Rb冷原子在磁光阱和磁阱中的碰撞截面
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摘要
激光冷却与囚禁技术的发展,为原子、分子与光物理的研究打开了新的篇章。超冷原子碰撞作为冷原子物理研究中的前沿课题之一受到了人们极大的关注。在超冷原子碰撞中,原子的碰撞截面研究是一个热门的研究课题。粒子的碰撞截面的大小反映了粒子发生碰撞的可能性大小。通过研究粒子的碰撞截面,可以获得原子冷却及BEC实验中被捕获粒子的数目、粒子的损失率、粒子的两体及多体碰撞参数、冷原子势阱深度等重要信息,对超冷原子物理研究有十分重要的作用。本论文旨在研究磁光阱与磁阱中超冷Rb原子与背景气体(Ar, He)碰撞实验过程,提出一种测量冷原子碰撞截面的新技术。对Rb冷原子与背景气体碰撞展开实验及理论研究。论文的主要研究内容如下:
提出在磁光阱和磁阱中利用超冷87Rb原子与室温下背景气体40Ar碰撞测量完全碰撞截面的新技术。利用该技术在磁光阱及磁阱中可以精确测量不同背景气体密度下的超冷Rb原子的损失率、碰撞截面。可以将此技术作为标准方法测量超冷原子的碰撞截面。磁光阱与磁阱的系统的是实现碰撞截面测量实验重要的环节。实验装置包括真空系统、激光器系统及激光稳频系统和Rb冷原子源三个主要组成部分。实验中通过计算机软件控制来实现冷却激光的打开或关闭,简单的实现磁光阱与磁阱的切换。
利用冷原子碰撞截面测量技术,在磁光阱及磁阱中,对Rb原子两种同位素85Rb和87Rb与惰性气体Ar与He碰撞进行研究。实验研究发现,Rb冷原子与惰性气体的碰撞损失率、碰撞截面在磁光阱与磁阱中有很大差别。利用原子碰撞物理学理论,通过分步法拟合法计算碰撞截面、平均速度损失率与L-J势函数系数、势阱深度、碰撞速度、碰撞能量等参量的演化关系;通过理论计算与实验测量的碰撞截面、平均速度损失率值比较,发现理论与实验值基本吻合,并给出理论计算的碰撞截面、平均速度损失率与势阱深度的关系,可以得到由于实验磁场条件限制不能达到势阱深度下的碰撞截面或平均速度损失率值。
利用理论计算平均速度损失率与势阱深度的关系,提出利用磁光阱与磁阱中87Rb冷原子与室温40Ar背景气体之间碰撞测量势阱深度的新方法。与在光阱利用激光催化测量Rb冷原子确定势阱深度的方法相比,该方法操作更简单,只需要测量Rb原子与背景气体之间一阶碰撞损失率Γ,避免测量冷原子间碰撞损失率β时对原子密度要求较高的影响,测量原子密度很低条件下的势阱深度;该方法可以在磁光阱及磁阱中测量势阱深度,扩大了势阱深度测量范围。
最后,腔量子电动力学是冷原子物理的前沿领域。研究了k光子Jaynes-Cummings腔QED模型与运动原子相互作用中的熵相互关系及纠缠特性。发现原子与光场之间具有熵交换特性。讨论了原子运动、光子数和场模结构等因素对原子与光场熵相互关系的影响。此外,讨论了原子与场系统熵交换与纠缠之间的关系。
Ultracold atomic collisional physics is a promsing field in ultracold physics, scientists play more and more attention to this area because it is significant and has the possibility of broad applications in future. The atom collisional cross section is a more popular research topic in the field of ultracold atom collision physics. In nuclear and particle physics, the concept of cross section is used to express the likelihood of interaction between particles. The informations of the trapped atom numbers of laser cooling or BEC experiments, particle loss rate, collision parameters, trap depth of cold atoms can be achieved by measured collision cross section of cold atoms. It is very important to the research on ultracold atomic physics. In this dissertation, we study the experiments of ultracold Rb atom collided with background Ar or He gas using magneto-optic and magnetic traps. A new technique to measure collision loss rate and absolute collision cross sections is proposed. An overview of both experimental and theoretical results for the case of trapped Rb and background argon or helium gas will be given. The research work has been summarized in detail as follows.
We present a new technique to measure the absolute total collision cross sections for a room-temperature background gas of 40Ar using laser cooled 87Rb atoms confined in either a magneto-optic or a magnetic quadrupole trap. By using this method, loss rate of trapped atoms and the total cross section can be accurately achieved from knowledge of the background gas density. This technique can be a normative method to acquire collision cross sections of ultracold atoms with other background gases in the further work. Building up the MOT and magnetic trap is the most important task in this experiment work. Three requisite instruments are involved in this experiment, which are vacuum system, laser light systems and Rb injection system. Using software control system can turn on and off lasers to simply transfer MOT to magnetic trap.
By using this new technique, we measure 85Rb or 87Rb collided with room-temperature background rgon or helium gas in the MOT and magnetic trap. The loss rates from the magneto-optic trap (MOT) and the pure magnetic trap are compared and show significant differences. The initial discussion focuses on a theoretical overview of the principles involved in atom collisional physics fields. Finally, an overview of both experimental and theoretical results including cross sections and loss rates for the case of trapped 85Rb or 87Rb and background Ar or He gas will be given. These results suggest that this theory may be a better tool for measuring total elastic collision cross section on arbitrary trap depth.
Then, we present a new method for determining the trap depth of an atomic or molecular trap of any type and any depth. This method relies on measurements of the trap loss rate induced by elastic collisions of ultracold 87Rb atoms with room temperature background 40Ar gases. We compare this method with an independent technique that relies on measurements of atom loss rates during optical excitation of colliding pairs to a repulsive molecular state. The main advantage of the method presented here is its simplicity and applicability to traps of any type requiring only knowledge of the background gas pressure between the trapped particles and the background gas particles. Another advantage is that the technique is applicable to any type of traps, including the optical and magnetic traps, and at extremely low densities where intra-trap collisions are rare.
Finally, cavity quantum electrodynamics is a promising research field of the cold atom physics. The entropy correlation and entanglement of a moving atom interacting with k-photon Jaynes-Cummings model are investigated. Entropy exchange, which is a form of anti-correlated behavior between atomic and field subsystems, is explored. Analytical results represents that the atomic motion, transition number k of field and field-mode structure show some influence on entropy exchange. Moreover, the relationship between entropy correlations and entanglement is also discussed.
提出在磁光阱和磁阱中利用超冷87Rb原子与室温下背景气体40Ar碰撞测量完全碰撞截面的新技术。利用该技术在磁光阱及磁阱中可以精确测量不同背景气体密度下的超冷Rb原子的损失率、碰撞截面。可以将此技术作为标准方法测量超冷原子的碰撞截面。磁光阱与磁阱的系统的是实现碰撞截面测量实验重要的环节。实验装置包括真空系统、激光器系统及激光稳频系统和Rb冷原子源三个主要组成部分。实验中通过计算机软件控制来实现冷却激光的打开或关闭,简单的实现磁光阱与磁阱的切换。
利用冷原子碰撞截面测量技术,在磁光阱及磁阱中,对Rb原子两种同位素85Rb和87Rb与惰性气体Ar与He碰撞进行研究。实验研究发现,Rb冷原子与惰性气体的碰撞损失率、碰撞截面在磁光阱与磁阱中有很大差别。利用原子碰撞物理学理论,通过分步法拟合法计算碰撞截面、平均速度损失率与L-J势函数系数、势阱深度、碰撞速度、碰撞能量等参量的演化关系;通过理论计算与实验测量的碰撞截面、平均速度损失率值比较,发现理论与实验值基本吻合,并给出理论计算的碰撞截面、平均速度损失率与势阱深度的关系,可以得到由于实验磁场条件限制不能达到势阱深度下的碰撞截面或平均速度损失率值。
利用理论计算平均速度损失率与势阱深度的关系,提出利用磁光阱与磁阱中87Rb冷原子与室温40Ar背景气体之间碰撞测量势阱深度的新方法。与在光阱利用激光催化测量Rb冷原子确定势阱深度的方法相比,该方法操作更简单,只需要测量Rb原子与背景气体之间一阶碰撞损失率Γ,避免测量冷原子间碰撞损失率β时对原子密度要求较高的影响,测量原子密度很低条件下的势阱深度;该方法可以在磁光阱及磁阱中测量势阱深度,扩大了势阱深度测量范围。
最后,腔量子电动力学是冷原子物理的前沿领域。研究了k光子Jaynes-Cummings腔QED模型与运动原子相互作用中的熵相互关系及纠缠特性。发现原子与光场之间具有熵交换特性。讨论了原子运动、光子数和场模结构等因素对原子与光场熵相互关系的影响。此外,讨论了原子与场系统熵交换与纠缠之间的关系。
Ultracold atomic collisional physics is a promsing field in ultracold physics, scientists play more and more attention to this area because it is significant and has the possibility of broad applications in future. The atom collisional cross section is a more popular research topic in the field of ultracold atom collision physics. In nuclear and particle physics, the concept of cross section is used to express the likelihood of interaction between particles. The informations of the trapped atom numbers of laser cooling or BEC experiments, particle loss rate, collision parameters, trap depth of cold atoms can be achieved by measured collision cross section of cold atoms. It is very important to the research on ultracold atomic physics. In this dissertation, we study the experiments of ultracold Rb atom collided with background Ar or He gas using magneto-optic and magnetic traps. A new technique to measure collision loss rate and absolute collision cross sections is proposed. An overview of both experimental and theoretical results for the case of trapped Rb and background argon or helium gas will be given. The research work has been summarized in detail as follows.
We present a new technique to measure the absolute total collision cross sections for a room-temperature background gas of 40Ar using laser cooled 87Rb atoms confined in either a magneto-optic or a magnetic quadrupole trap. By using this method, loss rate of trapped atoms and the total cross section can be accurately achieved from knowledge of the background gas density. This technique can be a normative method to acquire collision cross sections of ultracold atoms with other background gases in the further work. Building up the MOT and magnetic trap is the most important task in this experiment work. Three requisite instruments are involved in this experiment, which are vacuum system, laser light systems and Rb injection system. Using software control system can turn on and off lasers to simply transfer MOT to magnetic trap.
By using this new technique, we measure 85Rb or 87Rb collided with room-temperature background rgon or helium gas in the MOT and magnetic trap. The loss rates from the magneto-optic trap (MOT) and the pure magnetic trap are compared and show significant differences. The initial discussion focuses on a theoretical overview of the principles involved in atom collisional physics fields. Finally, an overview of both experimental and theoretical results including cross sections and loss rates for the case of trapped 85Rb or 87Rb and background Ar or He gas will be given. These results suggest that this theory may be a better tool for measuring total elastic collision cross section on arbitrary trap depth.
Then, we present a new method for determining the trap depth of an atomic or molecular trap of any type and any depth. This method relies on measurements of the trap loss rate induced by elastic collisions of ultracold 87Rb atoms with room temperature background 40Ar gases. We compare this method with an independent technique that relies on measurements of atom loss rates during optical excitation of colliding pairs to a repulsive molecular state. The main advantage of the method presented here is its simplicity and applicability to traps of any type requiring only knowledge of the background gas pressure between the trapped particles and the background gas particles. Another advantage is that the technique is applicable to any type of traps, including the optical and magnetic traps, and at extremely low densities where intra-trap collisions are rare.
Finally, cavity quantum electrodynamics is a promising research field of the cold atom physics. The entropy correlation and entanglement of a moving atom interacting with k-photon Jaynes-Cummings model are investigated. Entropy exchange, which is a form of anti-correlated behavior between atomic and field subsystems, is explored. Analytical results represents that the atomic motion, transition number k of field and field-mode structure show some influence on entropy exchange. Moreover, the relationship between entropy correlations and entanglement is also discussed.
引文
[1] Chu S, Pretiss M, Bjorkholm J, and Cable A. Laser Spectroscopy VIII[C]. Springer-Verlag, Berlin. 1987: 58.
[2] Souominen K -A, Burnett K, and Julienne P S. Role of Off-resonant Excitation in Cold Collisions in a Ctrong Laser Field[J]. Phys. Rev. A, 1996, 53(3): R1220-R1223.
[3] Souominen K -A, Burnett K, and Julienne P S. Ultracold Collision and Optical Shielding in Metastable Xenon[J]. Phys. Rev. A, 1996, 53(3): 1678-1689.
[4] Weiner J, Bagnato V S, Zillo S, and Julienne P S. Experiments and Theory in Cold and Ultracold Collisions[J]. Rev. Mod. Phys., 1999, 71: 1-85.
[5] Chu S, Bjorkholm J E, Ashkin A, and Cable A. Experimental observation of optically trapped atoms. Phys. Rev. Lett., 1986, 57(3): 314-318.
[6] Ranb E, Prenlis M, Cable A, Chu S, and Pritchard D. Trapping of Neutral Sodium Atoms with Radiation Pressure. Phys. Rev. Lett., 1987, 59(23): 2631-2634.
[7] Lin Z, Shimizu K, Zhan M S, Shimizu F, and Takuma H. Laser Cooling and Trapping of Li[J]. Jap. J. of Appl. Phys., 1991, 30(7B): L1324-L1326.
[8]王育竹,刘勋铭,林岳明,周善钰,霍芸生,徐信业,蔡惟泉,李佛生,洪涛.一种新型的钠原子磁光陷阱(MOT) [J].中国激光, 1996, 23: 448-451.
[9] Gan J H, Li Y M, Chen X Z, Liu H F, Yang D H, and Wang Y Q. Magneto-Optical Trap of Cesium Atoms[J]. Chin Phys. Lett., 1996, 13(11): 821-824.
[10]王义遒.原子的激光冷却与捕陷[J].物理. 1990, 19: 389-449.
[11] Hess H F. Evaporative Cooling of Magnetically Trapped and Compressed spin- polarized hydrogen[J]. Phys. Rev. B, 1986, 34(5): 3476-3479.
[12] Anderson M H, Ensher J R, Matthews M R, Wieman C E, and Cornell E A. Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor[J]. Science, 1995, 269(5221): 198-201.
[13] Chu S, and Wieman C E. Laser Cooling and Trapping of Atoms[J]. J. Opt. Soc. Am. B, 1989, 6(11): 2020-2020.
[14] Bradley C C, Sackett C A, Tollett J J, and Hulet R G. Evidence of Bose-Eintein Condensation in an Atomic Gas with Attractive Interactions[J]. Phys. Rev. Lett., 1995, 75(9): 1687-1690.
[15] Bradley C, Sackett C A, and Hulet R G. Bose-Einstein Condensation ofLithium: Observation of Limited Condens Number[J]. Phys. Rev. Lett., 1997, 78(6): 985-989.
[16] Davis B, Mewes M -O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, and Ketterle W. Bose-Einstein Condensation in a Gas of Sodium Atoms[J]. Phys. Rev. Lett., 1995, 75(22): 3969-3973.
[17] Mewes M -O, Andrews M R, van Druten N J, Kurn D M, Durfee D S, and Ketterle W. Bose-Einstein Condensation in a Tightly Confining DC Magnetic Trap[J], Phys. Rev. Lett., 1996, 77(3): 416-419.
[18] Kestenbaum D. Hydrogen Coaxed into Quantum Condensate[J]. Science, 1998, 281(5375): 321-321.
[19] Bagnato V, Pritchard D E, and Kleppner D. Bose-Einstein Condensation in an External Potential[J]. Phys. Rev. A., 1987, 35(10): 4354-4358.
[20] DeMarco B, and Jin D S. Onset of Fermi Degeneracy in a Trapped Atomic Gas[J]. Science, 1999, 285(5434): 1703-1706.
[21] Truscott A G, Strecker K E, McAlexander W I, Partridge G B, and Hulet R G. Observation of Fermi Pressure in a Gas of Trapped Atoms[J]. Science, 2001, 291(5513): 2570-2572.
[22] Schreck F, Khaykovich L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, and Salomon C. Quasipure Bose-Einstein Condensate Immersed in a Fermi Sea[J]. Phys. Rev. Lett., 2001, 87(8): 080403.
[23] Granade S R, Gehm M E, O’Hara K M, and Tomas J E. All-optical Production of a Degenerate Fermi Gas[J]. Phys. Rev. Lett., 2002, 88(12): 120405.
[24] Hadzibabic Z, Stan C A, Dieckmann K, Gupta S, Zwierlein M W, G?rliz A, and Ketterle W. Two Species Mixture of Quantum Degenerate Bose and Fermi Gases[J]. Phys. Rev. Lett., 2002, 88(16): 160401.
[25] Jochim S, Bartenstein M, Altmeyer A, Hendl G, Chin C, Denschlag J H, Grimm R. Bose-Einstein Condensation of Molecules[J]. Science, 2003, 302(5653): 2101-2103.
[26] Regal C A, Tickner C, Bohn J L, and Jin D S. Creation of Ultracold Molecules from a Fermi Gas of Atoms[J]. Nature, 2003, 424(6944): 47-50.
[27] Cubizolles J, Bourdel T, Kokkelmans S, Shlyapnikov G V, and Salomon C. Production of Long-lived Ultracold Li2 Molecules from a Fermi Gas[J]. Phys. Rev. Lett., 2003, 91(24): 240401.
[28] Kohl M, Moritz H, Stoferle T. Fermionic Atoms in a Three Dimensional Optical Lattice: Observing Fermi Surfaces, Dynamics, and Interactions[J]. Phys. Rev. Lett., 2005, 94: 080403.
[29] Silber C, Gunther S, Marzok C, Deh B, Courteille P W, and Zimmermann C. Quantum-degenerate Mixture of Fermionic Lithium and Boseonic Rubidium Gases[J]. Phys. Rev. Lett., 2005, 95(17): 170408.
[30] Ospelkaus C, Ospekaus S, Sengetock K, and Bongs K. Interaction-driven Dynamics of 40K-87Rb Fermion-Boson Gas Mixture in the Large-particle- number Limit[J]. Phys. Rev. Lett., 2006, 96(2): 020401.
[31] Aubin S, Myrskog S, Extavour M H T, S. Myrskog, Leblanc L J, Esteve J, Singh S, Scrutton P, Mckay D, McKenzie R, Lerous I D, Stummer A, and Thywissen J H. Trapping Fermionic 40K and Bosonic 87Rb on a Chip[J]. J. Low Temp. Phys., 2006, 140(5): 377-396.
[32] Fukuhara T, Takasu Y, Kumakura M, and Takahashi Y. Degenerate Fermi Gases of Ytterbium[J]. Phys. Rev. Lett., 2007, 98(3): 030401.
[33] McNamara J M, Jeltes T, Tychkov A S, Hogervorst W, and Vassen W. Degenerate Bose-Fermi Mixture of Metastable Atoms. Phys. Rev. Lett., 2006, 97(8): 080404.
[34] Goldwin J M. Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture[D]. Ph.D Thesis of University of Colorado, 2005, 103-114.
[35] Datz S, Drake G W F, Gallagher T F, and Putlitz G. Atomic Physics[J]. Rev. Mod. Phys., 1999, 71(2): S223-S241.
[36] Decamp D, Deschizeaux B, Lees J -P, and Minard M -N, et al. A Detector for Electron-position Annihilations at LEP[J]. Nucl. Instr. & Meth. A, 1990, 294(1): 121-178.
[37] Staanum P, Kraft S D, Lange J, Wester R, and Weidemüller M. Experiment Investigation of Ultracold Atom-molecule Collisions. Phys. Rev. Lett., 2006, 96(2): 023201.
[38] Hutson J M, and Soldan P. Molecular Collisions in Ultracold Atomic Gases[J]. Inter. Rev. in Phys. Chem. 2007, 26(1): 1-28.
[39] Stringari S. Collective Excitations of a Trapped Bose-condensed Gas. Phys. Rev. Lett., 1996, 77(12): 2360-2363.
[40] Bradley C C, Sackett C A, and Hulet R G. Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number[J]. Phys. Rev. Lett., 1997, 78(6): 985-989.
[41] Tiesinga E, Verhaar B J, and Stoof H T C. Threshold and Resonance Phenomena in Ultracold Ground-state Collisions[J]. Phys. Rev. A, 1993, 47(5): 4114-4122.
[42] Inouye S, Andrews M R, Stenger J, Miesner H -J, Stamper -K D M, and Ketterle W. Observation of Feshbach Resonances in a Bose-Einstein Condensate[J]. Nature, 1998, 392(6672): 151-154.
[43] Roberts J L, Claussen N R, Burke Jr. J P, Greene C H, Cornell E A, and Weiman C E. Resonant Magnetic Field Control of Elastic Scattering in Cold 85Rb[J]. Phys. Rev. Lett., 1998, 81(23): 5109-5112.
[44] Volz T, Durr S, Ernst S, Marte A, and Rempe G. Characterization of Elastic Scattering near a Feshbach Resonance in 87Rb[J]. Phys. Rev. A, 2003, 68(1): 010702.
[45] Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y, and Salomon C. Formation of a Matter-wave Bright Soliton[J]. Science, 2002, 296(5571): 1290-1293.
[46] Strecker K E, Partridge G B, Truscott A G, Hulet R G. Formation and Propagation of Matter-wave Solution Trains[J]. Nature, 2002, 417(6885): 150-153.
[47] Chin C, Vuletic V, Kerman A J, and Chu S. High Resolution Feshbach Spectroscopy of Cesium[J]. Phys. Rev. Lett., 2000, 85(13): 2717-2720.
[48] Loftus C, Regal C A, Ticknor C, Bohn J L, Jin D S. Resonant Control of Elastic Collisions in an Optically Trapped Fermi Gas of Atoms[J]. Phys. Rev. Lett., 2002, 88(17): 173201.
[49] Schunck C H, Zwierlein M W, Stan C A, Raupach S M F, and Ketterle W. Feshbach Resonances in Fermionic 6Li[J]. Phys. Rev. A, 2005, 71(4): 045601.
[50] Ferlaino F, D’Errico C, Roati G, Inguscio M, and Modugno G. Feshbach Spectroscopy of a K-Rb Atomic Mixture[J]. Phys. Rev. A, 2006, 73(4): 040702(R).
[51] Ospelkaus S, Ospelkaus C, Humbert L, Sengstock K, Bong K. Tuning of Heteronuclear Interactions in a Degenerate Fermi-Bose Mixture[J]. Phys. Rev. Lett., 2006, 97(12): 120403.
[52] Li Z, and Madison K W. Effects of Electric Fields on Heteronuclear Feshbach Resonances in Ultracold 6Li-87Rb Mixtures[J]. Phys. Rev. A, 2009, 79(4): 042711.
[53] Gacesa M, Pellegrini P, and Cote R. Feshbach Resonances in Ultracold 6,7Li-23Na Atomic Mixtures[J]. Phys. Rev. A, 2008, 78(1): 010701(R).
[54] Donley E A, Claussen N R, Cornish S L, Cornish S L, Roberts J L, Cornell E A, and Weiman C E. Dynamics of Collapsing and Exploding Bose-Einstein Condensates[J]. Nature, 2001, 412(6844): 295-299.
[55] Greiner M, Regal C A, and Jin D S. Emergence of a Molecular Bose-Einstein Condensate from a Fermi Gas[J]. Nature, 2003, 426(6966): 537-540.
[56] Regal C A, Greiner M, and Jin D S. Observation of Resonance Condensation of Fermionic Atom Pairs[J]. Phys. Rev. Lett., 2004, 92(4): 040403.
[57] Anderlini M, Ciampini D, Cossart D, Courtade E, Cristiani M, Sias C, and Arimondo E. Model for Collisions in Ultracold-atom Mixtures[J]. Phys. Rev. A, 2005, 72(3): 033408.
[58] Stenger J, Inouye S D, and Stamper-kurn M. Spin Domains in Ground State Spinor Bose-Einstein Condensates[J]. Nature, 1998, 396(6709): 345-348.
[59] Kerman A J, Sage J M, Sainis S, Bergeman T, and DeMille D. Production and State-selective Detection of Ultracold RbCs* Molecules[J]. Phys. Rev. Lett., 2004, 92(15): 153001.
[60] Lewenstein M, Santos L, Baranov M A, and Fehrmann H. Atomic Bose-Fermi Mixture in an Optical Lattice[J]. Phys. Rev. Lett., 2004, 92(5): 050401.
[61] Sengstock K, Sterr U, Hennig G, Bettermann D, Müller J H, and Ertmer W. Optical Ramsey Interferences on Laser Cooled and Trapped Atoms, Detected by Electron Shelving[J]. Opt. Commun., 1993, 103(1-2): 73-78.
[62] Binnewies T, Wilpers G, and Sterr U. Doppler Cooling and Trapping on Forbidden Transitions. Phys. Rev. Lett., 2001, 87(12): 123002.
[63] Ido T, Isoya Y, and Katori H. Optical-dipole Trapping of Sr Atoms at a High Phase-space Density[J]. Phys. Rev. A, 2000, 61(6): 061403.
[64] Allard O, Pashov A, and Tiemann E. Ground-statr Potential of Ca Dimmer from Fourier-transform Spectroscopy[J]. Phys. Rev. A, 2002, 66(4): 042503.
[65] Quéméner G, Honvault P, and Jean-Michel L. Ultracold Quantum Dynamics: Spin-Polarized K+K2 Collisions with Three Identical Bosons of Fermions[J]. Phys. Rev. A, 2005, 71(3): 032722.
[66] Quéméner G, and Launay J -M. Ultracold Collisions Between Li Atoms and Li2 Diatoms in High Vibrational States[J]. Phys. Rev. A, 2007, 75(5): 050701(R).
[67] Ticknor C. Collisional Control of Ground State Polar Molecules and Universal Dipolar Scattering[J]. Phys. Rev. Lett., 2008, 100(13): 133202.
[68] Yamaguchi A, Uetake S, Hashimoto D, Doyle J M, and Takahashi Y. Inelastic Collisions in Optically Trapped Ultracold Metastable Ytterbium[J]. Phys. Rev. Lett., 2008, 101(23): 233002.
[69] Hudson E R, Gilfoy N B, Kotochigova S, Sage J M, and DeMille D. Inelastic Collisions of Ultracold Heteronuclear Molecules in an Optical Trap[J]. Phys. Rev. Lett., 2008, 100(20): 203201.
[70] Li Z, Alyabyshev S V, and Krems R V. Ultracold Inelastic Collisions in Two Dimensions[J]. Phys. Rev. Lett., 2008, 100(7): 073202.
[71] Lysebo M, and Veseth L. Cold Collisions between Atoms and Diatomic Molecules[J]. Phys. Rev. A, 2008, 77(3): 032721.
[72] A Gorges R, Bingham N S, DeAngelo M K, Hamilton M S, and Roberts J L. Light-assisted Collisional Loss in a 85,87Rb Ultracold Optical Trap[J]. Phys. Rev. A, 2008, 78(3): 033420.
[73] Herrera F. Magnetic-field-induced Interference of Scattering States in Ultracold Collisions[J]. Phys. Rev. A, 2008, 78(5): 054702.
[74] Traverso A, Chakraborty R, de Escobar Y N M, Mickelson P G, Nagel S B, Yan M, and Killian T C. Inelastic and Elastic Collision Rates for Triplet Statesof Ultracold Strontium[J]. Phys. Rev. A, 2009, 79(6): 060702.
[75] Li Z, and Krems R V. Inelastic Collisions in an Ultracold Quasi-two- dimensional Gas[J]. Phys. Rev. A, 2009, 79(5): 050701.
[76] Zuchowski P S, and Hutson J M. Low-energy Collisions of NH3 and ND3 with Ultracold Rb Atoms[J]. Phys. Rev. A, 2009, 79(6): 062708.
[77] Tscherbul T V, Buchachenko A A, Dalgarno A, Lu M -J, and Weinstein J D. Suppression of Zeeman Relaxation in Cold Collisions of 2P1/2 Atoms[J]. Phys. Rev. A, 2009, 80(4): 040701(R).
[78] Tacconi M, and Gianturco F A. Translational Cooling versus Vibrational Quenching in Ultracold OH-Rb Collisions: A Quantum Assessment[J]. J. Chem. Phys., 2009, 131(9): 094301.
[79] Hutson J M, and Beyene M. Dramatic Reductions in Inelastic Cross Sections for Ultracold Collisions near Feshbach Resonances. Phys. Rev. Lett., 2009, 103(16): 163201.
[80] Wallis A O G, and Hutson J M. Production of Ultracold NH Molecules by Sympathetic Cooling with Mg[J]. Phys. Rev. Lett., 2009, 103(18): 183201.
[81] Wang Y, D’Incao J P, Nagerl H -C, and Esry B D. Colliding Bose-Einstein Condensates to Observe Efimov Physics[J]. Phys. Rev. Lett., 2010, 104(11): 113201.
[82] Hopkins S A, Webster S, Arlt J, Bance P, Cornish S, Marago O, and Foot C J. Measurement of Elastic Cross Section for Cold Cesium Collisions[J]. Phys. Rev. A, 2000, 61(3): 032707.
[83] Wipple V, Brinder C, and Windholz L. Cross-section for Collisions of Ultracold 7Li with Na[J]. Euro. Phys. J. D, 2002, 21(1): 101-104.
[84] Matherson K J, Glover R D, Laban D E, and Sang R T. Absolute Mestastable Atom-atom Collision Cross Section Measurements Using a Magneto-optical Trap[J]. Rev. Sci. Instr., 2007, 78(7): 073102.
[85] Matherson K J, Glover R D, Laban D E, and Sang R T. Measurement of Low-energy Total Atomic Collision Cross Sections with Metastable 3P2 State of Neon Using a Magneto-optical Trap[J]. Phys. Rev. A, 2008, 78(4): 042712.
[86] Frank A I, Geltenbort P, Kulin G V, and Srepetov A N. Experimental Verification of the 1/v Law for the Absorption Cross Section of Ultracold Neutrons in Natural Gadolinium[J]. JETP Lett., 2006, 84(3): 105-109.
[87] Bohn J L, Cavagnero M, and Ticknor C. Quasi-universal Dipolar Scattering in Cold and Ultracold Gases[J]. New J. Phys., 2009, 11: 055039.
[88] Chandler D W. Cold and Ultracold Molecules: Spotlight on Orbiting Resonances[J]. J. Chem. Phys., 2010, 132(11): 110901.
[89] Wurtz P, Gericke T, and Vogler A. Ultracold Atoms as a Target: Absolute Scattering Cross-section Measurements[J]. New J. Phys., 2010, 12: 065033.
[90] Zipkes C, Palzer S, Ratschbacher L, Sias C, and Kohl M. Cold Heteronuclear Atom-Ion Collisions[J]. Phys. Rev. Lett., 2010, 105(13): 133201.
[91] Wright K W A, and Lane I C. Ab Initio Potentials of F+Li2 Accessible at Ultracold Temperatures[J]. Phys. Rev. A, 2010, 82(3): 032715.
[92] Sultanov R A, Adhikari S K, and Guster D. Quenching of Para-H2 with an Ultracold Antihydrogen Atom H1S[J]. Phys. Rev. A, 2010, 81(2): 022705.
[93] Peters A, Chung K Y, and Chu S. Measurement of Gravitational Acceleration by Dropping Atoms[J]. Nature, 1999, 400(6747): 849-852.
[94] Fray S, and Diez C A, Hansch T W, and Weitz M. Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle[J]. Phys. Rev. Lett., 2004, 93(24): 240404.
[95] Snadden M J, McGuirk J M, Bouyer P, Haritos K G, and Kasevich M A. Measurement of the Earth’s Gravity Gradient with an Atom Interferometer- based Gravity Gradiameter[J]. Phys. Rev. Lett., 1998, 81(5): 971-974.
[96] Bertoldi A, Lamporesi G, Cacciapuoti L, de Angelis M, Petelski T, Peters A, Prevedelli M, Stuhler J, and Tino G M. Atom Interferometry Gravity- gradiometer for the Determination of the Newtonian Gravitation Constant G[J]. Eur. Phys. J. D, 2006, 40(2): 271-279.
[97] Ferrari G, Poli N, Sorrentino F, and Tino G M. Long-lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale[J]. Phys. Rev. Lett., 2006, 97(6): 060402.
[98] Chandler D W. Cold and Ultracold Molecules: Spotlight on Orbiting Resonances[J]. J. Chem. Phys., 2010, 132(11): 110901.
[99] Ludlow A D, Martin M, Zelevinsky T, Foreman S M, Blatt S, Notcutt M, Ido T, and Ye J. Systematic Study of the 87Sr Clock Transition in an Optical Lattice[J]. Phys. Rev. Lett., 2006, 96(3): 033003.
[100] Barber Z W, Hoyt C W, Oates C W, and L Hollberg. Direct Excitation of the Forbidden Clock Transition in Neutral 174Yb Atoms Confined to an Optical Lattice[J]. Phys. Rev. Lett., 2006, 96(8): 083002.
[101] Jo G B, Shin Y, Will S, Pasquini T A, Saba M, Ketterle W, and Pritchard D E. Long Phase Coherence Time and Number Squeezing of Two Bose-Einstein Condensates on a Atom Chip[J]. Phys. Rev. Lett., 2007, 98(3): 030407.
[102] Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, and Reichel J. Strong Atom-Field Coupling for Bose-Einstein Condensates in an Optical Cavity on a Chip[J]. Nature, 2007, 450(7167): 272-279.
[103] Treutlein P, Hunger D, Camerer S, H?nsch T W, Reichel J. Bose-Einstein Condensate Coupled to a Nanochanical Resonator on an Atom Chip[J]. Phys. Rev. Lett., 2007, 99(14): 140403.
[104] Scott R G, Judd T E, and Fromhold T M. Exploiting Soliton Decay and PhaseFluctuations in Atom Chip Interferometry of Bose-Einstein Condensates[J]. Phys. Rev. Lett., 2008, 100(10): 100402.
[105] Bohi P, Riedel M F, Hoffrogge J, Reichel J, Hansch T W, Treutlein P. Coherent Manipulation of Bose-Einstein Condensates with State-dependent Micowave Potentials on an Atom Chip[J]. Nature Phys., 2009, 5(8): 592-597.
[106] Hufnagel C, Mukai T, and Shimizu F. Stability of a Superconductive Atom Chip with Persistent Current[J]. Phys. Rev. A, 2009, 79(5): 053641.
[107] Sewell R J, Dingjan J, Baumgartner F, Liorente -G I, Eriksson S, Hinds E A, Lewis G, Strinvasan P, Moktadir Z, and Kraft M. Atom Chip for BEC Interferometry[J]. J. Phys. B, 2010, 43(5): 051003.
[108] Raab E, Prentis M, Cable A, Chu S and Pritchard D. Trapping of Netral Sodium Atoms with Radiation Pressure[J]. Phys. Rev. Lett., 1987, 59(23): 2631-2634.
[109] Migdall A L, Prodan J V, Phillips W D, Bergeman T H and Metcalf H J. First Observation of Magnetically Trapped Neutral Atoms[J]. Phys. Rev. Lett., 1985, 54(24): 2596-2599.
[110] Chu S, Bjorkholm J E, Ashkin A and Cable A. Experimental Observation of Optically Trapped Atoms[J]. Phys. Rev. Lett., 1986, 57(24): 314-317.
[111] Bergeman T, Erez G,Metoalf H J. Magnctostatic Trapping Fields for Neutral Atoms[J]. Phys. Rev. A, 1987, 35(4): 1535-1546.
[112] Griffiths D J. Introduction to Quantum Mechanics[M]. Pearson Prentice Hall, Upper saddle River, New Jersey, 2005: 12-22.
[113] van Kempen E G M, Kokkelmans D J, Heinzen S J J M F, and Verhaar B J. Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments[J]. Phys. Rev. Lett., 2002, 88(9): 093201.
[114] Cornish S L, Claussen N R, Roberts J L, Cornell E A and Wieman C E. Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions[J]. Phys. Rev. Lett., 2000, 85(9): 1795-1798.
[115] Roberts J L, Claussen N R, Cornish S L, Donley E A, Cornell E A and Wieman C E. Controlled Collapse of a Bose-Einstein Condensate[J]. Phys. Rev. Lett., 2001, 86(19): 4211-4214.
[116] Kobayashi S, Yamada J, Machida S, and Kimura T. Single-mode Operation of 500Mbit/s Modulate AlGaAs Semiconductor Laser by Injection Locking[J]. Electr. Lett. 1980, 16(19): 746-748.
[117] Flectcher C S, Close J D. Extended Temperature Tuning of an External Cavity Diode Laser[J]. Appl. Phys. B, 2004, 78(3-4): 305-313.
[118] Hawthorn C J, Weber K P, and Scholten R E. Littrow Configuration Tunable External Cavity Diode Laser with Fixed Direction Output Beam[J]. Rev. Sci. Inst., 2001, 72(12): 4477-4479.
[119] Singh S. Progress Towards Ultra-cold Ensembles of Rubidium and Lithium[D]. M. Sc. Thesis, University of British of Columbia, 2007, 19-35.
[120] Stoehr H, Mensing F, Helmcke J, and Sterr U. Diode Laser with 1Hz Linewidth[J]. Opt. Lett., 2006, 31(6): 736-738.
[121] Zhang J, Wei D, Xie C, and Peng K. Characteristics of Absorption and Dispersion for Rubidium D2 Lines with the Modulation Transfer Spectrum[J]. Opt. Exp., 2003, 11(11): 1338-1344.
[122] Djuricanin P. Magnetic Coil: Assembly and Instruction[D]. Technical Report, University of British Columia, 2009, 4-8.
[123] Markovi? N. Notes on Scttering Theory[D]. Chalmers University of Technology, 2003, 28-31.
[124] Bali S, O’Hara K, M. Gehm, S. Granade, and J. Thomas. Quantum-diffractive Background Gas Collisions in Atom-trap Heating and Loss[J]. Phys. Rev. A, 1999 60(1): R29-R32.
[125] Mitroy J, and Zhang J -Y. Long-range Dispersion Interactions II. Alkali-metal and Rare-gas Atoms[J]. Phys. Rev. A, 2007, 76(7): 032706.
[126] Landau L D, and Lifshitz E M. Quantum Mechanics, Non-relativistic Theory [M]. 1958, 71-75.
[127] Hoffmann D, Bali S, and Walker T. Trap-depth Measurements Using Ultracold Collsions[J]. Phys. Rev. A, 1996, 54(2): R1030-R1033.
[128] E Boukobza, and Tannor D J. Entropy Exchange and Entanglement in the Jaynes-Cummings Model[J]. Phys. Rev. A, 2005, 71(6): 06382.
[129] Xiang Y, and Xiong S J. Entropy Exchange, Coherent Information, and Concurrence[J]. Phys. Rev. A, 2007, 76(1): 014306.
[130] Yan X Q, Shao B, and Zou J. Entropy Exchange and Entanglement of an in Motion Two-level Atom with a Quantized Field[J]. Chaos Solitons & Fractals, 2008, 37: 835-841.
[131] Catani J, Barontini G, Lamporesi G, Rabatti F, Thalhammer G, Minardi F, Stringari S, and Inguscio M. Entropy Exchange in a Mixture of Ultracold Atoms[J]. Phys. Rev. Lett., 2009, 103(14): 140401.
[132] Metcalf H. Entropy Exchange in Laser Cooling. Phys. Rev. A, 2009, 77(6): 061401(R).
[133] Zhang J, Shao B, and Zou J. Entropy Exchange and Entanglement in Superconducting Charge Qubit inside a Resonant Cavity with Intrinsic Decoherence[J]. Theor. Phys. Commun., 2008, 49(6): 1463-1467.
[134] Hou X W, Chen J H, Wan M F, and Ma Z Q. Entropy Correlation and Entanglement for Mixed States in an Algebraic Model[J]. J. Phys. A, 2009, 42(7): 075301.
[135] Virmani S, and Plenio M B. Ordering States with Entanglemnet Measures[J].Phys. Lett. A, 2000, 268(1-2): 31.
[136] Hill S, and Wootters W K. Entanglement of a Pair of Quantum Bits[J]. Phys. Rev. Lett., 1997, 78(26): 5022.
[137] Wootters W K. Entanglement of Formation of an Arbitrary State of Two Qubits[J]. Phys. Rev. Lett., 1998, 80(10): 2245.
[138] Bose S, Fuentes -G I, Knight P L, Vedral V. Subsystem Purity as an Enforcer of Entanglement[J]. Phys. Rev. Lett., 2001, 87(5): 050401.
[139] Yu T and Eberly J H. Evolution from Entanglement to Decoherence[J]. Quant. Inf. Comput., 2007, 7: 459-468.
[2] Souominen K -A, Burnett K, and Julienne P S. Role of Off-resonant Excitation in Cold Collisions in a Ctrong Laser Field[J]. Phys. Rev. A, 1996, 53(3): R1220-R1223.
[3] Souominen K -A, Burnett K, and Julienne P S. Ultracold Collision and Optical Shielding in Metastable Xenon[J]. Phys. Rev. A, 1996, 53(3): 1678-1689.
[4] Weiner J, Bagnato V S, Zillo S, and Julienne P S. Experiments and Theory in Cold and Ultracold Collisions[J]. Rev. Mod. Phys., 1999, 71: 1-85.
[5] Chu S, Bjorkholm J E, Ashkin A, and Cable A. Experimental observation of optically trapped atoms. Phys. Rev. Lett., 1986, 57(3): 314-318.
[6] Ranb E, Prenlis M, Cable A, Chu S, and Pritchard D. Trapping of Neutral Sodium Atoms with Radiation Pressure. Phys. Rev. Lett., 1987, 59(23): 2631-2634.
[7] Lin Z, Shimizu K, Zhan M S, Shimizu F, and Takuma H. Laser Cooling and Trapping of Li[J]. Jap. J. of Appl. Phys., 1991, 30(7B): L1324-L1326.
[8]王育竹,刘勋铭,林岳明,周善钰,霍芸生,徐信业,蔡惟泉,李佛生,洪涛.一种新型的钠原子磁光陷阱(MOT) [J].中国激光, 1996, 23: 448-451.
[9] Gan J H, Li Y M, Chen X Z, Liu H F, Yang D H, and Wang Y Q. Magneto-Optical Trap of Cesium Atoms[J]. Chin Phys. Lett., 1996, 13(11): 821-824.
[10]王义遒.原子的激光冷却与捕陷[J].物理. 1990, 19: 389-449.
[11] Hess H F. Evaporative Cooling of Magnetically Trapped and Compressed spin- polarized hydrogen[J]. Phys. Rev. B, 1986, 34(5): 3476-3479.
[12] Anderson M H, Ensher J R, Matthews M R, Wieman C E, and Cornell E A. Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor[J]. Science, 1995, 269(5221): 198-201.
[13] Chu S, and Wieman C E. Laser Cooling and Trapping of Atoms[J]. J. Opt. Soc. Am. B, 1989, 6(11): 2020-2020.
[14] Bradley C C, Sackett C A, Tollett J J, and Hulet R G. Evidence of Bose-Eintein Condensation in an Atomic Gas with Attractive Interactions[J]. Phys. Rev. Lett., 1995, 75(9): 1687-1690.
[15] Bradley C, Sackett C A, and Hulet R G. Bose-Einstein Condensation ofLithium: Observation of Limited Condens Number[J]. Phys. Rev. Lett., 1997, 78(6): 985-989.
[16] Davis B, Mewes M -O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, and Ketterle W. Bose-Einstein Condensation in a Gas of Sodium Atoms[J]. Phys. Rev. Lett., 1995, 75(22): 3969-3973.
[17] Mewes M -O, Andrews M R, van Druten N J, Kurn D M, Durfee D S, and Ketterle W. Bose-Einstein Condensation in a Tightly Confining DC Magnetic Trap[J], Phys. Rev. Lett., 1996, 77(3): 416-419.
[18] Kestenbaum D. Hydrogen Coaxed into Quantum Condensate[J]. Science, 1998, 281(5375): 321-321.
[19] Bagnato V, Pritchard D E, and Kleppner D. Bose-Einstein Condensation in an External Potential[J]. Phys. Rev. A., 1987, 35(10): 4354-4358.
[20] DeMarco B, and Jin D S. Onset of Fermi Degeneracy in a Trapped Atomic Gas[J]. Science, 1999, 285(5434): 1703-1706.
[21] Truscott A G, Strecker K E, McAlexander W I, Partridge G B, and Hulet R G. Observation of Fermi Pressure in a Gas of Trapped Atoms[J]. Science, 2001, 291(5513): 2570-2572.
[22] Schreck F, Khaykovich L, Corwin K L, Ferrari G, Bourdel T, Cubizolles J, and Salomon C. Quasipure Bose-Einstein Condensate Immersed in a Fermi Sea[J]. Phys. Rev. Lett., 2001, 87(8): 080403.
[23] Granade S R, Gehm M E, O’Hara K M, and Tomas J E. All-optical Production of a Degenerate Fermi Gas[J]. Phys. Rev. Lett., 2002, 88(12): 120405.
[24] Hadzibabic Z, Stan C A, Dieckmann K, Gupta S, Zwierlein M W, G?rliz A, and Ketterle W. Two Species Mixture of Quantum Degenerate Bose and Fermi Gases[J]. Phys. Rev. Lett., 2002, 88(16): 160401.
[25] Jochim S, Bartenstein M, Altmeyer A, Hendl G, Chin C, Denschlag J H, Grimm R. Bose-Einstein Condensation of Molecules[J]. Science, 2003, 302(5653): 2101-2103.
[26] Regal C A, Tickner C, Bohn J L, and Jin D S. Creation of Ultracold Molecules from a Fermi Gas of Atoms[J]. Nature, 2003, 424(6944): 47-50.
[27] Cubizolles J, Bourdel T, Kokkelmans S, Shlyapnikov G V, and Salomon C. Production of Long-lived Ultracold Li2 Molecules from a Fermi Gas[J]. Phys. Rev. Lett., 2003, 91(24): 240401.
[28] Kohl M, Moritz H, Stoferle T. Fermionic Atoms in a Three Dimensional Optical Lattice: Observing Fermi Surfaces, Dynamics, and Interactions[J]. Phys. Rev. Lett., 2005, 94: 080403.
[29] Silber C, Gunther S, Marzok C, Deh B, Courteille P W, and Zimmermann C. Quantum-degenerate Mixture of Fermionic Lithium and Boseonic Rubidium Gases[J]. Phys. Rev. Lett., 2005, 95(17): 170408.
[30] Ospelkaus C, Ospekaus S, Sengetock K, and Bongs K. Interaction-driven Dynamics of 40K-87Rb Fermion-Boson Gas Mixture in the Large-particle- number Limit[J]. Phys. Rev. Lett., 2006, 96(2): 020401.
[31] Aubin S, Myrskog S, Extavour M H T, S. Myrskog, Leblanc L J, Esteve J, Singh S, Scrutton P, Mckay D, McKenzie R, Lerous I D, Stummer A, and Thywissen J H. Trapping Fermionic 40K and Bosonic 87Rb on a Chip[J]. J. Low Temp. Phys., 2006, 140(5): 377-396.
[32] Fukuhara T, Takasu Y, Kumakura M, and Takahashi Y. Degenerate Fermi Gases of Ytterbium[J]. Phys. Rev. Lett., 2007, 98(3): 030401.
[33] McNamara J M, Jeltes T, Tychkov A S, Hogervorst W, and Vassen W. Degenerate Bose-Fermi Mixture of Metastable Atoms. Phys. Rev. Lett., 2006, 97(8): 080404.
[34] Goldwin J M. Quantum Degeneracy and Interactions in the 87Rb-40K Bose-Fermi Mixture[D]. Ph.D Thesis of University of Colorado, 2005, 103-114.
[35] Datz S, Drake G W F, Gallagher T F, and Putlitz G. Atomic Physics[J]. Rev. Mod. Phys., 1999, 71(2): S223-S241.
[36] Decamp D, Deschizeaux B, Lees J -P, and Minard M -N, et al. A Detector for Electron-position Annihilations at LEP[J]. Nucl. Instr. & Meth. A, 1990, 294(1): 121-178.
[37] Staanum P, Kraft S D, Lange J, Wester R, and Weidemüller M. Experiment Investigation of Ultracold Atom-molecule Collisions. Phys. Rev. Lett., 2006, 96(2): 023201.
[38] Hutson J M, and Soldan P. Molecular Collisions in Ultracold Atomic Gases[J]. Inter. Rev. in Phys. Chem. 2007, 26(1): 1-28.
[39] Stringari S. Collective Excitations of a Trapped Bose-condensed Gas. Phys. Rev. Lett., 1996, 77(12): 2360-2363.
[40] Bradley C C, Sackett C A, and Hulet R G. Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number[J]. Phys. Rev. Lett., 1997, 78(6): 985-989.
[41] Tiesinga E, Verhaar B J, and Stoof H T C. Threshold and Resonance Phenomena in Ultracold Ground-state Collisions[J]. Phys. Rev. A, 1993, 47(5): 4114-4122.
[42] Inouye S, Andrews M R, Stenger J, Miesner H -J, Stamper -K D M, and Ketterle W. Observation of Feshbach Resonances in a Bose-Einstein Condensate[J]. Nature, 1998, 392(6672): 151-154.
[43] Roberts J L, Claussen N R, Burke Jr. J P, Greene C H, Cornell E A, and Weiman C E. Resonant Magnetic Field Control of Elastic Scattering in Cold 85Rb[J]. Phys. Rev. Lett., 1998, 81(23): 5109-5112.
[44] Volz T, Durr S, Ernst S, Marte A, and Rempe G. Characterization of Elastic Scattering near a Feshbach Resonance in 87Rb[J]. Phys. Rev. A, 2003, 68(1): 010702.
[45] Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr L D, Castin Y, and Salomon C. Formation of a Matter-wave Bright Soliton[J]. Science, 2002, 296(5571): 1290-1293.
[46] Strecker K E, Partridge G B, Truscott A G, Hulet R G. Formation and Propagation of Matter-wave Solution Trains[J]. Nature, 2002, 417(6885): 150-153.
[47] Chin C, Vuletic V, Kerman A J, and Chu S. High Resolution Feshbach Spectroscopy of Cesium[J]. Phys. Rev. Lett., 2000, 85(13): 2717-2720.
[48] Loftus C, Regal C A, Ticknor C, Bohn J L, Jin D S. Resonant Control of Elastic Collisions in an Optically Trapped Fermi Gas of Atoms[J]. Phys. Rev. Lett., 2002, 88(17): 173201.
[49] Schunck C H, Zwierlein M W, Stan C A, Raupach S M F, and Ketterle W. Feshbach Resonances in Fermionic 6Li[J]. Phys. Rev. A, 2005, 71(4): 045601.
[50] Ferlaino F, D’Errico C, Roati G, Inguscio M, and Modugno G. Feshbach Spectroscopy of a K-Rb Atomic Mixture[J]. Phys. Rev. A, 2006, 73(4): 040702(R).
[51] Ospelkaus S, Ospelkaus C, Humbert L, Sengstock K, Bong K. Tuning of Heteronuclear Interactions in a Degenerate Fermi-Bose Mixture[J]. Phys. Rev. Lett., 2006, 97(12): 120403.
[52] Li Z, and Madison K W. Effects of Electric Fields on Heteronuclear Feshbach Resonances in Ultracold 6Li-87Rb Mixtures[J]. Phys. Rev. A, 2009, 79(4): 042711.
[53] Gacesa M, Pellegrini P, and Cote R. Feshbach Resonances in Ultracold 6,7Li-23Na Atomic Mixtures[J]. Phys. Rev. A, 2008, 78(1): 010701(R).
[54] Donley E A, Claussen N R, Cornish S L, Cornish S L, Roberts J L, Cornell E A, and Weiman C E. Dynamics of Collapsing and Exploding Bose-Einstein Condensates[J]. Nature, 2001, 412(6844): 295-299.
[55] Greiner M, Regal C A, and Jin D S. Emergence of a Molecular Bose-Einstein Condensate from a Fermi Gas[J]. Nature, 2003, 426(6966): 537-540.
[56] Regal C A, Greiner M, and Jin D S. Observation of Resonance Condensation of Fermionic Atom Pairs[J]. Phys. Rev. Lett., 2004, 92(4): 040403.
[57] Anderlini M, Ciampini D, Cossart D, Courtade E, Cristiani M, Sias C, and Arimondo E. Model for Collisions in Ultracold-atom Mixtures[J]. Phys. Rev. A, 2005, 72(3): 033408.
[58] Stenger J, Inouye S D, and Stamper-kurn M. Spin Domains in Ground State Spinor Bose-Einstein Condensates[J]. Nature, 1998, 396(6709): 345-348.
[59] Kerman A J, Sage J M, Sainis S, Bergeman T, and DeMille D. Production and State-selective Detection of Ultracold RbCs* Molecules[J]. Phys. Rev. Lett., 2004, 92(15): 153001.
[60] Lewenstein M, Santos L, Baranov M A, and Fehrmann H. Atomic Bose-Fermi Mixture in an Optical Lattice[J]. Phys. Rev. Lett., 2004, 92(5): 050401.
[61] Sengstock K, Sterr U, Hennig G, Bettermann D, Müller J H, and Ertmer W. Optical Ramsey Interferences on Laser Cooled and Trapped Atoms, Detected by Electron Shelving[J]. Opt. Commun., 1993, 103(1-2): 73-78.
[62] Binnewies T, Wilpers G, and Sterr U. Doppler Cooling and Trapping on Forbidden Transitions. Phys. Rev. Lett., 2001, 87(12): 123002.
[63] Ido T, Isoya Y, and Katori H. Optical-dipole Trapping of Sr Atoms at a High Phase-space Density[J]. Phys. Rev. A, 2000, 61(6): 061403.
[64] Allard O, Pashov A, and Tiemann E. Ground-statr Potential of Ca Dimmer from Fourier-transform Spectroscopy[J]. Phys. Rev. A, 2002, 66(4): 042503.
[65] Quéméner G, Honvault P, and Jean-Michel L. Ultracold Quantum Dynamics: Spin-Polarized K+K2 Collisions with Three Identical Bosons of Fermions[J]. Phys. Rev. A, 2005, 71(3): 032722.
[66] Quéméner G, and Launay J -M. Ultracold Collisions Between Li Atoms and Li2 Diatoms in High Vibrational States[J]. Phys. Rev. A, 2007, 75(5): 050701(R).
[67] Ticknor C. Collisional Control of Ground State Polar Molecules and Universal Dipolar Scattering[J]. Phys. Rev. Lett., 2008, 100(13): 133202.
[68] Yamaguchi A, Uetake S, Hashimoto D, Doyle J M, and Takahashi Y. Inelastic Collisions in Optically Trapped Ultracold Metastable Ytterbium[J]. Phys. Rev. Lett., 2008, 101(23): 233002.
[69] Hudson E R, Gilfoy N B, Kotochigova S, Sage J M, and DeMille D. Inelastic Collisions of Ultracold Heteronuclear Molecules in an Optical Trap[J]. Phys. Rev. Lett., 2008, 100(20): 203201.
[70] Li Z, Alyabyshev S V, and Krems R V. Ultracold Inelastic Collisions in Two Dimensions[J]. Phys. Rev. Lett., 2008, 100(7): 073202.
[71] Lysebo M, and Veseth L. Cold Collisions between Atoms and Diatomic Molecules[J]. Phys. Rev. A, 2008, 77(3): 032721.
[72] A Gorges R, Bingham N S, DeAngelo M K, Hamilton M S, and Roberts J L. Light-assisted Collisional Loss in a 85,87Rb Ultracold Optical Trap[J]. Phys. Rev. A, 2008, 78(3): 033420.
[73] Herrera F. Magnetic-field-induced Interference of Scattering States in Ultracold Collisions[J]. Phys. Rev. A, 2008, 78(5): 054702.
[74] Traverso A, Chakraborty R, de Escobar Y N M, Mickelson P G, Nagel S B, Yan M, and Killian T C. Inelastic and Elastic Collision Rates for Triplet Statesof Ultracold Strontium[J]. Phys. Rev. A, 2009, 79(6): 060702.
[75] Li Z, and Krems R V. Inelastic Collisions in an Ultracold Quasi-two- dimensional Gas[J]. Phys. Rev. A, 2009, 79(5): 050701.
[76] Zuchowski P S, and Hutson J M. Low-energy Collisions of NH3 and ND3 with Ultracold Rb Atoms[J]. Phys. Rev. A, 2009, 79(6): 062708.
[77] Tscherbul T V, Buchachenko A A, Dalgarno A, Lu M -J, and Weinstein J D. Suppression of Zeeman Relaxation in Cold Collisions of 2P1/2 Atoms[J]. Phys. Rev. A, 2009, 80(4): 040701(R).
[78] Tacconi M, and Gianturco F A. Translational Cooling versus Vibrational Quenching in Ultracold OH-Rb Collisions: A Quantum Assessment[J]. J. Chem. Phys., 2009, 131(9): 094301.
[79] Hutson J M, and Beyene M. Dramatic Reductions in Inelastic Cross Sections for Ultracold Collisions near Feshbach Resonances. Phys. Rev. Lett., 2009, 103(16): 163201.
[80] Wallis A O G, and Hutson J M. Production of Ultracold NH Molecules by Sympathetic Cooling with Mg[J]. Phys. Rev. Lett., 2009, 103(18): 183201.
[81] Wang Y, D’Incao J P, Nagerl H -C, and Esry B D. Colliding Bose-Einstein Condensates to Observe Efimov Physics[J]. Phys. Rev. Lett., 2010, 104(11): 113201.
[82] Hopkins S A, Webster S, Arlt J, Bance P, Cornish S, Marago O, and Foot C J. Measurement of Elastic Cross Section for Cold Cesium Collisions[J]. Phys. Rev. A, 2000, 61(3): 032707.
[83] Wipple V, Brinder C, and Windholz L. Cross-section for Collisions of Ultracold 7Li with Na[J]. Euro. Phys. J. D, 2002, 21(1): 101-104.
[84] Matherson K J, Glover R D, Laban D E, and Sang R T. Absolute Mestastable Atom-atom Collision Cross Section Measurements Using a Magneto-optical Trap[J]. Rev. Sci. Instr., 2007, 78(7): 073102.
[85] Matherson K J, Glover R D, Laban D E, and Sang R T. Measurement of Low-energy Total Atomic Collision Cross Sections with Metastable 3P2 State of Neon Using a Magneto-optical Trap[J]. Phys. Rev. A, 2008, 78(4): 042712.
[86] Frank A I, Geltenbort P, Kulin G V, and Srepetov A N. Experimental Verification of the 1/v Law for the Absorption Cross Section of Ultracold Neutrons in Natural Gadolinium[J]. JETP Lett., 2006, 84(3): 105-109.
[87] Bohn J L, Cavagnero M, and Ticknor C. Quasi-universal Dipolar Scattering in Cold and Ultracold Gases[J]. New J. Phys., 2009, 11: 055039.
[88] Chandler D W. Cold and Ultracold Molecules: Spotlight on Orbiting Resonances[J]. J. Chem. Phys., 2010, 132(11): 110901.
[89] Wurtz P, Gericke T, and Vogler A. Ultracold Atoms as a Target: Absolute Scattering Cross-section Measurements[J]. New J. Phys., 2010, 12: 065033.
[90] Zipkes C, Palzer S, Ratschbacher L, Sias C, and Kohl M. Cold Heteronuclear Atom-Ion Collisions[J]. Phys. Rev. Lett., 2010, 105(13): 133201.
[91] Wright K W A, and Lane I C. Ab Initio Potentials of F+Li2 Accessible at Ultracold Temperatures[J]. Phys. Rev. A, 2010, 82(3): 032715.
[92] Sultanov R A, Adhikari S K, and Guster D. Quenching of Para-H2 with an Ultracold Antihydrogen Atom H1S[J]. Phys. Rev. A, 2010, 81(2): 022705.
[93] Peters A, Chung K Y, and Chu S. Measurement of Gravitational Acceleration by Dropping Atoms[J]. Nature, 1999, 400(6747): 849-852.
[94] Fray S, and Diez C A, Hansch T W, and Weitz M. Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle[J]. Phys. Rev. Lett., 2004, 93(24): 240404.
[95] Snadden M J, McGuirk J M, Bouyer P, Haritos K G, and Kasevich M A. Measurement of the Earth’s Gravity Gradient with an Atom Interferometer- based Gravity Gradiameter[J]. Phys. Rev. Lett., 1998, 81(5): 971-974.
[96] Bertoldi A, Lamporesi G, Cacciapuoti L, de Angelis M, Petelski T, Peters A, Prevedelli M, Stuhler J, and Tino G M. Atom Interferometry Gravity- gradiometer for the Determination of the Newtonian Gravitation Constant G[J]. Eur. Phys. J. D, 2006, 40(2): 271-279.
[97] Ferrari G, Poli N, Sorrentino F, and Tino G M. Long-lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale[J]. Phys. Rev. Lett., 2006, 97(6): 060402.
[98] Chandler D W. Cold and Ultracold Molecules: Spotlight on Orbiting Resonances[J]. J. Chem. Phys., 2010, 132(11): 110901.
[99] Ludlow A D, Martin M, Zelevinsky T, Foreman S M, Blatt S, Notcutt M, Ido T, and Ye J. Systematic Study of the 87Sr Clock Transition in an Optical Lattice[J]. Phys. Rev. Lett., 2006, 96(3): 033003.
[100] Barber Z W, Hoyt C W, Oates C W, and L Hollberg. Direct Excitation of the Forbidden Clock Transition in Neutral 174Yb Atoms Confined to an Optical Lattice[J]. Phys. Rev. Lett., 2006, 96(8): 083002.
[101] Jo G B, Shin Y, Will S, Pasquini T A, Saba M, Ketterle W, and Pritchard D E. Long Phase Coherence Time and Number Squeezing of Two Bose-Einstein Condensates on a Atom Chip[J]. Phys. Rev. Lett., 2007, 98(3): 030407.
[102] Colombe Y, Steinmetz T, Dubois G, Linke F, Hunger D, and Reichel J. Strong Atom-Field Coupling for Bose-Einstein Condensates in an Optical Cavity on a Chip[J]. Nature, 2007, 450(7167): 272-279.
[103] Treutlein P, Hunger D, Camerer S, H?nsch T W, Reichel J. Bose-Einstein Condensate Coupled to a Nanochanical Resonator on an Atom Chip[J]. Phys. Rev. Lett., 2007, 99(14): 140403.
[104] Scott R G, Judd T E, and Fromhold T M. Exploiting Soliton Decay and PhaseFluctuations in Atom Chip Interferometry of Bose-Einstein Condensates[J]. Phys. Rev. Lett., 2008, 100(10): 100402.
[105] Bohi P, Riedel M F, Hoffrogge J, Reichel J, Hansch T W, Treutlein P. Coherent Manipulation of Bose-Einstein Condensates with State-dependent Micowave Potentials on an Atom Chip[J]. Nature Phys., 2009, 5(8): 592-597.
[106] Hufnagel C, Mukai T, and Shimizu F. Stability of a Superconductive Atom Chip with Persistent Current[J]. Phys. Rev. A, 2009, 79(5): 053641.
[107] Sewell R J, Dingjan J, Baumgartner F, Liorente -G I, Eriksson S, Hinds E A, Lewis G, Strinvasan P, Moktadir Z, and Kraft M. Atom Chip for BEC Interferometry[J]. J. Phys. B, 2010, 43(5): 051003.
[108] Raab E, Prentis M, Cable A, Chu S and Pritchard D. Trapping of Netral Sodium Atoms with Radiation Pressure[J]. Phys. Rev. Lett., 1987, 59(23): 2631-2634.
[109] Migdall A L, Prodan J V, Phillips W D, Bergeman T H and Metcalf H J. First Observation of Magnetically Trapped Neutral Atoms[J]. Phys. Rev. Lett., 1985, 54(24): 2596-2599.
[110] Chu S, Bjorkholm J E, Ashkin A and Cable A. Experimental Observation of Optically Trapped Atoms[J]. Phys. Rev. Lett., 1986, 57(24): 314-317.
[111] Bergeman T, Erez G,Metoalf H J. Magnctostatic Trapping Fields for Neutral Atoms[J]. Phys. Rev. A, 1987, 35(4): 1535-1546.
[112] Griffiths D J. Introduction to Quantum Mechanics[M]. Pearson Prentice Hall, Upper saddle River, New Jersey, 2005: 12-22.
[113] van Kempen E G M, Kokkelmans D J, Heinzen S J J M F, and Verhaar B J. Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments[J]. Phys. Rev. Lett., 2002, 88(9): 093201.
[114] Cornish S L, Claussen N R, Roberts J L, Cornell E A and Wieman C E. Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions[J]. Phys. Rev. Lett., 2000, 85(9): 1795-1798.
[115] Roberts J L, Claussen N R, Cornish S L, Donley E A, Cornell E A and Wieman C E. Controlled Collapse of a Bose-Einstein Condensate[J]. Phys. Rev. Lett., 2001, 86(19): 4211-4214.
[116] Kobayashi S, Yamada J, Machida S, and Kimura T. Single-mode Operation of 500Mbit/s Modulate AlGaAs Semiconductor Laser by Injection Locking[J]. Electr. Lett. 1980, 16(19): 746-748.
[117] Flectcher C S, Close J D. Extended Temperature Tuning of an External Cavity Diode Laser[J]. Appl. Phys. B, 2004, 78(3-4): 305-313.
[118] Hawthorn C J, Weber K P, and Scholten R E. Littrow Configuration Tunable External Cavity Diode Laser with Fixed Direction Output Beam[J]. Rev. Sci. Inst., 2001, 72(12): 4477-4479.
[119] Singh S. Progress Towards Ultra-cold Ensembles of Rubidium and Lithium[D]. M. Sc. Thesis, University of British of Columbia, 2007, 19-35.
[120] Stoehr H, Mensing F, Helmcke J, and Sterr U. Diode Laser with 1Hz Linewidth[J]. Opt. Lett., 2006, 31(6): 736-738.
[121] Zhang J, Wei D, Xie C, and Peng K. Characteristics of Absorption and Dispersion for Rubidium D2 Lines with the Modulation Transfer Spectrum[J]. Opt. Exp., 2003, 11(11): 1338-1344.
[122] Djuricanin P. Magnetic Coil: Assembly and Instruction[D]. Technical Report, University of British Columia, 2009, 4-8.
[123] Markovi? N. Notes on Scttering Theory[D]. Chalmers University of Technology, 2003, 28-31.
[124] Bali S, O’Hara K, M. Gehm, S. Granade, and J. Thomas. Quantum-diffractive Background Gas Collisions in Atom-trap Heating and Loss[J]. Phys. Rev. A, 1999 60(1): R29-R32.
[125] Mitroy J, and Zhang J -Y. Long-range Dispersion Interactions II. Alkali-metal and Rare-gas Atoms[J]. Phys. Rev. A, 2007, 76(7): 032706.
[126] Landau L D, and Lifshitz E M. Quantum Mechanics, Non-relativistic Theory [M]. 1958, 71-75.
[127] Hoffmann D, Bali S, and Walker T. Trap-depth Measurements Using Ultracold Collsions[J]. Phys. Rev. A, 1996, 54(2): R1030-R1033.
[128] E Boukobza, and Tannor D J. Entropy Exchange and Entanglement in the Jaynes-Cummings Model[J]. Phys. Rev. A, 2005, 71(6): 06382.
[129] Xiang Y, and Xiong S J. Entropy Exchange, Coherent Information, and Concurrence[J]. Phys. Rev. A, 2007, 76(1): 014306.
[130] Yan X Q, Shao B, and Zou J. Entropy Exchange and Entanglement of an in Motion Two-level Atom with a Quantized Field[J]. Chaos Solitons & Fractals, 2008, 37: 835-841.
[131] Catani J, Barontini G, Lamporesi G, Rabatti F, Thalhammer G, Minardi F, Stringari S, and Inguscio M. Entropy Exchange in a Mixture of Ultracold Atoms[J]. Phys. Rev. Lett., 2009, 103(14): 140401.
[132] Metcalf H. Entropy Exchange in Laser Cooling. Phys. Rev. A, 2009, 77(6): 061401(R).
[133] Zhang J, Shao B, and Zou J. Entropy Exchange and Entanglement in Superconducting Charge Qubit inside a Resonant Cavity with Intrinsic Decoherence[J]. Theor. Phys. Commun., 2008, 49(6): 1463-1467.
[134] Hou X W, Chen J H, Wan M F, and Ma Z Q. Entropy Correlation and Entanglement for Mixed States in an Algebraic Model[J]. J. Phys. A, 2009, 42(7): 075301.
[135] Virmani S, and Plenio M B. Ordering States with Entanglemnet Measures[J].Phys. Lett. A, 2000, 268(1-2): 31.
[136] Hill S, and Wootters W K. Entanglement of a Pair of Quantum Bits[J]. Phys. Rev. Lett., 1997, 78(26): 5022.
[137] Wootters W K. Entanglement of Formation of an Arbitrary State of Two Qubits[J]. Phys. Rev. Lett., 1998, 80(10): 2245.
[138] Bose S, Fuentes -G I, Knight P L, Vedral V. Subsystem Purity as an Enforcer of Entanglement[J]. Phys. Rev. Lett., 2001, 87(5): 050401.
[139] Yu T and Eberly J H. Evolution from Entanglement to Decoherence[J]. Quant. Inf. Comput., 2007, 7: 459-468.