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研究生:謝易家
研究生(外文):Yi-Chia Hsieh
論文名稱:利用平衡式雙雪崩光二極體架構之暗記數抑制及應用於量子密鑰分配系統之研究
論文名稱(外文):Dark Counts Suppression Based on Balanced Dual-APD Scheme and for QKD System
指導教授:何文章何文章引用關係
指導教授(外文):Wen-Jeng Ho
口試委員:廖枝旺童儒達游本懋
口試日期:2012-07-25
學位類別:碩士
校院名稱:國立臺北科技大學
系所名稱:光電工程系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:71
中文關鍵詞:雪崩光二極體(APD)暗記數機率(DCP)單光子檢測效率(SPDE)雜訊等效功率(NEP)量子密鑰分配系統(QKD)量子誤碼率(QBER)後脈衝效應(Afterpulsing effect)
外文關鍵詞:Avalanche Photodiode (APD)Dark Count Probability (DCP)Single Photon Detection Efficiency (SPDE)Noise Equipment Power (NEP)Quantum Bit Error Rate (QBER)Quantum Key Distribution (QKD)
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本論文利用平衡式雙雪崩光二極體的架構來抑制暗記數及提高其檢測頻率,為了能夠將此架構運用在量子密鑰分配系統(Quantum Key Distribution System)中,我們先針對平衡式雙雪崩光二極體架構的單光子檢測特性參數加以討論與分析,其參數包含暗記數機率(DCP)、單光子檢測效率(SPDE)、雜訊等效功率(NEP)、檢測頻率以及量子誤碼率(QBER)。
其次,將檢測出的單光子訊號輸入至Self-Differencing電路處理,使其進一步降低Spike雜訊。我們選擇轉換率(Slew Rate, SR)較大的放大器以符合Self- Differencing電路需求,達到降低暗記數機率且增加檢測頻率。所架設出簡易的量子密鑰分配系統,當溫度為-50℃及檢測頻率為1~2 MHz時,可獲得較佳的量子誤碼率。我們也探討在-60℃低溫及10 MHz高頻率下所產生的後脈衝效應。從實驗數據中選取最適當的檢測參數進行量子誤碼率計算,並依照量子密鑰分配理論之誤碼率進一步計算出其傳輸距離。
最後,在溫度為-50℃、檢測頻率1 MHz及超額偏壓2.0 V時,我們獲得暗記數機率為9.26×10-4,單光子檢測效率為11.6%及等效雜訊功率為1.06×10-15 W/Hz1/2。利用上述實驗值所計算出Back to Back與傳輸10.5公里後的量子誤碼率分別為7%與10.65%。當量子誤碼率為15%,所計算出最大傳輸距離為22公里,但實際利用光纖傳輸10.5公里後其QBER上升至14.47%,因此實際值與計算值相差3.82%。


In this thesis, dark counts suppression and detection frequency improvement by using a balanced dual avalanche photodiode scheme was proposed. In order to apply this experimental setup to the quantum key distribution (QKD) system, we discuss and analyze the characteristic parameters of the used APD, including dark count probability (DCP), single photon detection efficiency (SPDE), noise equipment power (NEP), detection frequency and quantum bit error rate (QBER).
The signal from the single photon detection was feed into the self-differencing circuit which can reduce the spiking noise. In accordance with self-differencing circuit requirements, we choose the amplifier with a large slew rate for achieving low dark count probability and higher detection frequency. We are also constructed a simple QKD system at the same time. The system would be has best quantum bit error rate (QBER) under -50℃ and 1 MHz、2 MHz.
In this study, we surveyed the influence of different parameters, such as temperature, excess bias voltage and pulse width. To demonstrate the afterpulsing effect by releasing the trapped carriers at lower temperature and high detection frequency, the APD was cooled down to a temperature of -60℃ and raised the frequency to 10 MHz. And then we calculated the optimum QBER and transmission distance from the obtained date of the best detection parameter in theory.
Finally, at a temperature of -50℃ and detection frequency of 1 MHz, the excess bias voltage of 2.0 V was applied on balanced dual avalanche photodiode schematic to characterize single-photon performance. The best single photon detection efficiency of 11.6% at dark count probability 9.26×10-4 and noise equipment power as low as 1.06×10-15 W/Hz1/2 are obtained. Based on the above conditions, the calculated corresponding QBER values of back to back and after 10.5 km fiber length are 7% and 10.65%. The maximum available transmission distance was 22 km as the QBER below 15%. However, after actual transmission through optical fiber of 10.5 km the obtained QBER was 14.47%. The difference of QBER between the actual transmission value and the calculated value was 3.82 percent.

目 錄
摘 要 i
ABSTRACT iii
誌 謝 v
目 錄 vi
圖目錄 viii
表目錄 x
第一章 緒論 1
1.1 量子通訊(Quantum Communnication) 1
1.2 量子密鑰分配系統(Quantum Key Distribution System) 2
1.3 單光子檢測(Single Photon Detection) 6
1.4 研究動機與論文架構 7
第二章 單光子檢測應用於QKD系統之工作原理 8
2.1 雪崩光二極體(APD) 8
2.1.1 基本概念 8
2.1.2 操作於線性區(Liner Mode)特性 9
2.1.3 操作於蓋格區(Geiger Mode)特性 10
2.1.4 閘模抑制(Gated-Mode Quenching ) 11
2.2 自我差分(Self-differencing)單光子檢測器 11
2.2.1 同軸電纜反射線 11
2.2.2 單雪崩光二極體自我差分架構 12
2.2.3 平衡式雙雪崩光二極體檢測 13
2.3 後脈衝效應(Afterpulsing Effect) 14
2.3.1 後脈衝效應的量測 14
2.3.2 後脈衝與暗記數率之間關係 15
2.4 主要參數介紹 15
2.4.1 暗記數率與暗記數機率(Dark Count Rate and Dark Count Probability) 16
2.4.2 單光子檢測效率(Single Photon Detection Efficiency) 17
2.4.3 雜訊等效功率(Nosie Equivalent Power) 18
2.4.4 量子誤碼率(Quantum Bit Error Rate) 18
第三章 研究方法與實驗架構 20
3.1 檢測系統架構 20
3.2 閘模抑制電路(Gated-Mode Quenching Circuit) 22
3.2.1 自我差分電路(Self-Differencing Circuit) 23
3.3 RC電路 27
3.4 溫度控制系統 28
3.5 系統架構同步 29
3.6 單光子光源計算 31
3.7 實驗步驟與量測方法 32
第四章 實驗結果與討論 34
4.1 崩潰電壓(Breakdown Voltage) 34
4.2 暗記數機率 36
4.2.1 暗記數機率對超額偏壓關係 36
4.2.2 暗記數機率對溫度關係 37
4.2.3 暗記數機率對Gated脈衝寬度關係 38
4.2.4 後脈衝效應對暗記數機率影響 39
4.3 單光子檢測效率 42
4.3.1 單光子檢測效率對超額偏壓關係 42
4.3.2 單光子檢測效率對溫度關係 43
4.3.3 單光子檢測效率對Gated脈衝寬度關係 44
4.3.4 後脈衝效應對單光子檢測效率影響 45
4.4 雜訊等效功率 46
4.4.1 雜訊等效功率對超額偏壓關係 46
4.4.2 雜訊等效功率對溫度關係 47
4.4.3 雜訊等效功率對Gated脈衝寬度關係 48
4.5 系統檢測頻率 49
4.6 暗記數機率對單光子檢測效率比 51
4.7 量子誤碼率與傳輸距離 53
4.8 本架構與參考文獻各項參數值及特性之比較 62
第五章 結論與未來展望 65
參考文獻 67

圖目錄
圖1.1 BB84協議中,將四種量子態表示在布洛赫球上 3
圖1.2 Mμ與Mν基底示意圖 3
圖1.3 B92協議中,將兩種量子態表示在布若赫球上 5
圖2.1 雪崩光二極體電流-電壓曲線圖(I-V curve) 9
圖2.2 不同光功率所對應到的光電流值 10
圖2.3 閘模抑制電路與其產生訊號 11
圖2.4 同軸電纜反射線架構 12
圖2.5 單雪崩光二極體自我差分架構 12
圖2.6 平衡式雪崩光二極體檢測架構 13
圖2.7 檢測後脈衝機率參數示意圖 14
圖2.8 Gated 脈衝寬度與次數 16
圖3.1 利用平衡式雙雪崩光二極體簡易架構 20
圖3.2 平衡式雙雪崩光二極體完整架構 21
圖3.3 閘模抑制電路 22
圖3.4 通過Bias-Tee的逆向偏壓圖 23
圖3.5 自我差分電路架構圖 24
圖3.6 在進入Self-differencing電路之前調整APD2電纜線長度之架構圖 24
圖3.7 脈衝寬度為2 ns的APD1訊號與APD2訊號 25
圖3.8 脈衝寬度為4 ns的APD1訊號與APD2訊號 25
圖3.9 脈衝寬度為2 ns的APD1與 APD2完全同步相消訊號 26
圖3.10 APD1與 APD2訊號(同軸電纜線過長或過短) 27
圖3.11 溫度控制系統架構圖 28
圖3.12 光脈衝訊號與Gated電訊號同步示意圖 29
圖3.13 Gated電訊號與光脈衝訊號延遲時間示意圖 30
圖3.14 Gated電訊號與光脈衝訊號控制延遲時間示波器圖 30
圖3.15 不同平均光子數μ的Poisson分佈關係圖 31
圖3.16 實驗步驟流程圖 33
圖4.1 APD1在-50℃對應的崩潰電壓 34
圖4.2 崩潰電壓與溫度關係 35
圖4.3 APD1與APD2之C-V圖 35
圖4.4 (a) 不同溫度下暗記數機率對超額偏壓關係圖(1 MHz) 36
圖4.4 (b) 不同溫度下暗記數機率對超額偏壓關係圖(2 MHz) 37
圖4.5 (a) 不同超額偏壓下暗記數機率對溫度關係圖(1 MHz) 37
圖4.5 (b) 不同超額偏壓下暗記數機率對溫度關係圖(2 MHz) 38
圖4.6 不同Gated脈衝寬度下暗記數機率對超額偏壓關係圖 38
圖4.7 (a) 不同超額偏壓下暗記數機率對溫度關係圖(1 MHz) 39
圖4.7 (b) 不同超額偏壓下暗記數機率對溫度關係圖(2 MHz) 40
圖4.8 (a) 不同溫度下暗記數機率對超額偏壓關係圖(1 MHz) 40
圖4.8 (b) 不同溫度下暗記數機率對超額偏壓關係圖(2 MHz) 41
圖4.9 (a) 不同溫度下單光子檢測效率對超額偏壓關係圖(1 MHz) 42
圖4.9 (b) 不同溫度下單光子檢測效率對超額偏壓關係圖(1 MHz) 43
圖4.10 (a) 不同超額偏壓下單光子檢測效率對溫度關係圖(1 MHz) 43
圖4.10 (b) 不同超額偏壓下單光子檢測效率對溫度關係圖(2 MHz) 44
圖4.11 不同Gated脈衝寬度下暗記數機率對單光子檢測效率關係圖 44
圖4.12 (a) 不同超額偏壓下單光子檢測效率對溫度關係圖(1 MHz) 45
圖4.12 (b) 不同超額偏壓下單光子檢測效率對溫度關係圖(2 MHz) 45
圖4.13 (a) 不同溫度下雜訊等效功率對超額偏壓關係圖(1 MHz) 46
圖4.13 (b) 不同溫度下雜訊等效功率對超額偏壓關係圖(2 MHz) 47
圖4.14 (a) 不同超額偏壓下雜訊等效功率對溫度關係圖(1 MHz) 47
圖4.14 (b) 不同超額偏壓下雜訊等效功率對溫度關係圖(2 MHz) 48
圖4.15 不同Gated脈衝寬度下雜訊等效功率對超額偏壓關係圖 48
圖4.16 不同溫度下的暗記數機率對檢測效率圖 49
圖4.17 不同檢測頻率下暗記數機率對超額偏壓關係圖 50
圖4.18 不同溫度下每單位Gated脈衝的暗記數機率比單光子檢測效率關係圖(1 MHz) 51
圖4.19 不同溫度下每單位Gated脈衝的暗記數機率比單光子檢測效率關係圖(2 MHz) 52
圖4.20 不同檢測頻率下及條紋可見度為99.5%時量子誤碼率對傳輸距離圖 54
圖4.21 不同暗記數機率下及條紋可見度為99.5%時量子誤碼率對傳輸距離圖 54
圖4.22 (a) 不同溫度下超額偏壓為1.6 V的量子誤碼率對傳輸距離關係圖
(1 MHz) 55
圖4.22 (b) 不同溫度下超額偏壓為1.6 V的量子誤碼率對傳輸距離關係圖
(2 MHz) 55
圖4.23 (a) 不同超額偏壓下量子誤碼率對傳輸距離關係圖(1 MHz) 56
圖4.23 (b) 不同超額偏壓下量子誤碼率對傳輸距離關係圖(2 MHz) 57
圖4.24 經10.5公里光纖傳輸後調整延遲時間示波器圖 58
圖4.25 (a) 不同超額偏壓下暗記數機率與單光子檢測效率關係圖(1 MHz) 59
圖4.25 (b) 不同超額偏壓下暗記數機率與單光子檢測效率關係圖(2 MHz) 59
圖4.26 (a) 經10.5公里光纖傳輸量子誤碼率對傳輸距離關係圖(1 MHz) 60
圖4.26 (b) 經10.5公里光纖傳輸量子誤碼率對傳輸距離關係圖(2 MHz) 61
圖4.27 文獻中(Fig.4.)暗記數機率與量子效率關係圖 62
圖4.28 本實驗暗記數機率與單光子檢測效率關係圖 62
圖4.29 文獻中(Fig.2.)暗記數機率與檢測頻率關係圖 63
圖4.30 本實驗暗記數機率與檢測頻率關係圖 63

表目錄
表1.1 在B84協議中所有可能的量子態與基底 4
表1.2 在B92協議中所有可能的量子態、基底與檢測機率 5
表4.1 不同超額偏壓下量子誤碼率計算值與實際值比較表 61
表4.2 比較其文獻與本論文中實驗設定參數 64
表4.3 比較其文獻與本論文中暗記數機率與單光子檢測效率值 64
表4.4 比較其文獻與本論文中NEP、DCP/SPDE、QBER及最佳傳輸距離 64


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