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作者(中文):陳柏松
作者(外文):Chen, Po-Sung
論文名稱(中文):玻色–愛因斯坦凝聚態之動態
論文名稱(外文):Dynamics of Bose-Einstein Condensates
指導教授(中文):劉怡維
指導教授(外文):Liu, Yi-Wei
口試委員(中文):郭西川
童世光
林育如
口試委員(外文):Gou, Shih-Chuan
Tung, Shih-Kuang
Lin, Yu-Ju
學位類別:碩士
校院名稱:國立清華大學
系所名稱:物理學系
學號:104022525
出版年(民國):107
畢業學年度:106
語文別:英文
論文頁數:77
中文關鍵詞:玻色愛因斯坦凝態雷射冷卻
外文關鍵詞:BECcondensatelaser cooling
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在這篇論文中,我們探討在磁四極陷阱(magnetic quadrupole trap)下量子簡併波色子氣體(玻色–愛因斯坦凝聚態, Bose-Einstein condensate, BEC)的動態。BEC是一個微米等級的巨型物質波。藉由光學成像的方式,我們能夠以微秒等級的最短時間尺度來觀測BEC。不同於一般的單粒子物質波,在量測BEC時,能夠量測到整個物質波的分布以及物質波隨著時間的變化。物質波進入和阱離開位能阱的過程可以等價於分子的鍵結以及游離過程,因此這樣的實驗架設可以做為分子鍵結的量子模擬。

在實驗上,我們用磁光混和陷阱(magneto-optical hybrid trap)將銣原子(rubidium 87)捕捉並冷卻至小於100nK的溫度來產生BEC。在這篇論文中,我們會介紹兩種BEC的動態。
首先,BEC在陷阱的深度降低時,會被”晃”出陷阱,並產生水滴狀的脈衝原子雷射(pulsed atom laser)。藉由BEC在陷阱內的運動,我們能夠產生重複率(repetition rate)等同於陷阱頻率(trap frequency)的脈衝原子雷射。我們提出一個簡易的模型來解釋水滴狀的密度分布。

在第二個實驗,我們先將BEC以自由落體的方式來獲得初始動能,接著將它載入磁陷阱中讓它在位能阱內週期性的上下運動。在結合重力場的情況下,總和位能阱會是一個非對稱的V型位能阱。BEC在這樣的位能阱內來回彈跳(bouncing)會產生許多有趣的動態。物質波會由最一開始的高斯分布(gaussian profile)隨時間演化至長條狀並產生干涉條紋。此外,在彈跳過程中,我們觀察到BEC的塌縮恢復現象(collapse and revival)。藉由薛丁格方程式(Schrödinger equation)的數值模擬,我們得到和實驗非常接近的結果。

在這篇論文,我們用BEC來探討對分子物理進行量子模擬的可能性。
The dynamics of bosonic quantum degenerate gas (Bose-Einstein condensate, BEC) in a magnetic potential well was reported. A BEC is considered as a giant microscopic matter wave that can be investigated by direct optical imaging with a time-scale of millisecond to second. In comparison with a single particle wave function, it can be closely observed, as a slow-motion movie. The evolution of matter wave in and out of a trap potential is equivalent to “binding” and “ionization” processes.

In our experiment, a BEC with 3×〖10〗^5 rubidium (87Rb) atoms was produced in a magneto-optic hybrid trap with a typical temperature < 100nK. Two kinds of BEC dynamics were then investigated in our experiment.

Firstly, the BEC was “shaken” out of the trap, forming droplets and generating a pulsed atom laser. We take advantage of the internal dynamics of BEC to generate pulses with a repetition rate equal to the trap frequency. A simple model was presented to explain the droplet-like density distribution.

Secondly, the BEC acquires initial kinetic energy via free fall in gravity, and then the magnetic trap was turned on to load the BEC, which then periodically moved up-and-down in the trap. Combining with the gravity, it was confined in an asymmetric V-type potential well. The wave function of atoms bounces inside the trap, enriching the dynamics of the system. The matter wave with an initial gaussian profile evolved to a long strip with interference pattern. During the bouncing, the collapses and revivals of BEC were also observed. Numerical simulations based on Schrodinger equation agree quantitatively with the experimental observation.

In the thesis, we explore the possibility of quantum simulation for molecular physics using BEC.
Chapter 1 Introducion 1
1.1 Motivation 5
1.2 Outline 5
Chapter 2 Theoretical background 6
2.1 Doppler cooling 6
2.2 Magnetic quadrupole trap 7
2.3 Magneto-optical trap(MOT) 9
2.4 Optical dipole trap for neutral atoms 10
2.5 Polarization gradient cooling 12
2.6 Evaporative cooling 13
2.7 Gross-Pitaevskii equation and hydrodynamic equations. 14
2.7.1 Time independent Gross-Pitaevskii equaiton 14
2.7.2 Time dependent Gross-Pitaevskii equaiton 16
2.7.3 The hydrodynamics equations 17
2.7.4 The Bogoliubov equations 22
Chapter 3 Experimental setup 24
3.1 Vacuum system 24
3.1.1 MOT chamber 25
3.1.2 Science cell 26
3.2 Laser system 27
3.2.1 Frequency 27
3.2.2 Lasers 28
3.2.3 Power amplifier and beam shaping 31
3.3 Optics around the MOT chamber 33
3.4 Coils 34
3.4.1 MOT coils 34
3.4.2 Balance coils 34
3.4.3 RF coils 35
3.5 Magnetic transportation System 35
3.6 Optical dipole trap 36
3.7 Detecting System 37
3.7.1 Fluorescence imaging 38
3.7.2 Absorption imaging 38
Chapter 4 Characterization and optimization of ultracold 87Rb 42
4.1 MOT characterization 42
4.2 Compressed MOT (CMOT) and polarization gradient cooling (PGC) 43
4.3 Magnetic transportation 44
4.4 RF-evaporative cooling 45
4.5 Loading to the Hybrid trap (magnetic trap and dipole trap) 47
4.6 Evaporative cooling in hybrid trap 50
4.7 Calibration of imaging system 51
Chapter 5 Dynamic of 87Rb BEC 53
5.1 Time evolution of BEC in the hybrid trap 53
5.2 Leakage of BEC 55
5.3 Bouncing BEC 60
Chapter 6 Conclusion and future work 69
6.1 Conclusion 69
6.2 Future work 70

[1] Bose, S. N. (1924). Planck’s law and light quantum hypothesis. Z. Phys, 26(1), 178.
[2] Einstein, A. (1924). Quantentheorie des einatomigen idealen Gases. Akademie der Wis-senshaften, in Kommission bei W. de Gruyter.
[3] Bradley, C. C., Sackett, C. A., Tollett, J. J., & Hulet, R. G. (1995). Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Physical Review Let-ters, 75(9), 1687.
[4] Davis, K. B., Mewes, M. O., Andrews, M. R., Van Druten, N. J., Durfee, D. S., Kurn, D. M., & Ketterle, W. (1995). Bose-Einstein condensation in a gas of sodium atoms. Physical re-view letters, 75(22), 3969.
[5] Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E., & Cornell, E. A. (1995). Observation of Bose-Einstein condensation in a dilute atomic vapor. science, 269(5221), 198-201.
[6] Dalibard, J., & Cohen-Tannoudji, C. (1989). Laser cooling below the Doppler limit by po-larization gradients: simple theoretical models. JOSA B, 6(11), 2023-2045.
[7] Hess, H. F. (1986). Evaporative cooling of magnetically trapped and compressed spin-polarized hydrogen. Physical Review B, 34(5), 3476.
[8] Adams, C. S., Lee, H. J., Davidson, N., Kasevich, M., & Chu, S. (1995). Evaporative cool-ing in a crossed dipole trap. Physical review letters, 74(18), 3577.
[9] Pethick, C. J., & Smith, H. (2002). Bose-Einstein condensation in dilute gases. Cambridge university press.
[10] Petrich, W., Anderson, M. H., Ensher, J. R., & Cornell, E. A. (1995). Stable, tightly con-fining magnetic trap for evaporative cooling of neutral atoms. Physical Review Letters, 74(17), 3352.
[11] Raab, E. L., Prentiss, M., Cable, A., Chu, S., & Pritchard, D. E. (1987). Trapping of neu-tral sodium atoms with radiation pressure. Physical Review Letters, 59(23), 2631.
[12] Chu, S., Bjorkholm, J. E., Ashkin, A., & Cable, A. (1986). Experimental observation of optically trapped atoms. Physical review letters, 57(3), 314.
[13] Davis, K. B., Mewes, M. O., Joffe, M. A., Andrews, M. R., & Ketterle, W. (1995). Evap-orative cooling of sodium atoms. Physical review letters, 74(26), 5202.
[14] Steck, D. A. (2001). Rubidium 87 D line data.
[15] Petrich, W., Anderson, M. H., Ensher, J. R., & Cornell, E. A. (1994). Behavior of atoms in a compressed magneto-optical trap. JOSA B, 11(8), 1332-1335.
[16] Lin, Y. J., Perry, A. R., Compton, R. L., Spielman, I. B., & Porto, J. V. (2009). Rapid pro-duction of R 87 b Bose-Einstein condensates in a combined magnetic and optical potential. Physical Review A, 79(6), 063631.
[17] Lin, Y. J., Jiménez-García, K., & Spielman, I. B. (2011). Spin–orbit-coupled Bose–Einstein condensates. Nature, 471(7336), 83.
[18] Schweikhard, V., Coddington, I., Engels, P., Mogendorff, V. P., & Cornell, E. A. (2004). Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level. Physical re-view letters, 92(4), 040404.
[19] Spreeuw, R. J. C., Pfau, T., Janicke, U., & Wilkens, M. (1995). Laser-like scheme for atomic-matter waves. EPL (Europhysics Letters), 32(6), 469.
[20] Holland, M., Burnett, K., Gardiner, C., Cirac, J. I., & Zoller, P. (1996). Theory of an atom laser. Physical Review A, 54(3), R1757.
[21] Wiseman, H., Martins, A., & Walls, D. (1996). An atom laser based on evaporative cooling. Quantum and Semiclassical Optics: Journal of the European Optical Society Part B, 8(3), 737.
[22] Mewes, M. O., Andrews, M. R., Kurn, D. M., Durfee, D. S., Townsend, C. G., & Ketterle, W. (1997). Output coupler for Bose-Einstein condensed atoms. Physical Review Letters, 78(4), 582.
[23] Bloch, I., Hänsch, T. W., & Esslinger, T. (1999). Atom laser with a cw output coupler. Physical Review Letters, 82(15), 3008.
[24] Hagley, E. W., Deng, L., Kozuma, M., Wen, J., Helmerson, K., Rolston, S. A., & Phillips, W. D. (1999). A well-collimated quasi-continuous atom laser. Science, 283(5408), 1706-1709.
[25] Le Coq, Y., Thywissen, J. H., Rangwala, S. A., Gerbier, F., Richard, S., Delannoy, G., ... & Aspect, A. (2001). Atom laser divergence. Physical review letters, 87(17), 170403.
[26] Bloch, I., Hansch, T. W., & Esslinger, T. (2001). Atom lasers and phase coherence of atomic Bose gases. RIKEN REVIEW, 6-9.
[27] Cennini, G., Ritt, G., Geckeler, C., & Weitz, M. (2003). All-optical realization of an atom laser. Physical Review Letters, 91(24), 240408.
[28] Guerin, W., Riou, J. F., Gaebler, J. P., Josse, V., Bouyer, P., & Aspect, A. (2006). Guided quasicontinuous atom laser. Physical review letters, 97(20), 200402.
[29] Robins, N. P., Figl, C., Haine, S. A., Morrison, A. K., Jeppesen, M., Hope, J. J., & Close, J. D. (2006). Achieving peak brightness in an atom laser. Physical review letters, 96(14), 140403.
[30] Morinaga, M., Yasuda, M., Kishimoto, T., Shimizu, F., Fujita, J. I., & Matsui, S. (1996). Holographic manipulation of a cold atomic beam. Physical review letters, 77(5), 802.
[31] Sarkar, S., Mangaonkar, J., Vishwakarma, C., & Rapol, U. D. (2018). Diffraction of a CW atom laser in the Raman-Nath regime. arXiv preprint arXiv:1802.01524.
[32] Wright, E. M., Walls, D. F., & Garrison, J. C. (1996). Collapses and revivals of Bose-Einstein condensates formed in small atomic samples. Physical review letters, 77(11), 2158.
[33] Imamoglu, A., Lewenstein, M., & You, L. (1997). Inhibition of coherence in trapped Bose-Einstein condensates. Physical review letters, 78(13), 2511.
[34] Wright, E. M., Wong, T., Collett, M. J., Tan, S. M., & Walls, D. F. (1997). Collapses and revivals in the interference between two Bose-Einstein condensates formed in small atomic samples. Physical Review A, 56(1), 591.
[35] Greiner, M., Mandel, O., Hänsch, T. W., & Bloch, I. (2002). Collapse and revival of the matter wave field of a Bose–Einstein condensate. Nature, 419(6902), 51.
[36] Straatsma, C. J. E., Colussi, V. E., Davis, M. J., Lobser, D. S., Holland, M. J., Anderson, D. Z., ... & Cornell, E. A. (2016). Collapse and revival of the monopole mode of a degenerate Bose gas in an isotropic harmonic trap. Physical Review A, 94(4), 043640.
[37] Kasprzak, J., Richard, M., Kundermann, S., Baas, A., Jeambrun, P., Keeling, J. M. J., ... & Savona, V. (2006). Bose–Einstein condensation of exciton polaritons. Nature, 443(7110), 409.
[38] Jin, D. S., Ensher, J. R., Matthews, M. R., Wieman, C. E., & Cornell, E. A. (1996). Col-lective excitations of a Bose-Einstein condensate in a dilute gas. Physical review letters, 77(3), 420.
[39] Streltsova, O. I., Alon, O. E., Cederbaum, L. S., & Streltsov, A. I. (2014). Generic regimes of quantum many-body dynamics of trapped bosonic systems with strong repulsive interactions. Physical Review A, 89(6), 061602.
[40] Bongs, K., Burger, S., Birkl, G., Sengstock, K., Ertmer, W., Rzazewski, K., ... & Lewen-stein, M. (1999). Coherent evolution of bouncing Bose-Einstein condensates. Physical review letters, 83(18), 3577.
[41] Ott, H., Fortágh, J., Kraft, S., Günther, A., Komma, D., & Zimmermann, C. (2003). Non-linear dynamics of a Bose-Einstein condensate in a magnetic waveguide. Physical review letters, 91(4), 040402.
[42] Streltsov, A. I. (2013). Quantum systems of ultracold bosons with customized interparticle interactions. Physical Review A, 88(4), 041602.
[43] Streltsova, O. I., Alon, O. E., Cederbaum, L. S., & Streltsov, A. I. (2014). Generic regimes of quantum many-body dynamics of trapped bosonic systems with strong repulsive interactions. Physical Review A, 89(6), 061602.
[44] Grimm, R., Weidemüller, M., & Ovchinnikov, Y. B. (2000). Optical dipole traps for neutral atoms. In Advances in atomic, molecular, and optical physics (Vol. 42, pp. 95-170). Academic Press.
 
 
 
 
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