簡易檢索 / 詳目顯示

研究生: 陳俊任
Chen, Jun-Ren
論文名稱: 銣原子與銣分子之超冷碰撞研究
Ultracold collisions of rubidium atoms and molecules
指導教授: 劉怡維
Liu, Yi-Wei
口試委員: 林育如
Lin, Yu-Ju
王立邦
Wang, Li-Bang
余怡德
Yu, Ite A.
蔡錦俊
Cai, Jin-Jun
張銘顯
Chang, Ming-Shien
學位類別: 博士
Doctor
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2016
畢業學年度: 104
語文別: 英文
論文頁數: 153
中文關鍵詞: 玻色愛因斯坦超冷碰撞光結合冷分子磁轉移光偶極阱磁位能阱超冷原子
外文關鍵詞: Bose-Einstein Condensate, ultracold collision, Rubidium, photoassociation, cold molecule, magnetic transfer, optical dipole trap, quadrupole trap, ultracold atom
相關次數: 點閱:3下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 在此論文中,我們利用所謂的光結合法(photo-association)來產生銣分子並發展出一套方法來偵測他們;透過捕捉於光偶極阱中的原子與分子的碰撞,我們得以偵測到這些基態分子的訊號。
    在銣原子(85Rb)磁光陷阱原子團中,透過上述的光結合過程將可以組成激發態的超冷銣分子。 同時,透過所謂的共振耦合效應(resonance coupling effect)將可大幅增加上述已生成的激發態分子自發銳變至基態的數量。這些生成的基態銣分子將同時和磁光陷阱中剩餘未結合的銣原子一併載入一個交叉形式的光偶極阱中。透過光結合過程所產生的基態分子對光偶極阱中的原子團所造成的額外碰撞損耗,將可以用來估計光偶極阱中分子的數目和密度,分別為Nm=44-110×10^3以及nm>5.2×10^11 cm^(-3)。
    為了改善此偵測方法的靈敏度,我們將需要更長的原子團生命期,而此目標可以透過將原子團轉移至另一具備超高真空度的環境來達成。在實驗上,原子在空間上的轉移是透過一個架設在線性磁軌上的磁位能阱來實現。同時,在此超高真空度的環境裡,原子的生命期獲得了顯著的延長,而原子和分子的碰撞效應將因此而較原子與背景殘留氣體的碰撞效應敏感。
    我們實驗系統的許多特性得以透過成功產生銣原子(87Rb)的玻色‧愛因斯坦凝結體(BEC)來檢驗。此實驗裝置的主要配置結合了單一光束的光偶極阱與提供軸向束縛力的微弱磁位能阱。最終,我們的系統產生約由6.3×10^5個原子所組成的BEC。同時,在將來的實驗上此玻色‧愛因斯坦凝結體將用在和應冷卻(sympathetic cooling)鉀原子,鉀分子以及銣分子上。


    This thesis studies the formation of rubidium molecules by photoassociation (PA) method and develops a method for detecting the formed ground state molecules using collisions of atoms and molecules in an optical dipole trap.
    In the magneto-optical trap of 85Rb, ultracold rubidium molecules, in the excited-electronic state, were produced using the photoassociation process. With the help of resonance coupling effect, the number of molecules in the ground-electronic state which decay spontaneously from the excited molecular state can be enhanced. The formed ground state molecules and the remaining atoms in the trap were simultaneously loaded into a crossed optical dipole trap. Addition to the background collision losses, the extra losses of 85Rb atoms due to the photoassociated molecules in the optical trap can then be used to estimate the number and density of molecules in the trap, which is Nm=44-110×10^3以及nm>5.2×10^11 cm^(-3).
    In order to improve the sensitivity of our detecting method, a longer trapping lifetime is needed. It was achieved by transporting atoms to an ultra-high vacuum chamber. In our apparatus, such a transportation of atoms was realized using a magnetic trap settled on a linear motor track. In the ultra-high vacuum chamber, the atomic lifetime is extended signi_cantly, and the collisions between atoms and molecules become more sensitive than the background residual gas collision.
    Several important characteristics of our apparatus was verified by producing the
    Bose-Einstein condensate (BEC) of 87Rb in a hybrid configuration: a single beam optical dipole trap within axial confinement supported by a weak magnetic trap. A pure condensate with 6.3×10^5 atoms are formed in this hybrid trap. This 87Rb BEC can be a refrigerant for the future sympathetic cooling with K, Rb2 and K2.

    1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1 Collision theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 Elastic collision . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 Low energy limit . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.3 Inelastic collisions . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Feshbach resonances . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Photoassociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Photoassociation spectroscopy . . . . . . . . . . . . . . . . . . 14 2.3.2 Born-Oppenheimer approximation . . . . . . . . . . . . . . . . 15 2.3.3 Long range interaction . . . . . . . . . . . . . . . . . . . . . . 19 2.3.4 Spin-orbit interaction . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.5 Movre-Pichier model . . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Magnetic quadrupole trap . . . . . . . . . . . . . . . . . . . . . . . . 22 2.5 Optical dipole trap for neutral atoms . . . . . . . . . . . . . . . . . . 24 2.6 Evaporation cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7 Bose-Einstein condensation . . . . . . . . . . . . . . . . . . . . . . . . 28 2.7.1 Transition temperature and phase-space density . . . . . . . . 29 2.7.2 Condensate fraction . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Experimental setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1 Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.1.1 MOT chamber . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.1.2 Science cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.1 Frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2.2 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2.3 Power amplifier and beam shaping . . . . . . . . . . . . . . . 42 3.3 Optics around the MOT chamber . . . . . . . . . . . . . . . . . . . . 45 3.4 Coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.1 MOT coils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4.2 Balance coils . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.4.3 RF coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.5 MOT characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.6 Magnetic transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.7 Optical dipole trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.8 Detecting systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.8.1 Fluorescence imaging . . . . . . . . . . . . . . . . . . . . . . . 57 3.8.2 Absorption imaging . . . . . . . . . . . . . . . . . . . . . . . . 59 3.9 Experimental control . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.10 Titanium Sapphire laser . . . . . . . . . . . . . . . . . . . . . . . . . 67 4 Two-color spectroscopy by two photon transition of 85Rb; 5D5=2 state . . 69 4.1 Two-color laser transition . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2 Experimental procedure and results . . . . . . . . . . . . . . . . . . . 70 4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5 Ultracold chemistry: from atoms to molecules . . . . . . . . .75 5.1 Photoassociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.2 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.3 Trap-loss signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.3.1 Slow scanning of trap-loss spectroscopy . . . . . . . . . . . . . 81 5.3.2 Step scanning of trap-loss spectroscopy . . . . . . . . . . . . . 83 5.3.3 Collision rate to trap-loss spectroscopy . . . . . . . . . . . . . 83 5.4 Detecting ultracold molecules using atom-molecule collision . . . . . . 85 5.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 5.4.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.4.3 Collision rate and molecular number . . . . . . . . . . . . . . 91 5.4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.5 Dynamics of the photoassociation process . . . . . . . . . . . . . . . . 95 6 Transfer atoms from MOT chamber to the UHV science cell 101 6.1 Magnetic transportation . . . . . . . . . . . . . . . . . . . . . . . . . 101 6.1.1 Loading atoms into the quadrupole trap . . . . . . . . . . . . 102 6.1.2 Transportation of atoms . . . . . . . . . . . . . . . . . . . . . 103 6.1.3 In the science cell . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.2 Loading atoms in the hybrid trap . . . . . . . . . . . . . . . . . . . . 106 6.2.1 RF-evaporative cooling . . . . . . . . . . . . . . . . . . . . . . 108 6.2.2 Majorana loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.2.3 Loading the optical dipole trap . . . . . . . . . . . . . . . . . 113 6.2.4 RF evaporative cooling in the magnetic trap . . . . . . . . . . 114 6.2.5 Hybrid trap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.2.6 Calibration of the imaging system . . . . . . . . . . . . . . . . 120 6.2.7 Alignment of the hybrid trap . . . . . . . . . . . . . . . . . . 122 6.2.8 Trap frequency in the hybrid trap . . . . . . . . . . . . . . . . 123 7 Evaporative cooling in hybrid trap. . . . . . . . . . . . . . . . . . . . . . . .126 7.1 Optical evaporative cooling in a hybrid trap . . . . . . . . . . . . . . 127 7.2 Cooling efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.3 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.3.1 Trajectory of the condensates . . . . . . . . . . . . . . . . . . 132 7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 8 Conclusions and future work. . . . . . . . . . . . . . . . . . . . 136 8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 I Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 A Fundamental constants . . . . . . . . . . . . . . . . . . . . . . . . . .140 B AOM controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 C Analog PI controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

    [1] Weiner, J., Bagnato, V. S., Zilio, S. & Julienne, P. S. Experiments and theory in cold and ultracold collisions. Rev. Mod. Phys. 71, 1{85 (1999).
    [2] Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198{201 (1995).
    [3] Bradley, C. C., Sackett, C. A., Tollett, J. J. & Hulet, R. G. Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett. 75, 1687{1690 (1995).
    [4] Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys.
    Rev. Lett. 75, 3969{3973 (1995).
    [5] Ni, K.-K. et al. A high phase-space-density gas of polar molecules. Science 322, 231{235 (2008).
    [6] Ospelkaus, S. et al. Controlling the hyperfine state of rovibronic ground-state polar molecules. Phys. Rev. Lett. 104, 030402 (2010).
    [7] Weinstein, J. D., deCarvalho, R., Guillet, T., Friedrich, B. & Doyle, J. M. Magnetic trapping of calcium monohydride molecules at millikelvin temperatures. Nature 395, 148 (1998).
    [8] Bethlem, H. L. et al. Electrostatic trapping of ammonia molecules. Nature 406, 491{494 (2000).
    [9] Wynar, R., Freeland, R. S., Han, D. J., Ryu, C. & Heinzen, D. J. Molecules in a Bose-Einstein condensates. Science 287, 1016{1019 (2000).
    [10] McKenzie, C. et al. Photoassociation of sodium in a Bose-Einstein condensates.
    Phys. Rev. Lett. 88, 120403 (2002).
    [11] Donley, E. A., Claussen, N. R., Thompson, S. T. & Wieman, C. E. Atom-molecule coherence in a Bose-Einstein condensate. Nature 417, 529{533 (2002).
    [12] Durr, S., Volz, T., Marte, A. & Rempe, G. Observation of molecules produced from a Bose-Einstein condensate. Phys. Rev. Lett. 92, 020406 (2004).
    [13] Miller, J. D., Cline, R. A. & Heinzen, D. J. Photoassociation spectrum of ultracold rb atoms. Phys. Rev. Lett. 71, 2204{2207 (1993).
    [14] Zahzam, N., Vogt, T., Mudrich, M., Comparat, D. & Pillet, P. Atom-molecule collisions in an optically trapped gas. Phys. Rev. Lett. 96, 023202 (2006).
    [15] Vanhaecke, N., de Souza Melo, W., Laburthe Tolra, B., Comparat, D. & Pillet,
    P. Accumulation of cold cesium molecules via photoassociation in a mixed atomic and molecular trap. Phys. Rev. Lett. 89, 063001 (2002).
    [16] Wang, D. et al. Photoassociative production and trapping of ultracold krb molecules. Phys. Rev. Lett. 93, 243005 (2004).
    [17] Chin, C. et al. Observation of feshbach-like resonances in collisions between ultracold molecules. Phys. Rev. Lett. 94, 123201 (2005).
    [18] Fioretti, A., Lozeille, J., Massa, C., Mazzoni, M. & Gabbanini, C. An optical trap for cold rubidium molecules. Optics Communications 243, 203 { 208
    (2004). Ultra Cold Atoms and Degenerate Quantum Gases.
    [19] Quemener, G. et al. Ultracold quantum dynamics: Spin-polarized K + k2 collisions with three identical bosons or fermions. Phys. Rev. A 71, 032722 (2005).
    [20] Mukaiyama, T., Abo-Shaeer, J. R., Xu, K., Chin, J. K. & Ketterle, W. Dissociation and decay of ultracold sodium molecules. Phys. Rev. Lett. 92, 180402
    (2004).
    [21] Regal, C. A., Greiner, M. & Jin, D. S. Lifetime of molecule-atom mixtures near a feshbach resonance in 40K. Phys. Rev. Lett. 92, 083201 (2004).
    [22] Staanum, P., Kraft, S. D., Lange, J., Wester, R. & Weidemuller, M. Experimental investigation of ultracold atom-molecule collisions. Phys. Rev. Lett. 96, 023201 (2006).
    [23] Fioretti, A. et al. Formation of cold Cs2 molecules through photoassociation. Phys. Rev. Lett. 80, 4402{4405 (1998).
    [24] Wang, D., Eyler, E. E., Gould, P. L. & Stwalley, W. C. State-selective detection of near-dissociation ultracold KRb X1_+ and a3_+molecules. Phys. Rev. A 72, 032502 (2005).
    [25] Takekoshi, T., Patterson, B. M. & Knize, R. J. Observation of optically trapped cold cesium molecules. Phys. Rev. Lett. 81, 5105{5108 (1998).
    [26] Handel, S. Experiments on ultracold quantum gases of 85Rb and 87Rb. Ph.D. thesis, Durham University (2011).
    [27] Lewandowski, H. J., Harber, D. M., Whitaker, D. L. & Cornell, E. A. Simplified system for creating a Bose-Einstein condensate. Journal of Low Temperature Physics 132, 309{367 (2003).
    REFERENCES 147
    [28] Modugno, G. et al. Bose-Einstein condensation of potassium atoms by sympathetic cooling. Science 294, 1320{1322 (2001).
    [29] Campbell, R. L. D. et al. Efficient production of large 39K Bose-Einstein condensates. Phys. Rev. A 82, 063611 (2010).
    [30] Metcalf, H. J. & van der Straten, P. Laser cooling and trapping of atoms. J. Opt. Soc. Am. B 20, 887{908 (2003).
    [31] Julienne, P. S., Mies, F. H., Tiesinga, E. & Williams, C. J. Collisional stability of double Bose-Einstein condensate. Phys. Rev. Lett. 78, 1880{1883 (1997).
    [32] Burt, E. A. et al. Coherence, correlations, and collisions: what one learns about Bose-Einstein condensate from their decay. Phys. Rev. Lett. 79, 337{340 (1997).
    [33] Feshbach, H. Unified theory of nuclear reactions. Annals of Physics 5, 357 { 390 (1958).
    [34] Inouye1, S. et al. Observation of Feshbach resonances in a Bose-Einstein condensate. Nature 392, 151{154 (1998).
    [35] Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225{1286 (2010).
    [36] Krems, R., Friedrich, B. & Stwalley, W. C. Cold Molecules: Theory, Experiment, Applications (CRC Press, 2009).
    [37] Moerdijk, A. J., Verhaar, B. J. & Axelsson, A. Resonances in ultracold collisions of 6Li, 7Li, and 23Na. Phys. Rev. A 51, 4852{4861 (1995).
    [38] Jones, K. M., Tiesinga, E., Lett, P. D. & Julienne, P. S. Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering. Rev Mod Phys 78, 1041{1041 (2006).
    [39] Huang, Y. Production, detection and trapping of ultracold molecular rubidium. Ph.D. thesis, University of Connecticut (2006).
    [40] Ji, B., Tsai, C.-C. & Stwalley, W. C. Proposed modification of the criterion for the region of validity of the inverse-power expansion in diatomic long-range potentials. Chemical Physics Letters 236, 242 { 246 (1995).
    [41] Movre, M. & Pichler, G. Resonance interaction and self-broadening of alkali resonance lines. i. adiabatic potential curves. Journal of Physics B: Atomic and Molecular Physics 10, 2631 (1977).
    [42] Stwalley, W. C., Uang, Y.-H. & Pichler, G. Pure long-range molecules. Phys.
    Rev. Lett. 41, 1164{1167 (1978).
    [43] Wang, H., Gould, P. L. & Stwalley, W. C. Long-range interaction of the 39k(4s)+39k(4p) asymptote by photoassociative spectroscopy. i. the 0g pure long-range state and the long-range potential constants. The Journal of Chemical Physics 106, 7899{7912 (1997).
    [44] Miller, J. D. Photoassociation of Ultracold Rb Atoms in a Far Off Resonance Optical Dipole Trap. Ph.D. thesis, University of Texas at Austin (1994).
    [45] Kitson, H. Experiments on Ultracold Rb: Rydberg atoms and Rb2 molecules. Ph.D. thesis, Swinburne University of Technology (2006).
    [46] Paul, W. Electromagnetic traps for charged and neutral particles. Rev. Mod. Phys. 62, 531{540 (1990).
    [47] Migdall, A. L., Prodan, J. V., Phillips, W. D., Bergeman, T. H. & Metcalf, H. J. First observation of magnetically trapped neutral atoms. Phys. Rev. Lett. 54, 2596{2599 (1985).
    [48] Raab, E. L., Prentiss, M., Cable, A., Chu, S. & Pritchard, D. E. Trapping of neutral sodium atoms with radiation pressure. Phys. Rev. Lett. 59, 2631{2634
    (1987).
    [49] Chu, S., Bjorkholm, J. E., Ashkin, A. & Cable, A. Experimental observation of optically trapped atoms. Phys. Rev. Lett. 57, 314{317 (1986).
    [50] Grimm, R., Weidemller, M. & Ovchinnikov, Y. B. Optical dipole traps forneutral atoms. Advances In Atomic, Molecular, and Optical Physics 42, 95 {170 (2000).
    [51] Safronova, M. S., Arora, B. & Clark, C. W. Frequency-dependent polarizabilities of alkali-metal atoms from ultraviolet through infrared spectral regions. Phys. Rev. A 73, 022505 (2006).
    [52] Ozeri, R., Khaykovich, L. & Davidson, N. Long spin relaxation times in a single-beam blue-detuned optical trap. Phys. Rev. A 59, R1750{R1753 (1999).
    [53] Boiron, D. et al. Cold and dense cesium clouds in far-detuned dipole traps.
    Phys. Rev. A 57, R4106{R4109 (1998).
    [54] Hess, H. F. Evaporative cooling of magnetically trapped and compressed spinpolarized hydrogen. Phys. Rev. B 34, 3476{3479 (1986).
    [55] Davis, K. B., Mewes, M. O., Joffe, M. A. & Ketterle, W. In Fourteenth International Conference on Atomic Physics, Boulder Colorado (1994, Book of Abstracts, 1M-3).
    [56] Petrich, W., Anderson, M. H., Ensher, J. R. & Cornell, E. A. In Fourteenth
    International Conference on Atomic Physics, Boulder Colorado (1994, Book of Abstracts, 1M-7).
    [57] Davis, K. B., Mewes, M. O., Joffe, M. A., Andrews, M. R. & Ketterle, W. Evaporative cooling of sodium atoms. Phys. Rev. Lett. 74, 5202{5205 (1995).
    [58] Olson, A. J., Niffenegger, R. J. & Chen, Y. P. Optimizing the efficiency of evaporative cooling in optical dipole traps. Phys. Rev. A 87, 053613 (2013).
    [59] Barrett, M. D., Sauer, J. A. & Chapman, M. S. All-optical formation of an atomic Bose-Einstein condensate. Phys. Rev. Lett. 87, 010404 (2001).
    [60] Bose, S. N. Planck's law and light quantum hypothesis. Z. Phys. 26, 178 (1924).
    [61] Einstein, A. Quantentheorie des einatomigen idealen gases. Sitzungsber. Kgl.
    Preuss. Akad. Wiss 261 (1924).
    [62] Pethick, C. J. & Smith, H. Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, 2008), second edn. Cambridge Books Online.
    [63] Papp, S. B. & of Colorado at Boulder. Physics, U. Experiments with a two- species Bose-Einstein condensate utilizing widely tunable interparticle interac- tions. Ph.D. thesis, University of Colorado at Boulder (2007).
    [64] Nyman, R. A. et al. Tapered-ampliflied antireection-coated laser diodes for
    potassium and rubidium atomic-physics experiments. Review of Scientific Instruments 77, { (2006).
    [65] Harsono, A. Dipole trapping and manipulation of ultra-cold atoms. Ph.D. thesis, University of Oxford (2006).
    [66] Kao, C.-Y. Interactions between light and ultracold 85Rb atoms. Ph.D. thesis, National Tsing Hua University (2010).
    [67] Steck, D. A. Rubidium 87 d line data. http://steck.us/alkalidata (2008).
    [68] Chen, J.-R., Kao, C.-Y., Chen, H.-B. & Liu, Y.-W. Detecting high-density
    ultracold molecules using atommolecule collision. New Journal of Physics 15, 043035 (2013).
    [69] Snadden, M. J., Bell, A., Riis, E. & Ferguson, A. Two-photon spectroscopy of laser-cooled Rb using a mode-locked laser. Optics Communications 125, 70 {76 (1996).
    [70] van Rooij, R. et al. Frequency metrology in quantum degenerate helium: Direct measurement of the 23S1 ! 21S0 transition. Science 333, 196{198 (2011).
    [71] Lukin, M. D. & Hemmer, P. R. Quantum entanglement via optical control of atom-atom interactions. Phys. Rev. Lett. 84, 2818{2821 (2000).
    [72] Jaksch, D. et al. Fast quantum gates for neutral atoms. Phys. Rev. Lett. 85, 2208{2211 (2000).
    [73] Saffman, M., Walker, T. G. & Molmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313{2363 (2010).
    [74] Isenhower, L. et al. Demonstration of a neutral atom controlled-not quantum gate. Phys. Rev. Lett. 104, 010503 (2010).
    [75] Fahey, D. P. & Noel, M. W. Excitation of Rydberg states in rubidium with near infrared diode lasers. Opt. Express 19, 17002{17012 (2011).
    [76] Viteau, M. et al. Rydberg spectroscopy of a Rb mot in the presence of applied or ion created electric fields. Opt. Express 19, 6007{6019 (2011).
    [77] Pillet, P. et al. Photoassociation in a gas of cold alkali atoms: I. perturbative quantum approach. Journal of Physics B: Atomic, Molecular and Optical Physics 30, 2801 (1997).
    [78] Drag, C. et al. Experimental versus theoretical rates for photoassociation and for formation of ultracold molecules. Quantum Electronics, IEEE Journal of 36, 1378{1388 (2000).
    [79] Wang, H., Gould, P. L. & Stwalley, W. C. Photoassociative spectroscopy of
    ultracold 39K atoms in a high-density vapor-cell magneto-optical trap. Phys.
    Rev. A 53, R1216{R1219 (1996).
    [80] Jones, K. M., Tiesinga, E., Lett, P. D. & Julienne, P. S. Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering. Rev. Mod. Phys. 78, 483{535 (2006).
    [81] Huang, Y. et al. Formation, detection and spectroscopy of ultracold Rb2 in the ground X1_+g state. J Phys B-At Mol Opt 39, S857{S869 (2006).
    [82] Napolitano, R., Weiner, J., Williams, C. J. & Julienne, P. S. Line shapes of high resolution photoassociation spectra of optically cooled atoms. Phys. Rev. Lett. 73, 1352{1355 (1994).
    [83] Cline, R. A., Miller, J. D. & Heinzen, D. J. Study of Rb2 long-range states by high-resolution photoassociation spectroscopy. Phys. Rev. Lett. 73, 632{635
    (1994).
    [84] Krems, R. V., Friedrich, B. & Stwalley, W. C. (eds.) Cold Molecules: Theory, Experiment, Applications (CRC Press, Boca Roton, 2009).
    [85] Kohler, T., Goral, K. & Julienne, P. Production of cold molecules via magnetically tunable Feshbach resonances. Rev Mod Phys 78, 1311{1361 (2006).
    [86] Dion, C. et al. Resonant coupling in the formation of ultracold ground state molecules via photoassociation. Phys. Rev. Lett. 86, 2253{2256 (2001).
    [87] Pechkis, H. et al. Enhancement of the formation of ultracold 85Rb2 molecules due to resonant coupling. Phys. Rev. A 76, 022504 (2007).
    [88] Abraham, E. R. I., McAlexander, W. I., Sackett, C. A. & Hulet, R. G. Spectroscopic determination of the s-wave scattering length of lithium. Phys. Rev. Lett. 74, 1315{1318 (1995).
    [89] Stwalley, W. C. & Wang, H. Photoassociation of ultracold atoms: A new spectroscopic technique. J. Mol. Spectrosc. 195, 194{228 (1999).
    [90] Kerman, A. J., Sage, J. M., Sainis, S., Bergeman, T. & DeMille, D. Production of Ultracold, Polar RbCs* Molecules via Photoassociation. Phys. Rev. Lett. 92, 033004 (2004).
    [91] Wester, R. et al. Photoassociation inside an optical dipole trap: absolute rate
    coefficients and Franck-Condon factors. Appl. Phys. B 79, 993{999 (2004).
    [92] Moal, S., Portier* M., Kim, J., Arimondo, E. & Leduc, M. Mechanical effect of photoassociation for ultracold metastable helium atoms: A new method to measure the scattering length. Europhys. Lett. 83, 23001 (2008).
    [93] Wang, D. et al. Direct absorption imaging of ultracold polar molecules. Phys.
    Rev. A 81, 061404(R) (2010).
    [94] Mukaiyama, T., Abo-Shaeer, J. R., Xu, K., Chin, J. K. & Ketterle, W. Dissociation and decay of ultracold sodium molecules. Phys. Rev. Lett. 92, 180402
    (2004).
    [95] Menegatti, C. R., Marangoni, B. S. & Marcassa, L. G. Observation of cold Rb2 molecules trapped in an optical dipole trap using a laser-pulse-train technique. Phys. Rev. A 84, 053405 (2011).
    [96] Fioretti, A., Lozeille, J., Massa, C. A., Mazzoni, M. & Gabbanini, C. An optical trap for cold rubidium molecules. Opt. Comm. 243, 203{208 (2004).
    [97] Hudson, E. R., Gilfoy, N. B., Kotochigova, S., Sage, J. M. & DeMille, D. Inelastic collisions of ultracold heteronuclear molecules in an optical trap. Phys.
    Rev. Lett. 100, 203201 (2008).
    [98] Cvitas, M. T., Soldan, P., Hutson, J. M., Honvault, P. & Launay, J. M. Ultracold
    Li+Li2 collisions: Bosonic and fermionic cases. Phys. Rev. Lett. 94, 033201
    (2005).
    [99] Viteau, M. et al. Optical pumping and vibrational cooling of molecules. Science 321, 232{234 (2008).
    [100] Sofikitis, D. et al. Vibrational cooling of cesium molecules using noncoherent broadband light. Phys. Rev. A 80, 051401 (2009).
    [101] Shapiro, E., Shapiro, M., Pe'er, A. & Ye, J. Photoassociation adiabatic passage of ultracold Rb atoms to form ultracold Rb2 molecules. Phys. Rev. A 75, 013405
    (2007).
    [102] Aikawa, K. et al. Coherent transfer of photoassociated molecules into the rovibrational ground state. Phys. Rev. Lett. 105, 203001 (2010).
    [103] Andrews, M. R. et al. Direct, nondestructive observation of a bose condensate. Science 273, 84{87 (1996).
    [104] Kadlecek, S., Sebby, J., Newell, R. & Walker, T. G. Nondestructive spatial heterodyne imaging of cold atoms. Opt. Lett. 26, 137{139 (2001).
    [105] Knoop, S. et al. Magnetically controlled exchange process in an ultracold atomdimer mixture. Phys. Rev. Lett. 104, 053201 (2010).
    [106] Knoop, S. et al. Observation of an Efimov-like trimer resonance in ultracold atom-dimer scattering. Nature Phys 5, 227{230 (2009).
    [107] Ospelkaus, S. et al. Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules. Science 327, 853{857 (2010).
    [108] Thorsheim, H. R., Weiner, J. & Julienne, P. S. Laser-induced photoassociation of ultracold sodium atoms. Phys. Rev. Lett. 58, 2420{2423 (1987).
    [109] Ciury lo, R., Tiesinga, E., Kotochigova, S. & Julienne, P. S. Photoassociation spectroscopy of cold alkaline-earth-metal atoms near the intercombination line. Phys. Rev. A 70, 062710 (2004).
    [110] Petrich, W., Anderson, M. H., Ensher, J. R. & Cornell, E. A. Stable, tightly
    confining magnetic trap for evaporative cooling of neutral atoms. Phys. Rev. Lett. 74, 3352{3355 (1995).
    [111] Esslinger, T., Bloch, I. & Hansch, T. W. Bose-Einstein condensation in a quadrupole-ioffe-configuration trap. Phys. Rev. A 58, R2664{R2667 (1998).
    [112] Dubessy, R. et al. Rubidium-87 Bose-Einstein condensate in an optically plugged quadrupole trap. Phys. Rev. A 85, 013643 (2012).
    [113] Lin, Y.-J., Perry, A. R., Compton, R. L., Spielman, I. B. & Porto, J. V. Rapid production of 87Rb Bose-Einstein condensates in a combined magnetic and optical potential. Phys. Rev. A 79, 063631 (2009).
    [114] Zaiser, M. et al. Simple method for generating Bose-Einstein condensates in a weak hybrid trap. Phys. Rev. A 83, 035601 (2011).
    [115] Gericke, T., Wrtz, P., Reitz, D., Utfeld, C. & Ott, H. All-optical formation of a Bose-Einstein condensate for applications in scanning electron microscopy. Applied Physics B 89, 447{451 (2007).
    [116] Friebel, S., D'Andrea, C., Walz, J., Weitz, M. & Hansch, T. W. CO2-laser optical lattice with cold rubidium atoms. Phys. Rev. A 57, R20{R23 (1998).
    [117] Landau, L. & Lifshitz, E. Mechanics. Butterworth Heinemann (Butterworth- Heinemann, 1976).
    [118] Stamper-Kurn, D. M. et al. Optical confinement of a Bose-Einstein condensate. Phys. Rev. Lett. 80, 2027{2030 (1998).
    [119] Mewes, M.-O. et al. Bose-Einstein condensation in a tightly confining dc magnetic trap. Phys. Rev. Lett. 77, 416{419 (1996).
    [120] Miesner, H.-J. et al. Observation of metastable states in spinor Bose-Einstein condensates. Phys. Rev. Lett. 82, 2228{2231 (1999).
    [121] Anderson, B. P. & Kasevich, M. A. Macroscopic quantum interference from atomic tunnel arrays. Science 282, 1686{1689 (1998).
    [122] Adams, C. S., Lee, H. J., Davidson, N., Kasevich, M. & Chu, S. Evaporative cooling in a crossed dipole trap. Phys. Rev. Lett. 74, 3577{3580 (1995).
    [123] Lauber, T., Kuber, J., Wille, O. & Birkl, G. Optimized Bose-Einstein condensate production in a dipole trap based on a 1070-nm multifrequency laser:
    Inuence of enhanced two-body loss on the evaporation process. Phys. Rev. A 84, 043641 (2011).
    [124] Hung, C.-L., Zhang, X., Gemelke, N. & Chin, C. Accelerating evaporative cooling of atoms into Bose-Einstein condensation in optical traps. Phys. Rev. A 78, 011604 (2008).
    [125] Clement, J.-F. et al. All-optical runaway evaporation to Bose-Einstein condensation. Phys. Rev. A 79, 061406 (2009).
    [126] Lye, J. E., Fletcher, C. S., Kallmann, U., Bachor, H.-A. & Close, J. D. Images of evaporative cooling to Bose-Einstein condensation. Journal of Optics B: Quantum and Semiclassical Optics 4, 57 (2002).
    [127] Henn, E. A. L. et al. Bose-Einstein condensation in 87Rb: characterization of the Brazilian experiment. Brazilian Journal of Physics 38, 279 { 286 (2008).
    [128] Castin, Y. & Dum, R. Bose-Einstein condensate in time dependent traps. Phys.
    Rev. Lett. 77, 5315{5319 (1996).
    [129] Giovanazzi, S. et al. Expansion dynamics of a dipolar Bose-Einstein condensate. Phys. Rev. A 74, 013621 (2006).
    [130] Dutta, S., Lorenz, J., Altaf, A., Elliott, D. S. & Chen, Y. P. Photoassociation of ultracold LiRb* molecules: Observation of high effciency and unitarity-limited rate saturation. Phys. Rev. A 89, 020702 (2014).

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE