冷分子的静电囚禁及相关理论的研究
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摘要
冷分子可用于基本物理问题的研究、基本物理常数的精密测量，同时在高分辨激光光谱学、冷化学反应和冷分子碰撞、分子物质波的干涉计量、量子计算和量子信息处理等方面有着重要的应用，故冷分子的产生及其应用研究得到了快速的发展。本文首先简单介绍了中性分子的冷却、囚禁及其操控的基本原理，实验结果及其最新进展；然后对极性冷分子的静电囚禁新方案进行了理论研究，最后就本文的工作进行了总结，并对未来要做的工作作一下展望。
本文首先提出了利用单个环形电极(即圆环形导线)和两透明电极(即两无限大透明平板)实现冷分子静电囚禁的新方案。如果给金属导线加上一个正高压，左边透明电极的电压置零，右边透明电极接地，此时产生的电场分布是一个中心电场为零的三维空间静电阱。由于一阶Stark效应，当弱场搜寻态的分子处于这个静电阱中时，将会受到一个指向势阱中心的电场力作用，从而实现冷分子的静电囚禁。我们利用有限元软件分析了这种方案所产生的电场强度分布(包括相应的CO分子的Stark势分布)，研究了电场最小值位置和我们方案中系统参数之间的关系。研究表明：通过改变系统参数，既可以改变囚禁中心的位置，也可改变阱的深度。我们还从几个方面分析了这个囚禁方案的特点，并提出了一种有效的冷分子装载方法。这为我们研究冷分子光谱学、冷分子碰撞、偶极相互作用和分子系统的量子效应，甚至通过降低Stark囚禁势来进一步实现囚禁分子的蒸发冷却等开辟了一条新的途径。
在上一方案的基础上，本文又提出了双环形载荷导线和两透明电极实现冷分子静电囚禁的可控制静电双阱的新方案。同样地，利用数值计算的方法分析了该方案不同几何参数下产生的空间电场强度分布和对应的CO分子的Stark势分布，研究了电场最小值位置和该方案的系统参数之间的关系，同时还给出了双阱与单阱的演化过程，讨论了该可控静电双阱方案在分子的干涉、纠缠、碰撞，甚至进行双阱分子BEC研究等分子光学领域的潜在应用。
Cold molecules have some important applications in study of basic physics problems, high-resolution spectroscopy and precise measurement, cold chemical reaction and cold collision, interferometer of matter wave, and quantum computing and information possessing and so on, so the study on the generation and application of cold molecules has obtained fast development. In this thesis, firstly, the basic principle, experimental results and the recent progress on cooling, trapping and manipulating of neutral molecules have been briefly introduced. Secondly, we give the theoretical study of two new trapping schemes for cold poplar molecules.finally, our research work is summarized and the future investigation is briefly speculated later.
We propose a new scheme to realize electrostatic trap for cold poplar molecules by using an electrostatic field generated by the combination of a pair of parallel transparent electrodes (i.e., two infinite transparent pates) and a ring electrode (i.e., a ring wire). When the positive voltage is applied on the circular wire, and one of the transparent electrodes is not charged, another is grounded, an electrostatic well in free spare will be formed. If cold polar molecules in the low-field-seeking state are loaded into this trap, they will feel a dipole gradient force due to the first-order Stark effect, and then the cold molecules will be repelled to the minimum of the electric field and caught in the trap. We use commercial finite element software to calculate the relationships between the spatial distribution of the electrostatic field of our charged wire layout (including the distribution of the corresponding Stark trapping potential for CO molecules) and the geometric parameters, and study the dependences of the trap centre position on the system parameters. We also analyze the advantages of the scheme from several aspects, and propose an effective loading way. Our study shows that if we change the geometric parameters, we can both change the position of the trapping center and the depth of the well, which may open a new way to study cold molecular spectroscopy, cold collisions, dipolar-dipolar interaction and collective quantum effects in molecular system, even to realize efficient evaporative cooling of the trapped molecules by lowering the Stark trapping potential, and so on.
Based on the first scheme, we also propose another novel electrostatic trapping scheme (i.e., a controllable electrostatic double-well trap) by using two charged ring wires and two parallel transparent electrodes. The spatial distributions of the electrostatic fields from the above charged wires and the charged transparent electrodes for the different geometric parameters and the corresponding Stark potentials for cold CO molecules are also calculated. We study the relationships between the position of the trapping center and the system parameters, and analyze the evolution of our trap from a double-well trap to a single-well one, and discuss the potential applications of the present scheme in molecular interference, molecular entanglement, and molecular collisions, even to study the molecular BEC in the double-well trap, and so on.
本文首先提出了利用单个环形电极(即圆环形导线)和两透明电极(即两无限大透明平板)实现冷分子静电囚禁的新方案。如果给金属导线加上一个正高压，左边透明电极的电压置零，右边透明电极接地，此时产生的电场分布是一个中心电场为零的三维空间静电阱。由于一阶Stark效应，当弱场搜寻态的分子处于这个静电阱中时，将会受到一个指向势阱中心的电场力作用，从而实现冷分子的静电囚禁。我们利用有限元软件分析了这种方案所产生的电场强度分布(包括相应的CO分子的Stark势分布)，研究了电场最小值位置和我们方案中系统参数之间的关系。研究表明：通过改变系统参数，既可以改变囚禁中心的位置，也可改变阱的深度。我们还从几个方面分析了这个囚禁方案的特点，并提出了一种有效的冷分子装载方法。这为我们研究冷分子光谱学、冷分子碰撞、偶极相互作用和分子系统的量子效应，甚至通过降低Stark囚禁势来进一步实现囚禁分子的蒸发冷却等开辟了一条新的途径。
在上一方案的基础上，本文又提出了双环形载荷导线和两透明电极实现冷分子静电囚禁的可控制静电双阱的新方案。同样地，利用数值计算的方法分析了该方案不同几何参数下产生的空间电场强度分布和对应的CO分子的Stark势分布，研究了电场最小值位置和该方案的系统参数之间的关系，同时还给出了双阱与单阱的演化过程，讨论了该可控静电双阱方案在分子的干涉、纠缠、碰撞，甚至进行双阱分子BEC研究等分子光学领域的潜在应用。
Cold molecules have some important applications in study of basic physics problems, high-resolution spectroscopy and precise measurement, cold chemical reaction and cold collision, interferometer of matter wave, and quantum computing and information possessing and so on, so the study on the generation and application of cold molecules has obtained fast development. In this thesis, firstly, the basic principle, experimental results and the recent progress on cooling, trapping and manipulating of neutral molecules have been briefly introduced. Secondly, we give the theoretical study of two new trapping schemes for cold poplar molecules.finally, our research work is summarized and the future investigation is briefly speculated later.
We propose a new scheme to realize electrostatic trap for cold poplar molecules by using an electrostatic field generated by the combination of a pair of parallel transparent electrodes (i.e., two infinite transparent pates) and a ring electrode (i.e., a ring wire). When the positive voltage is applied on the circular wire, and one of the transparent electrodes is not charged, another is grounded, an electrostatic well in free spare will be formed. If cold polar molecules in the low-field-seeking state are loaded into this trap, they will feel a dipole gradient force due to the first-order Stark effect, and then the cold molecules will be repelled to the minimum of the electric field and caught in the trap. We use commercial finite element software to calculate the relationships between the spatial distribution of the electrostatic field of our charged wire layout (including the distribution of the corresponding Stark trapping potential for CO molecules) and the geometric parameters, and study the dependences of the trap centre position on the system parameters. We also analyze the advantages of the scheme from several aspects, and propose an effective loading way. Our study shows that if we change the geometric parameters, we can both change the position of the trapping center and the depth of the well, which may open a new way to study cold molecular spectroscopy, cold collisions, dipolar-dipolar interaction and collective quantum effects in molecular system, even to realize efficient evaporative cooling of the trapped molecules by lowering the Stark trapping potential, and so on.
Based on the first scheme, we also propose another novel electrostatic trapping scheme (i.e., a controllable electrostatic double-well trap) by using two charged ring wires and two parallel transparent electrodes. The spatial distributions of the electrostatic fields from the above charged wires and the charged transparent electrodes for the different geometric parameters and the corresponding Stark potentials for cold CO molecules are also calculated. We study the relationships between the position of the trapping center and the system parameters, and analyze the evolution of our trap from a double-well trap to a single-well one, and discuss the potential applications of the present scheme in molecular interference, molecular entanglement, and molecular collisions, even to study the molecular BEC in the double-well trap, and so on.
引文
[1] 印建平，物理．32(7)，449-454，(2003)；
[2] 印建平主编，《原子分子光学—基本概念、原理及其最新进展》讲义(2004)；《激光冷却与囚禁》讲义(2006)；
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[50] DeMille D, et al, Eur.phys.J.D., 31, 375 (2004);
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[1] Francoise M S, et al., Adv. At. Mol. Opt. Phys. 47 53 (2001);
[2] van Abeelen F A, et al., Phys. Rev. Lett. 83 1550 (1999);
[3] Bethlem H L, et al., Phys. Rev. Lett. 83 1558 (1999);
[4] Bethlem H L, et al., Nature 406 491 (2000);
[5] Bethlem H L, et al., Phy. Rev. A 65 053416 (2002);
[6] Bochinshi J R, et al., Phys. Rev. Lett. 91 243001-1 (2003);
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[11] Junglen T, et al., Eur. Phys. J. D 31 365 (2004);
[12] Burnett K, et al., Nature 416 225 (2002);
[13] Williams C J and Julienne P S Science 287 986-987 (2000);
[14] Stuhler J, et al., Phys. Rev. Lett. 95 150406 (2005);
[15] Hudson E R, et al., Phys. Rev. Lett. 96 143004-1 (2006);
[16] Weinstein J D, et al., Nature 395 148 (1998);
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[18] Takekoshi T, et al., Phys. Rev. Lett. 81 5105 (1998);
[19] Jongma R T, et al., Chem Phys Lett. 270 304 (1997);
[20] Bethlem H L, et al., Nature 406 491 (2000);
[21] van de Meerakker S Y T, et al., Phys. Rev. Lett. 94 023004 (2005);
[22] van Veldhoven J, et al., Phys. Rev. A 73 063408-1 (2006);
[23] Rieger T, et al., Phys. Rev. Lett. 95 173002-1 (2005);
[24] Katz D P J. Chem. Phys. 107 8491 (1997);
[25] Crompvoets F M H, et al., Nature 411 174 (2001);
[26] Paul W Rev. Mod. Phys. 62 531 (1990);
[27] Choi G W, et al., Electronics Letters. 42(8): 487-489 Apr 13 (2006);
[28] Junglen T, et al., Phys. Rev. Lett. 92 223001-1 (2004);
[29] Burnett K, et al., Nature 416 225 (2002);
[30] Goral K, et al., Phys. Rev. Lett. 88 170406-1 (2002);
[31] Deng L Z, et al., Chin. Phys. 16 707 (2007).
[1] Takekoshi T, et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[2] Weinstein J D, et al, Nature, 395, 148 (1998);
[3] Hendrick L. Bethlem et al, Nature, 406, 491-494(2000);
[4] Jacqueline van Veldhoven, et al, Phys. Rev., Lett. 94, 083001(2005);
[5] Jacqueline van Veldhoven, et al, Phys. Rev. A., 73, 063408 (2006);
[6] Daniel P. Katz, J. Chem. Phys., 107, 8491 (1997);
[7] Floris M.H. Crompvoets, et al, nature, 411, 174 (2001);
[8] Floris M. H. Crompvoets, et al, Phys. Rev. A., 69, 063406 (2004);
[9] Rienk T.Jongma et al, Chem.Phys.Lett. 270, 304 (1997);
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[18] 夸克工作室，有限元分析教学范本FEMLAB与Mathematica，清华大学出版社(2003)：
[19] 刘国强，赵凌志，蒋继娅，Ansoft工程电磁场有限元分析，电子工业出版社(2005)：
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[25] Donley E A, et al, Nature, 417, 529 (2002);
[26] Jens Herbig, et al, Science, 301, 1510 (2003);
[27] Hendrick L.Bethlem, et al, Phys. Rev. Lett., 83, 1558 (1999);
[28] Hendrick L. Bethlem, et al, Phys. Rev.A., 65(5), 053416 (2002);
[2] 印建平主编，《原子分子光学—基本概念、原理及其最新进展》讲义(2004)；《激光冷却与囚禁》讲义(2006)；
[3] Mosk A P et al, Phys. Rev. Lett., 82, 307 (1999);
[4] Herschbach N, et al, Phys. Rev. Lett., 84, 1874 (2000);
[5] McAlexander W I et al, Phys. Rev., A 51, R871 (1995);
[6] Blange J J, et al, Phys. Rev. Lett., 78, 3089 (1997);
[7] Nikolov A N, et al, Phys. Rev. Lett., 84, 246 (2002);
[8] Zinner G, et al, Phys. Rev., Lett., 85, 2292 (2000);
[9] Gabbanini C, et al, Phys. Rev. Lett., 84, 2814 (2000);
[10] Fioretti A, et al, Phys. Rev. Lett., 80, 4402 (1998);
[11] Takasu Y, et al, Phys. Rev. Lett., 93, 123202 (2004);
[12] Nagel S B, et al, Phys. Rev. Lett., 94, 083004 (2005);
[13] Haimberger C, et al, Phys. Rev.A., 70, 021402(R) (2004);
[14] Andrew J. Kerman, et al, Phys. Rev. Lett., 92, 033004 (2004);
[15] Kraft S D, et al, J. Phys. B: At. Mol. Opt. Phys., 39, S993 (2006);
[16] Drummond P D et al, Phys. Rev. Lett., 81, 3055 (1998);
[17] Kevin. E. Strecker, et al. Phys. Rev. Lett., 91, 080406, (2003);
[18] Xu K, et al, Phys. Rev. Lett., 91, 210402, (2003);
[19] Regal C A, et al, Nature, 424, 47, (2003);
[20] Donley E A, et al, Nature, 417, 529 (2002);
[21] Jens Herbig, et al, Science, 301, 1510 (2003);
[22] Hendrick L. Bethlem, et al, Phys. Rev. Lett., 83, 1558 (1999);
[23] Hendrick L. Bethlem, et al, Phys. Rev. A., 65(5), 053416 (2002);
[24] Bochinski J R, et al, Phys. Rev. Lett., 94, 023004(2005);
[25] van de Meerakker SY T, et al, Phys. Rev. Lett., 91, 243001 (2003);
[26] Tarbutt M R, et al, Phys. Rev. Lett., 92, 173002 (2004);
[27] Eric R. Hudson, et al, Phys. Rev.A., 73(6), 063404 (2006);
[28] Sebastian Jun, et al, Phys.Rev.A., 74(4), 040701 (2006);
[29] Weinstein J D, et al, Nature, 395, 148 (1998);
[30] deCarvalho R., et al, Eur. Phys. J. D., 7, 289 (1999);
[31] Maussang K, et al, Phys. Rev. Lett., 94 (12), 23002 (2005);
[32] Egorov D, et al, Eur. Phys. J. D., 31 (2),, 307 (2004);
[33] Egorov D, et al, Phys. Rev.A., 63 (3), 030501 (2001);
[34] Rangwala S A, et al, Phys. Rev., A. 67, 043406 (2003);
[35] Junglen T, et al, Eur.Phys.J.D., 31, 365 (2004);
[36] Fulton R, et al, Phys. Rev. Lett., 93, 243004 (2004);
[37] Fulton R, et al, Nature Phys., 2, 465 (2006);
[38] Manish Gupta, et al, J.Phys.Chem.A., 105,1626 (2001);
[39] Michael S. Elioff, et al, Science, 302,1940 (2003);
[40] Hendrick L. Bethlem et al, Nature, 406, 491-494(2000);
[41] Daniel P. Katz, J. Chem. Phys., 107, 8491 (1997);
[42] Floris M.H. Crompvoets, et al, nature, 411,174 (2001);
[43] Floris M. H. Crompvoets, et al, Phys. Rev. A., 69, 063406 (2004);
[44] Jacqueline van Veldhoven, et al, Phys. Rev., Lett. 94, 083001(2005);
[45] Hendrick L. Bethlem et al, Phys. Rev. A., 74, 063403 (2006);
[46] Jacqueline van Veldhoven, et al, Phys.Rev.A., 73, 063408 (2006);
[47] Takekoshi T, et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[48] Rienk T. Jongma et al, Chem.Phys.Lett. 270, 304 (1997);
[49] Brian C.Sawyer, et al, Phys. Rev. Lett., 98, 253002 (2007);
[50] DeMille D, et al, Eur.phys.J.D., 31, 375 (2004);
[51] Rieger T, et al, Phys. Rev. Lett., 95,173002 (2005);
[1] Francoise M S, et al., Adv. At. Mol. Opt. Phys. 47 53 (2001);
[2] van Abeelen F A, et al., Phys. Rev. Lett. 83 1550 (1999);
[3] Bethlem H L, et al., Phys. Rev. Lett. 83 1558 (1999);
[4] Bethlem H L, et al., Nature 406 491 (2000);
[5] Bethlem H L, et al., Phy. Rev. A 65 053416 (2002);
[6] Bochinshi J R, et al., Phys. Rev. Lett. 91 243001-1 (2003);
[7] Egorov D, et al., Phys. Rev. A 66 04340 (2002);
[8] Fulton R, et al., Phys. Rev. Lett. 91 243004-1 (2004);
[9] Fulton R, et al., Nature Phys. 2465 (2006);
[10] Rangwala S A, et al., Phys. Rev. 67 043406-1 (2003);
[11] Junglen T, et al., Eur. Phys. J. D 31 365 (2004);
[12] Burnett K, et al., Nature 416 225 (2002);
[13] Williams C J and Julienne P S Science 287 986-987 (2000);
[14] Stuhler J, et al., Phys. Rev. Lett. 95 150406 (2005);
[15] Hudson E R, et al., Phys. Rev. Lett. 96 143004-1 (2006);
[16] Weinstein J D, et al., Nature 395 148 (1998);
[17] van de Meerakker S Y T, et al., Phys. Rev. A 64 041401-1 (2001);
[18] Takekoshi T, et al., Phys. Rev. Lett. 81 5105 (1998);
[19] Jongma R T, et al., Chem Phys Lett. 270 304 (1997);
[20] Bethlem H L, et al., Nature 406 491 (2000);
[21] van de Meerakker S Y T, et al., Phys. Rev. Lett. 94 023004 (2005);
[22] van Veldhoven J, et al., Phys. Rev. A 73 063408-1 (2006);
[23] Rieger T, et al., Phys. Rev. Lett. 95 173002-1 (2005);
[24] Katz D P J. Chem. Phys. 107 8491 (1997);
[25] Crompvoets F M H, et al., Nature 411 174 (2001);
[26] Paul W Rev. Mod. Phys. 62 531 (1990);
[27] Choi G W, et al., Electronics Letters. 42(8): 487-489 Apr 13 (2006);
[28] Junglen T, et al., Phys. Rev. Lett. 92 223001-1 (2004);
[29] Burnett K, et al., Nature 416 225 (2002);
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