偏頻鎖相超短脈衝雷射以實現銫及銣原子高解析直接光梳光譜

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：38

、訪客IP：3.21.100.34

姓名

余欣鴻(Hsin-Hung Yu) 查詢紙本館藏

畢業系所

物理學系

論文名稱

偏頻鎖相超短脈衝雷射以實現銫及銣原子高解析直接光梳光譜
(High resolution direct comb spectra of Cs & Rb atoms by offset frequency locked pulse laser)

相關論文

★ 銫原子 6S-6D 雙光子超精細耦合常數	★ 同調性毫赫茲以下的光學偏頻鎖相系統測量高分辨率的銫原子 6S-6D 超精細躍遷
★ 銫原子穩頻822奈米二級光鐘	★ 銫原子6S1/2-6D3/2超精細躍遷絕對頻率與超精細結構
★ 銫原子蘭道g值之量測	★ 碘分子R(81)29-0 超精譜線用於539.5-nm 雷射穩頻
★ 銣原子光鐘絕對頻率之量測	★ 無頻率調制銣原子光鐘之研究
★ Direct comb laser spectroscopy of Cs 6S-8S, Rb 5S-5D hyperfine transitions—toward building up a novel Ti:sapphire comb laser with merely 6cm Cs-Rb mixed cell

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文試圖為實驗室發展一種偏頻鎖頻技術，我們稱為脈衝偏頻鎖相，讓一
般的鎖模雷射透過一台光梳雷射也能間接的參考到銫原子鐘上，關鍵在於利用一台有架設自參考系統的光梳雷射作為其他無法確認其自身偏移頻率的鎖模雷射的頻率參考。

這項技術主要是用來研究Cs&Rb 混合原子的直接光梳光譜，主要研究
Cs:6S1/2→6P3/2→8S1/2 與Rb:5S1/2→5P3/2→5D5/2 之階梯式雙光子躍遷(stepwise two-photon transition)。其中Rb 譜線是BIPM 建議的頻率標準之一，這項研究有助於發展利用光梳雷射與Cs&Rb 混合原子建立光鐘的實驗技術。

過去實驗室使用的脈衝雷射需要依賴與其他單頻穩頻雷射拍頻才能得知偏移頻率，然而我們的單頻穩頻雷射無法直接給出絕對頻率。當時實驗室的學長發現Cs光譜與理論計算可以有200~300 kHz的誤差，這現像由當時已知的所有可能的誤差來源都無法完全解釋，或是缺乏直接證據。為了彌補實驗無法直接給出絕對頻率的缺陷，我使用了脈衝偏頻鎖相技術鎖定雷射，並由此雷射掃描原子譜線，再次驗證了300 kHz的誤差，並且發現原因是原子受到磁場產生的Zeeman shift。我們嘗試修正這樣的誤差，並暫時驗證脈衝偏頻鎖相用於原子光譜掃描的可靠性。

我們依過去Cs:6S1/2→8S1/2 直接雙光子躍遷的實驗經驗，認為Cs 對於雙光子躍遷對於磁場並不敏感。透過這次實驗我們發現如果是階梯式雙光子躍遷則可能對磁場非常敏感，在論文中我將由基本的原子物理解釋這樣差異。

摘要(英)

This paper attempts to develop a offset-frequency locking technology for our laboratory, which we call pulse offset frequency locking technique. This technique can indirectly refer ordinary mode-locked lasers to cesium atomic clocks through an optical comb laser. The key is to use an optical comb laser with self-referencesystem as a frequency reference for other mode-locked lasers that cannot confirm their carrier-envelope offset frequency.

This technique is use to study direct frequency-comb spectroscopy of Cs&Rb atoms, mainly Cs:6S1/2→6P3/2→8S1/2and Rb:5S1/2→5P3/2→5D5/2stepwise two-photon transition. While Rb spectral line is one of the frequency standards suggested by BIPM. This research develops experimental techniques for building optical clocks using comb lasers and Cs&Rb mixed atomic cell.

In the past, mode-locked laser in our laboratory needs beat frequency with other stabilized single-frequency lasers to obtain the carrier envelope offset frequency. However, the absolute frequency of our stabilized single-frequency laser is unconfirmed. From past experiments in our laboratory, our senior member found that the Cs spectra had an error of 200~300 kHz compared with the theoretical calculation. In order to solve the defect that absolute frequency cannot be directly obtained in the experiment, I locked the mode-locked laser with pulse offset frequency locking technique, and use this laser to scan the atomic spectral lines. We confirmed the reason of 300 kHz error is Zeeman shift caused by magnetic field on atomic cell. We try to correct this error and verify the reliability of the pulse offset frequency locking technique for scanning atomic spectra.

According to experiences from Cs:6S1/2→8S1/2direct twophoton transition experiments, We think that the 6S1/2→8S1/2 two-photon transition of Cs is insensitive to magnetic fields. However, from this experiment we found that the transition may be very sensitive to magnetic fields if it is a stepped two-photon transition. In this paper I will explain the difference between the two types of two-photon transition from atomic physics.

關鍵字(中)

★ 光梳雷射
★ 偏頻鎖相
★ 脈衝同步
★ 直接光梳光譜

關鍵字(英)

★ Optical frequency comb
★ Offset-frequency locking
★ Pulse synchronization
★ Direct frequency-comb spectroscopy

論文目次

摘要v
Abstract vi
致謝vii
目錄ix
圖目錄xiii
表目錄xvii
符號列表xviii
第一章緒論1
1.1 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 實驗簡介. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3.1 脈衝時序同步. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3.2 脈衝偏頻鎖相. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.3 直接光梳光譜. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 論文導覽. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第二章基本原理7
2.1 原子能階. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 精細結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 超精細結構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 弱磁場下的Zeeman effect . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 躍遷電偶極. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 角動量相加. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Wigner-Eckart 定理. . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 精細結構躍遷電偶極. . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 超精細結構躍遷電偶極. . . . . . . . . . . . . . . . . . . . . . . . . 16
2.8 脈衝模態. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
第三章雙光子躍遷22
3.1 階梯式雙光子躍遷與直接雙光子躍遷. . . . . . . . . . . . . . . . . 22
3.1.1 階梯式雙光子躍遷. . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 同頻直接雙光子躍遷. . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.3 非同頻直接雙光子躍遷. . . . . . . . . . . . . . . . . . . . . . . 24
3.2 雙光子躍遷的選擇規則. . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 雙光子躍遷的譜線強度. . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.1 銫原子133 6S1/2→6P3/2→8S1/2 譜線強度. . . . . . . . . . . 28
3.3.2 銣原子85 5S1/2→5P1/2→5D3/2 譜線強度. . . . . . . . . . . 28
3.3.3 銣原子85 5S1/2→5P3/2→5D3/2 譜線強度. . . . . . . . . . . 29
3.3.4 銣原子85 5S1/2→5P3/2→5D5/2 譜線強度. . . . . . . . . . . 30
3.3.5 銣原子87 5S1/2→5P1/2→5D3/2 譜線強度. . . . . . . . . . . 31
3.3.6 銣原子87 5S1/2→5P3/2→5D3/2 譜線強度. . . . . . . . . . . 31
3.3.7 銣原子87 5S1/2→5P3/2→5D5/2 譜線強度. . . . . . . . . . . 32
3.4 雙光子躍遷的原子速度選擇. . . . . . . . . . . . . . . . . . . . . . 33
3.4.1 單光子都卜勒效應. . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4.2 直接雙光子都卜勒效應. . . . . . . . . . . . . . . . . . . . . . . 34
3.4.3 階梯式雙光子都卜勒效應. . . . . . . . . . . . . . . . . . . . . 35
3.5 原子譜線. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5.1 銫原子133 6S1/2→6P3/2→8S1/2 . . . . . . . . . . . . . . . . 38
3.5.2 銣原子85 5S1/2→5P1/2→5D3/2 . . . . . . . . . . . . . . . . . 40
3.5.3 銣原子85 5S1/2→5P3/2→5D3/2 . . . . . . . . . . . . . . . . . 41
3.5.4 銣原子85 5S1/2→5P3/2→5D5/2 . . . . . . . . . . . . . . . . . 42
3.5.5 銣原子87 5S1/2→5P1/2→5D3/2 . . . . . . . . . . . . . . . . . 43
3.5.6 銣原子87 5S1/2→5P3/2→5D3/2 . . . . . . . . . . . . . . . . . 44
3.5.7 銣原子87 5S1/2→5P3/2→5D5/2 . . . . . . . . . . . . . . . . . 45
3.6 銫與銣混合原子氣室頻率修正. . . . . . . . . . . . . . . . . . . . . 45
3.6.1 銫與銣混合原子氣室與純銫原子氣室比較. . . . . . . . . . . . 46
3.6.2 氦氣飄移. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
第四章實驗架構47
4.1 78-MHz 鈦藍寶石光梳雷射. . . . . . . . . . . . . . . . . . . . . . . 47
4.1.1 78-MHz 脈衝雷射重複率鎖定. . . . . . . . . . . . . . . . . . . 48
4.1.2 78-MHz 脈衝雷射偏移頻率量測. . . . . . . . . . . . . . . . . . 51
4.1.3 78M-Hz 脈衝雷射偏移頻率鎖定. . . . . . . . . . . . . . . . . . 54
4.2 1-GHz 鈦藍寶石鎖模雷射. . . . . . . . . . . . . . . . . . . . . . . 55
4.2.1 1-GHz 脈衝雷射重複率鎖定. . . . . . . . . . . . . . . . . . . . 56
4.3 脈衝偏頻鎖相系統. . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1 鎖定脈衝重複率. . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.2 雙脈衝拍頻量測. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3.3 鎖定脈衝拍頻. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.4 類比頻率電壓轉換器. . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.5 數位頻率電壓轉換器. . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.6 數位相位偵測器. . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 空間光調製器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.5 光功率穩定. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.6 光路調製器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.7 螢光訊號量測. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
第五章實驗結果與討論75
5.1 光梳雷射頻率穩定度. . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2 脈衝偏頻鎖相頻率穩定度. . . . . . . . . . . . . . . . . . . . . . . 76
5.3 銫原子直接光梳光譜. . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3.1 銫原子DTPT 直接光梳光譜. . . . . . . . . . . . . . . . . . . . 80
5.3.2 以直接光梳光譜測量絕對頻率的問題. . . . . . . . . . . . . . . 81
5.4 銣原子直接光梳光譜. . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4.1 銣原子直接光梳光譜(780 nm + 776 nm) . . . . . . . . . . . . . 83
5.4.2 銣原子直接光梳光譜(762 nm + 795 nm) . . . . . . . . . . . . . 88
5.5 譜線擬合. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.6 濾波器造成的訊號延遲. . . . . . . . . . . . . . . . . . . . . . . . . 95
5.7 光功率偏移. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.8 磁場偏移. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.8.1 測量1a 與8a 譜線對不同圓偏振的影響. . . . . . . . . . . . . 97
5.8.2 校正磁場偏移的方法一. . . . . . . . . . . . . . . . . . . . . . . 99
5.8.3 校正磁場偏移的方法二. . . . . . . . . . . . . . . . . . . . . . . 100
5.9 總結. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
參考文獻103

參考文獻

[1] 劉子維, “Direct comb laser spectroscopy of Cs 6S-8S, Rb 5S-5D hyperfine transitions
—toward building up a novel Ti:sapphire comb laser with merely 6cm Cs-Rb mixed
cell,” 博士論文，國立中央大學物理學系，2020。取自https://hdl.handle.net/
11296/nbp789.
[2] L.-S. Ma, R. K. Shelton, H. C. Kapteyn, M. M. Murnane, and J. Ye, “Sub-10-
femtosecond active synchronization of two passively mode-locked Ti:sapphire oscillators,”
Phys. Rev. A, vol. 64, p. 021802, Jul 2001.
[3] L.-S. Ma, R. K. Shelton, H. K. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye,
“Merging Two Independent Femtosecond Lasers Into One,” 2002.
[4] R. K. Shelton, L.-S. Ma, H. C. Kapteyn, M. M. Murnane, J. L. Hall, and J. Ye,
“Phase-Coherent Optical Pulse Synthesis from Separate Femtosecond Lasers,” Science,
vol. 293, no. 5533, pp. 1286–1289, 2001.
[5] A. Marian, M. C. Stowe, J. R. Lawall, D. Felinto, and J. Ye, “United time-frequency
spectroscopy for dynamics and global structure,” science, vol. 306, no. 5704,
pp. 2063–2068, 2004.
[6] H. Lu, J. Leng, and J. Zhao, “The Optimization of Cold Rubidium Atom Two-Photon
Transition Excitation with an Erbium-Fiber Optical Frequency Comb,” Applied Sciences,
vol. 9, no. 5, p. 921, 2019.
[7] V. Gerginov, C. Tanner, S. A. Diddams, A. Bartels, and L. Hollberg, “Optical frequency
measurements of 6s 2S1/2-6p 2P3/2 transition in 133Cs using an atomic
beam and a femtosecond laser frequency comb,” in Conference on Lasers and Electro-
Optics, p. CTuP72, Optica Publishing Group, 2004.
[8] V. Gerginov, C. Tanner, S. Diddams, A. Bartels, and L. Hollberg, “Precise frequency
measurements of 6s 2S1/2 -6p 2P3/2 transition in 133Cs atomic beam using a femtosecond
laser frequency comb,” in 2004 Conference on Precision Electromagnetic
Measurements, pp. 204–205, 2004.
[9] V. Gerginov, C. E. Tanner, S. A. Diddams, A. Bartels, and L. Hollberg, “Highresolution
spectroscopy with a femtosecond laser frequency comb,” Optics letters,
vol. 30, no. 13, pp. 1734–1736, 2005.
[10] J. E. Stalnaker, V. Mbele, V. Gerginov, T. M. Fortier, S. A. Diddams, L. Hollberg,
and C. E. Tanner, “Femtosecond frequency comb measurement of absolute frequencies
and hyperfine coupling constants in cesium vapor,” Phys. Rev. A, vol. 81,
p. 043840, Apr 2010.
[11] I. Barmes, S. Witte, and K. S. Eikema, “High-precision spectroscopy with counterpropagating
femtosecond pulses,” Physical review letters, vol. 111, no. 2, p. 023007,
2013.
[12] L.-R. Wang, Y.-C. Zhang, S.-S. Xiang, S.-K. Cao, L.-T. Xiao, and S.-T. Jia, “Twophoton
spectrum of 87Rb using optical frequency comb,” Chinese Physics B, vol. 24,
no. 6, p. 063201, 2015.
[13] J. E. Stalnaker, S. Chen, M. Rowan, K. Nguyen, T. Pradhananga, C. Palm, and D. J.
Kimball, “Velocity-selective direct frequency-comb spectroscopy of atomic vapors,”
Physical Review A, vol. 86, no. 3, p. 033832, 2012.
[14] D. A. Steck, ”Quantum and atom optics”, ch. Atomic Angular-Momentum Structure.
available online at http://steck.us/teaching, (revision 0.13.11, 7 April 2022).
[15] J. N. J.J. Sakurai, Modern Quantum Mechanics Second Edition, ch. Theory of Angular
Momentum, p. 231. Boston: Addison-Wesley, 2010.
[16] I. I. Sobelman, ”Atomic spectra and radiative transitions”, vol. 12, p. 228. Springer
Science & Business Media, 2012.
[17] R. J. Jones, J.-C. Diels, J. Jasapara, and W. Rudolph, “Stabilization of the frequency,
phase, and repetition rate of an ultra-short pulse train to a Fabry–Perot reference
cavity,” Optics communications, vol. 175, no. 4-6, pp. 409–418, 2000.
[18] W. Demtroder, Laser Spectroscopy: Basic Concepts and Instrumentation, ch. Nonlinear
Spectroscopy, pp. 476–477. Springer-Verlag Berlin Heidelberg New York, 2003.
[19] G. Grynberg and B. Cagnac, “Doppler-free multiphotonic spectroscopy,” Reports on
Progress in Physics, vol. 40, no. 7, p. 831, 1977.
[20] K. D. Bonin and T. J. McIlrath, “Two-photon electric-dipole selection rules,” JOSA
B, vol. 1, no. 1, pp. 52–55, 1984.
[21] D. A. Steck, “Cesium D Line Data,” available online at http://steck.us/alkalidata,
(revision 2.2.1, 21 November 2019).
[22] D. A. Steck, “Rubidium 85 D Line Data,” available online at http://steck.us/alkalidata,
(revision 2.2.3, 9 July 2021).
[23] D. A. Steck, “Rubidium 87 D Line Data,” available online at http://steck.us/alkalidata,
(revision 2.2.2, 9 July 2021).
[24] C.-M. Wu, T.-W. Liu, M.-H. Wu, R.-K. Lee, and W.-Y. Cheng, “Absolute frequency
of cesium 6S–8S 822nm two-photon transition by a high-resolution scheme,” Opt.
Lett., vol. 38, pp. 3186–3189, Aug 2013.
[25] F. Nez, F. Biraben, R. Felder, and Y. Millerioux, “Optical frequency determination
of the hyperfine components of the 5S12-5D32 two-photon transitions in rubidium,”
Optics Communications, vol. 102, no. 5, pp. 432–438, 1993.
[26] G. Barwood, P. Gill, and W. Rowley, “Frequency measurements on optically narrowed
Rb-stabilised laser diodes at 780 nm and 795 nm,” Applied Physics B, vol. 53,
no. 3, pp. 142–147, 1991.
[27] A. Banerjee, D. Das, and V. Natarajan, “Precise frequency measurements of atomic
transitions by use of a Rb-stabilized resonator,” Opt. Lett., vol. 28, pp. 1579–1581,
Sep 2003.
[28] J. Ye, S. Swartz, P. Jungner, and J. L. Hall, “Hyperfine structure and absolute
frequency of the 87 Rb 5P 3/2 state,” Optics letters, vol. 21, no. 16, pp. 1280–1282,
1996.
[29] K.-H. Chen, C.-M. Wu, S.-R. Wu, H.-H. Yu, T.-W. Liu, and W.-Y. Cheng, “Influence
of atmospheric helium on secondary clocks,” Opt. Lett., vol. 45, pp. 4088–4091, Jul
2020.
[30] B. Brannon and A. Barlow, “Aperture uncertainty and ADC system performance,
Applications Note AN-501,” Analog Devices, Inc.(September), 2000.
[31] W.-Y. Cheng, T.-J. Chen, C.-W. Lin, B.-W. Chen, Y.-P. Yang, and H. Y. Hsu,
“Robust sub-millihertz-level offset locking for transferring optical frequency accuracy
and for atomic two-photon spectroscopy,” Optics Express, vol. 25, no. 3, pp. 2752–
2762, 2017.
[32] S. Johansson, “New frequency counting principle improves resolution,” in Proceedings
of the 20th European Frequency and Time Forum, pp. 139–146, IEEE, 2006.
[33] W. Kester, “The good, the bad, and the ugly aspects of ADC input noise—Is no
noise good noise?,” Analog Devices, Inc., vol. 4, 2008.
[34] Atmel Corporation, https:// ww1.microchip.com/ downloads/ en/ Appnotes/
doc8003.pdf, “AVR121: Enhancing ADC resolution by oversampling,”
[35] Analog Devices, https://www.analog.com/media/en/technical-documentation/datasheets/
AD9901.pdf, “AD9901 Ultrahigh SpeedPhase/Frequency Discriminator,”
[36] PerkinElmer, https://.resources.perkinelmer.com/ lab-solutions/ resources/ docs/
DTS_010052A_01_SLM_DTS.pdf, “Spatial Light Modulators,”

指導教授

鄭王曜(Wang-Yau Cheng)

審核日期

2022-8-11

推文