundamental and application perspectives. This thesis gives detailed studies about the generation and manipulation of the time-energy entangled photons(biphotons) generated using the cold atomic medium by Spontaneous-Four-Wave-Mixing (SFWM) process. In particular, we have proposed and demonstrated an efficient way to generate biphotons by controlling the quantum interference existing in the detuned SFWM process in low Optical-Depth (OD) ensembles. Generated biphotons have a sub-natural(on-resonant) line-width of 859 kHz. The electro-optic modulation of these biphotons is also demonstrated. Our method opens opportunities for miniaturizing the atomic sources to generate sub-natural line-width biphotons also for quantum repeater based quantum communications as well. We also propose a narrowband biphoton source integrated with a switching function by considering a five-level atomic system. We have developed a theoretical formalism for this physical process, and experimentally demonstrated the biphoton switching. This method may provide opportunities to manipulating the biphotons by photon switching, thus paving a way to generate correlated optical-precursors for fundamental interest. The realization of quantum phase gates for the case of the non-resonant switching field is also discussed.

1 Introduction . . . . . . . . . . . . . . . . . 1
2 Theory of Four-Wave-Mixing(FWM) in double _ system 5
2.1 Optical response of the medium . . . . . . . . . . . . . . . . . 6
2.2 Biphoton wave-packets . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Biphoton Characteristics . . . . . . . . . . . . . . . . . . . . . 16
2.4 Rabi oscillation regime . . . . . . . . . . . . . . . . . . . . . . 17
2.4.1 Resonant case . . . . . . . . . . . . . . . . . . . . . . . 17
2.4.2 Non-Resonant case . . . . . . . . . . . . . . . . . . . . 21
2.5 Group delay regime . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Experimental Apparatus and set-up 26
3.1 Cigar shaped Magneto-Optical-Trap . . . . . . . . . . . . . . . 26
3.1.1 Laser cooling . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2 Magnetic Trapping . . . . . . . . . . . . . . . . . . . . 29
3.1.3 2D MOT quadruple magnetic coil . . . . . . . . . . . . 30
3.1.4 Protection circuit . . . . . . . . . . . . . . . . . . . . . 32
3.1.5 Vacuum Chamber . . . . . . . . . . . . . . . . . . . . . 33
3.2 Optical setup and Laser preparation . . . . . . . . . . . . . . 35
3.3 87Rb j5P3=2i D2 line lasers . . . . . . . . . . . . . . . . . . . . 37
3.3.1 D2 line Master laser . . . . . . . . . . . . . . . . . . . 37
3.3.2 Frequency locking . . . . . . . . . . . . . . . . . . . . . 40
3.3.3 Tapered Ampli_er . . . . . . . . . . . . . . . . . . . . . 43
3.3.4 D2 line Slave laser . . . . . . . . . . . . . . . . . . . . 44
iii
3.3.5 Electro-Optical-Modulator(EOM) . . . . . . . . . . . . 46
3.3.6 AOMs and home build driver . . . . . . . . . . . . . . 47
3.4 87Rb j5P1=2i D1 Master and slave laser . . . . . . . . . . . . . 49
3.5 Basic measurements . . . . . . . . . . . . . . . . . . . . . . . . 51
3.5.1 Optical-Depth measurements . . . . . . . . . . . . . . 51
3.5.2 D1 and D2 Line EIT measurement . . . . . . . . . . . 53
4 Narrowband Paired Photon Generation 55
4.1 Phase matching and mode matching . . . . . . . . . . . . . . 56
4.2 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Polarization Filtering . . . . . . . . . . . . . . . . . . . 56
4.2.2 Fabry-Perot Etalon Filtering . . . . . . . . . . . . . . . 57
4.3 Photon Detection . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.1 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.2 Timing sequence . . . . . . . . . . . . . . . . . . . . . 60
4.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4.1 Energy level scheme . . . . . . . . . . . . . . . . . . . 61
4.4.2 Experimental set-up . . . . . . . . . . . . . . . . . . . 62
4.4.3 Initial signal . . . . . . . . . . . . . . . . . . . . . . . . 63
4.5 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5.1 Phase matching optimization . . . . . . . . . . . . . . 64
4.5.2 Pump power, detuning and noise optimization . . . . . 65
4.5.3 Better signals. . . . . . . . . . . . . . . . . . . . . . . . 66
4.5.4 Non-classical nature veri_cation . . . . . . . . . . . . . 67
5 E_cient generation of paired photons by controlled quantum
interference 68
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2 Biphoton generation at low OD . . . . . . . . . . . . . . . . . 71
5.3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . 73
5.4 Controlled quantum interference . . . . . . . . . . . . . . . . . 75
5.5 Sub-natural line-width biphotons . . . . . . . . . . . . . . . . 77
5.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.7 Electro Optic Modulation of Biphotons at low OD . . . . . . . 80
5.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 80
5.7.2 Electro-Optical Amplitude Modulation
(EOAM) . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.7.3 Single Photon level EOAM . . . . . . . . . . . . . . . 81
5.7.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . 82
5.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6 Switching of Entangled photons by Quantum Interference 86
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2 Theory of photon switching in 0N0 type system . . . . . . . . 87
6.3 Theory of biphoton switching(Double 0N" type system) . . . . 92
6.3.1 Biphoton Characteristics . . . . . . . . . . . . . . . . . 96
6.3.2 Case 1: Large c and smaller OD ( e < _!g or _r > _g ) 96
6.3.3 Case 2: Smaller c and large OD ( e > _!g or _r <
_g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7 Conclusion 108
Appendices 110
A Electromagnetically Induced Transparency(EIT) 111
B Temporal Shaping of Correlated Photon Pairs by Phase Match-
ing Function 116
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
B.2 Theory of optical precursor at biphoton level . . . . . . . . . . 117
B.2.1 Resonant Case . . . . . . . . . . . . . . . . . . . . . . 117
B.2.2 Non-Resonant Case . . . . . . . . . . . . . . . . . . . . 122
B.2.3 E_ect of phase-matching angle . . . . . . . . . . . . . . 123
B.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 124
B.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
C Collapse and Revival of DLCZ Quantum memory 128
D Interfacing Single Photons
from Cavity-enhanced SPDC and Cigar-Shaped Atomic Cloud137
E Heisenberg Picture 139
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