臺灣博碩士論文加值系統

為了提高銣-87原子在光偶極陷阱（optical dipole trap，簡稱ODT）中的光學密度（optical density，簡稱OD）以進而在其中進行單光子實驗，本論文研究如何能有效地將原子分別從TOP（time-averaged orbiting potential，簡稱TOP）和黑暗壓縮型磁光陷阱（dark compressed magnetic-optical trap，簡稱dark-CMOT）以及黑暗型磁光陷阱（dark magnetic-optical trap，簡稱dark MOT）來載入ODT中。在TOP中的原子溫度和密度分別是57.5μK和1.2×1012 cm-3﹐dark MOT 和dark-CMOT後的原子溫度則為300μK，密度為3.8×1010 cm-3。我們使用的ODT其光源為波長1064nm的光纖雷射，最大輸出功率為10W，其聚焦後的光腰約為54 μm（e-2直徑），ODT的陷阱深度為850μK。
我們研究了原子在ODT中的溫度、原子數以及生存時間，光學密度（OD）的測量則是藉由分析一道頻率為├ |5S_(1/2),F=2⟩到├ |5P_(3/2),F'=2⟩之左旋探測雷射光對ODT中原子長軸的穿透率來達成。此探測光和ODT中原子的重合度對於測量OD有極大的影響，我們可藉由分析原子團影像被強度遠大於一個飽和吸收光強，頻率為├ |5S_(1/2),F=2⟩到├ |5P_(3/2),F'=3⟩的探測光作用掉的區域來分析ODT中原子團與探測光的重合度。
從TOP 3A（TOP線圈上的電流值）將原子載入ODT中，ODT中的原子數為1.6×106，溫度約為61μK，由原子數和雪茄形原子團的尺寸82×82×3000μm3（e-2直徑），可推算沿著原子團長軸的光學密度為170。實驗上用一道光腰為45μm（e-2直徑），的探測光對原子中心長軸的穿透率量測值只有20%，由此穿透率、探測光光強以及原子密度在空間上的分布所推算出的原子的長軸中心OD則只有11。
從dark -CMOT將原子載入ODT中，ODT中的原子數為2.7×106，溫度為350μK，當原子在基態F=2上時，原子在功率為10.7W的ODT內的生存時間約為0.43s，由原子數和雪茄形原子團的尺寸160×160×2800 μm3（e-2直徑），可推算沿著原子團長軸的光學密度為72。
從dark MOT將原子載入功率為1.7W的ODT中，ODT的原子數為4.4×106，溫度約為350μK，由原子數和雪茄形原子團的尺寸170×170×2500 μm3（e-2直徑），可推算沿著原子團長軸的光學密度為120。當原子在基態F=1上，其在功率為10.7W和1.6W的ODT內的生存時間分別為0.84s和11s。
之後我們的目標是降低從dark MOT載入ODT中的原子的溫度，使此種載入方式優於將原子從TOP載入ODT中的方法。

To maximize the optical density (OD) of cold 87Rb atoms in an optical dipole trap (ODT) for future single-photon experiments, we investigated the methods of loading the atoms into the ODT from a time-averaged orbiting potential (TOP) and from a dark magnetic-optical trap with and without the magnetic compression (abbreviated as dark-CMOT and dark-MOT, respectively). The atomic temperature and density in the TOP 3A (the current through the TOP coils) were 57.5 K and 1.2×1012 cm-3; those in the dark-CMOT or dark-MOT were 300 K and 3.8×1010 cm-3. The ODT was realized by a 1064 nm fiber laser with a maximum power of 10 W. The e-2 full width of the focused laser beam was approximately 54 μm, giving the ODT trap depth of about 850 K.
We studied the temperature, number, and life time of the atoms captured in the ODT. ODs of the atoms were measured by the absorption of a weak probe laser beam tuned to the D2 transition of 87Rb and propagating along the major axis of the ODT. The alignment of the probe beam is critical to the absorption measurement and was studied by imaging the atom cloud under the radiation pressure from the high-intensity probe field driving the cycling transition from |F=2 to |F’=3 resonantly.
With the loading from the TOP 3A, there were about 1.6×106 atoms with a temperature of 61 μK in the ODT with a power of 10.7 W. The OD along the central axis estimated by the atom number and the dimension of the cigar-shaped cloud of 82×82×3000 μm3 (e-2 full widths) is 170. However, the transmission of the probe field with the e-2 full width of 45 μm driving the non-cycling transition from |F=2 to |F’=2 resonantly and propagating through the major axis of the atom cloud is about 20%, showing that the OD along the central axis of the cloud is only 11.
With the loading from the dark-CMOT, there were about 2.7×106 atoms with a temperature of 350 μK and a life time of 0.43 s in the ODT with a power of 10.7 W. The life time was measured under the captured atoms being placed in the |F=2 ground state. The OD along the central axis estimated by the atom number and the dimension of the cigar-shaped cloud of 160×160×2800 μm3 (e-2 full widths) is 72.
With the loading from the dark-MOT, there were about 4.4×106 atoms with a temperature of 350 μK in the ODT with a power of 10.7 W. The OD along the central axis estimated by the atom number and the dimension of the cigar-shaped cloud of 170×170×2500 μm3 (e-2 full widths) is 120. When the captured atoms were placed in the |F=1 ground state, their lifetime of 0.84 and 11 s were observed in the 10.7-W and 1.6-W ODT, respectively. We will further cool down the atoms to make the simpler dark-MOT loading method outperform the more complicate TOP loading method.

中文摘要 ………………………………………………………………… i
英文摘要 ………………………………………………………………… iii
誌謝 ………………………………………………………………… v
目錄 ………………………………………………………………… vi
圖目錄 ………………………………………………………………… viii
表格目錄 …………………………………………………………………… xv
縮寫說明 ………………………………………………………………… xvi
第一章 引論 …………………………………………………………1
第二章 理論介紹………………………………………………………3
2-1 原子冷卻過程介紹……………………………………………3
2-1-1 都卜勒冷卻與磁光陷阱…………………………………………3
2-1-2 黑暗型壓縮磁光陷阱……………………………………………5
2-1-3 偏極梯度冷卻……………………………………………………6
2-1-4 TOP與蒸發式冷卻………………………………………………8
2-2 光偶極陷阱（ODT）的介紹……………………………………8
2-2-1 光偶極陷阱（ODT）的歷史發展………………………………8
2-2-2 光偶極陷阱（ODT）的古典模型………………………………9
2-2-3 光偶極陷阱（ODT）的半古典理論……………………………11
2-2-4 在高斯光偶極陷阱中的鹼金族原子……………………14
第三章 實驗系統介紹…………………………………………………17
3-1 雷射系統……………………………………………………………17
3-2 真空腔及磁場線圈……………………………………………18
3-3 量測方法的介紹及系統架設…………………………………19
3-3-1 螢光法……………………………………………………19
3-3-2 吸收影像法………………………………………………19
3-3-3 吸收影像-Image beam與光偶極陷阱（ODT）中原子長軸 夾角為〖45〗^°時的原子團參數計算方式……………………………24
3-3-4 光偶極陷阱（ODT）之光路架設…………………………26
3-3-5 光抽運法……………………………………………28
3-3-6 探測雷射光路架設………………………………………30
第四章 從TOP載入ODT之實驗數據及分析……………………………33
4-1 測量TOP原子參數………………………………………………33 4-2 從TOP載入ODT………………………………………………34
4-3 ODT中原子特性之量測及探測雷射穿透率分析…………………35
第五章 從dark-CMOT載入ODT之實驗數據及分析……………………39
5-1 dark-CMOT的最佳化………………………………………………39
5-2 dark-CMOT 後的偏極梯度冷卻時序最佳化……………………51
5-3 從dark-CMOT載入ODT的時序最佳化……………………………61
5-4 ODT中原子特性之量測……………………………………………63
5-4-1 原子在ODT中的Zeeman state的一致性對生存時間的影響…………………………………………………………………………66
5-4-2 影響ODT內原子溫度的實驗參數之研究………………………68
第六章 從dark-MOT載入ODT之實驗數據及分析……………………74
6-1 dark-MOT的最佳化…………………………………………74
6-2 dark MOT 後的偏極梯度冷卻……………………………101
6-3 影響ODT內原子溫度的實驗參數之研究…………………106
6-4 有無dark MOT對ODT內原子數的影響……………………113
6-5 陷阱深度對ODT內的原子數、溫度以及生存時間之影響119
第七章 結論…………………………………………………………123
參考資料………………………………………………………………125

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