冷分子静电表面囚禁及其静电晶格的理论研究
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摘要
由于冷分子或超冷分子在基本物理问题的研究、基本物理常数的精密测量、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、量子计算与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冷却与囚禁的基本原理、实验结果及其最新进展；然后就极性冷分子的静电表面囚禁及其静电晶格新方案进行了理论研究；最后就本文的研究工作进行了简单总结与展望。
本文首先提出了利用单个环形电极在介质板(芯片)表面实现极性冷分子静电囚禁的新方案。金属环形导体平放在介质板上表面，而介质板的下表面接地。如果给金属导体加上一个正高压，则在金属导体的周围将产生的一个非均匀静电场分布，并在介质板上方形成一个中心电场为零的静电阱。由于一阶Stark效应，如果处在弱场搜寻态的分子被装载到这个静电阱中，则将受到一个指向势阱中心的电场偶极力作用，从而冷分子将被囚禁在这一静电阱中。我们利用有限元软件计算了该囚禁方案在介质上方的空间电场强度分布(和相应的CO分子的Stark势分布)，分析了静电场及其Stark势与该方案几何参数间的关系，研究了电场最小值位置与该方案几何参数间的关系。我们还从三个方面分析了该表面囚禁方案的可行性，提出了一种有效的装载方法，并对冷分子装载的动力学过程进行了蒙特卡罗模拟，得到了一些重要的模拟结果，可为进一步的实验研究提供可靠的理论依据。
本文又提出了采用单个方形载荷电极实现极性冷分子静电表面囚禁的新方案。类似地，利用数值计算方法分析了该方案产生的静电场分布与势阱几何参数间的关系，研究了电场最小值位置与该方案几何参数间的关系。接着，我们将方形载荷导线扩展至二维空间，以形成芯片表面的二维(2D)静电晶格，实现极性冷分子的2D微静电表面囚禁，并计算了2D静电晶格的空间电场强度分布及其在x(或y)、z方向的电场分布及其阱深，讨论了这一2D静电晶格方案在集成分子光学及其分子芯片、量子光学、量子计算与量子信息处理等方面的潜在应用。
Cold molecules have some important applications in high-resolution spectroscopy and precise measurement, study of cold chemical reaction and cold collision, interferometer of matter wave, and quantum computing and information possessing and so on, the study of generation and application of cold molecules has obtained fast development. In this thesis, firstly, the principle, experiment and recent progress on cooling and trapping of neutral molecules have been briefly reviewed. Secondly, we give the theoretical study for the new schemes of electrostatic surface trapping and electrostatic lattice. In final, our research work is summarized and the future investigation is briefly looked ahead.
We propose a new scheme to realize electrostatic surface trap for cold poplar molecules on a substrate by a single charged circular wire on a substrate and a grounded metal plate. When the positive voltage is applied on the circular wire, there will be an electrostatic well on the substrate. If the cold molecules in the low-field-seeking state interact with the electric field, they will feel a dipole gradient force due to the first-order Stark effect, and then the molecules will be attracted to the minimum of the electric field. We use commercial finite element software to calculate the spatial distribution of the electrostatic field of our charged circular wire and the distribution of its corresponding Stark trapping potential for CO molecules, and study the relationship between the position of the trapping center and the geometric parameters. We also analyze the feasibility of the scheme from three aspects, and propose an effective loading way and perform Monte-Carlo simulation for the dynamics process. The important results obtained supply reliably theoretical base for the experiment study.
We also propose a novel electrostatic surface-trapping scheme by using a single charged square wire on the surface of the insulating substrate. We study the relationship between the position of the trapping center and the geometric parameters, and calculated the corresponding electric field distribution and its Stark trapping potential for cold CO molecules. We extend our single square wire to two-dimensional array for forming 2D molecular lattice, and realize electrostatic microstructure surface trapping. We calculated spatial electric field distribution in the x and z direction through the trapping center and the corresponding well depth, and discussed the potential applications of such 2D electrostatic lattice scheme in the
fields of integrated molecule optics and molecular chip, quantum optics, quantum computing and information processing, etc.
本文首先提出了利用单个环形电极在介质板(芯片)表面实现极性冷分子静电囚禁的新方案。金属环形导体平放在介质板上表面，而介质板的下表面接地。如果给金属导体加上一个正高压，则在金属导体的周围将产生的一个非均匀静电场分布，并在介质板上方形成一个中心电场为零的静电阱。由于一阶Stark效应，如果处在弱场搜寻态的分子被装载到这个静电阱中，则将受到一个指向势阱中心的电场偶极力作用，从而冷分子将被囚禁在这一静电阱中。我们利用有限元软件计算了该囚禁方案在介质上方的空间电场强度分布(和相应的CO分子的Stark势分布)，分析了静电场及其Stark势与该方案几何参数间的关系，研究了电场最小值位置与该方案几何参数间的关系。我们还从三个方面分析了该表面囚禁方案的可行性，提出了一种有效的装载方法，并对冷分子装载的动力学过程进行了蒙特卡罗模拟，得到了一些重要的模拟结果，可为进一步的实验研究提供可靠的理论依据。
本文又提出了采用单个方形载荷电极实现极性冷分子静电表面囚禁的新方案。类似地，利用数值计算方法分析了该方案产生的静电场分布与势阱几何参数间的关系，研究了电场最小值位置与该方案几何参数间的关系。接着，我们将方形载荷导线扩展至二维空间，以形成芯片表面的二维(2D)静电晶格，实现极性冷分子的2D微静电表面囚禁，并计算了2D静电晶格的空间电场强度分布及其在x(或y)、z方向的电场分布及其阱深，讨论了这一2D静电晶格方案在集成分子光学及其分子芯片、量子光学、量子计算与量子信息处理等方面的潜在应用。
Cold molecules have some important applications in high-resolution spectroscopy and precise measurement, study of cold chemical reaction and cold collision, interferometer of matter wave, and quantum computing and information possessing and so on, the study of generation and application of cold molecules has obtained fast development. In this thesis, firstly, the principle, experiment and recent progress on cooling and trapping of neutral molecules have been briefly reviewed. Secondly, we give the theoretical study for the new schemes of electrostatic surface trapping and electrostatic lattice. In final, our research work is summarized and the future investigation is briefly looked ahead.
We propose a new scheme to realize electrostatic surface trap for cold poplar molecules on a substrate by a single charged circular wire on a substrate and a grounded metal plate. When the positive voltage is applied on the circular wire, there will be an electrostatic well on the substrate. If the cold molecules in the low-field-seeking state interact with the electric field, they will feel a dipole gradient force due to the first-order Stark effect, and then the molecules will be attracted to the minimum of the electric field. We use commercial finite element software to calculate the spatial distribution of the electrostatic field of our charged circular wire and the distribution of its corresponding Stark trapping potential for CO molecules, and study the relationship between the position of the trapping center and the geometric parameters. We also analyze the feasibility of the scheme from three aspects, and propose an effective loading way and perform Monte-Carlo simulation for the dynamics process. The important results obtained supply reliably theoretical base for the experiment study.
We also propose a novel electrostatic surface-trapping scheme by using a single charged square wire on the surface of the insulating substrate. We study the relationship between the position of the trapping center and the geometric parameters, and calculated the corresponding electric field distribution and its Stark trapping potential for cold CO molecules. We extend our single square wire to two-dimensional array for forming 2D molecular lattice, and realize electrostatic microstructure surface trapping. We calculated spatial electric field distribution in the x and z direction through the trapping center and the corresponding well depth, and discussed the potential applications of such 2D electrostatic lattice scheme in the
fields of integrated molecule optics and molecular chip, quantum optics, quantum computing and information processing, etc.
引文
[1] 印建平，物理．32(7)，449(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)；
[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] Y. Takasu, et al, Phys. Rev. Lett., 93, 123202 (2004);
[12] S. B. Nagel, et al, Phys. Rev. Lett., 94, 083004 (2005);
[13] C. Haimberger, et al, Phys. Rev. A., 70, 021402(R) (2004);
[14] Andrew J. Kerman, et al, Phys. Rev. Lett., 92, 033004 (2004);
[15] S D Kraft, 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] K. Xu, et al, Phys. Rev. Lett., 91, 210402, (2003);
[19] C. A. Regal, et al, Nature, 424, 47, (2003);
[20] E. A. Donley, 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] J. R. Bochinski, et al, Phys. Rev. Lett., 94, 023004(2005);
[25] S.Y.T. van de Meerakker, et al, Phys. Rev. Lett., 91, 243001 (2003);
[26] M. R. Tarbutt, 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] J.D.Weinstein, et al, Nature, 395, 148 (1998);
[30] R.deCarvalho, 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] S. A. Rangwala, et al, Phys. Rev., A. 67,043406 (2003);
[35] T. Junglen, et al, Eur.Phys.J.D., 31,365 (2004);
[36] R. Fulton, et al, Phys. Rev. Lett., 93,243004 (2004);
[37] R. Fulton, 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 (2000);
[41] Jacqueline van Veldhoven, et al, Phys. Rev., Lett. 94, 083001(2005);
[42] Jacqueline van Veldhoven, et al, Phys.Rev.A., 73, 063408 (2006);
[43] Daniel P. Katz, J. Chem. Phys., 107, 8491 (1997);
[44] Floris M.H. Crompvoets, et al, nature, 411,174 (2001);
[45] Floris M. H. Crompvoets, et al, Phys. Rev. A., 69,063406 (2004);
[46] Rienk T.Jongma et al, Chem.Phys.Lett. 270, 304 (1997);
[47] D DeMille, et al, Eur.phys.J.D., 31, 375 (2004);
[48] T. Takekoshi et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[49]T. Rieger, et al, Phys. Rev. Lett., 95,173002 (2005);
[1] T. Takekoshi, et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[2] J.D.Weinstein, 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);
[10] T. Takekoshi et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[11] D DeMille, et al, Eur. phys.J.D., 31 375 (2004);
[12] 郭硕鸿，电动力学，高等教育出版社(1984)；
[13] 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)；
[14] 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)；
[15] 黄流兴，牛胜利，蒙特卡罗方法及其应用，陕西科技出版社(2004)；
[16] Yong Xia, et al, Applied Physics B., 81(4), 459 (2005);
[17] Lianzhong Deng, et al, Chin Phys Lett., 22(8), 1887 (2005);
[18] Hendrick L. Bethlem, et al, Physical Chemistry., 22, 73 (2003);
[1] K. S. Johnson, et al, Phys. Rev.Lett., 81(6), 1137 (1998);
[2] J. Denschlag, et al, Phys. Rev.Lett, 82(10), 2014 (1999);
[3] D. Muller, et al, Phys. Rev.Lett, 83(25), 5194 (1999);
[4] J. Denschlag, et al, Appl. Phys, B 69,291 (1999);
[5] J. H. Thywissen, et al, Eur. Phys. J, D 7, 361 (1999);
[6] N. H. Dekker, et al, Phys. Rev.Lett, 84(6), 1124 (2000);
[7] D. Cassettari, et al, Appl. Phys, B70, 721 (2000);
[8] D. Cassettari, et al, Phys. Rev.Lett, 85(26), 5483 (2000);
[9] D. Muller, et al, Opt. Lett, 25(18), 1382 (2000);
[10] Y. Xia, et al, Chin. Phys. Lett, 20(5), 674 (2003);
[11] E. Andersson, et al, Phys. Rev. Lett, 88(10), 100401 (2002);
[12] J. Schmiedmayer, Eur. Phys. J, D 4, 57 (1998);
[13] J. H. Thywissen, et al, Phys. Rev.Lett, 83(19), 3762 (1999);
[14] R.Folman, et al, Phys. Rev.Lett, 84(20), 4749 (2000);
[15] W. Hansel, et al, Nature, 413,498 (2001);
[16] D. E. Pritchard, Phys. Rev.Lett, 51,1336 (1995);
[17] W. Hansel, et al, Nature 413,498 (2001);
[18] J. Reichel, et al, Appl. Phys, B 74,469 (2002);
[19] M. P. AJones, et al, Phys. Rev.Lett, 91,080401 (2002);
[20] Philipp Treutlein, et al, Phys. Rev.Lett, 92,203005 (2004);
[21] D. DeMille, Phys. Rev.Lett, 88,067901 (2002);
[22] P.Rable, et al, Phys. Rev.Lett, 97,033003 (2006);
[23] A.Andre, et al, Nature Physics, 2, 636 (2006);
[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] Y. Takasu, et al, Phys. Rev. Lett., 93, 123202 (2004);
[12] S. B. Nagel, et al, Phys. Rev. Lett., 94, 083004 (2005);
[13] C. Haimberger, et al, Phys. Rev. A., 70, 021402(R) (2004);
[14] Andrew J. Kerman, et al, Phys. Rev. Lett., 92, 033004 (2004);
[15] S D Kraft, 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] K. Xu, et al, Phys. Rev. Lett., 91, 210402, (2003);
[19] C. A. Regal, et al, Nature, 424, 47, (2003);
[20] E. A. Donley, 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] J. R. Bochinski, et al, Phys. Rev. Lett., 94, 023004(2005);
[25] S.Y.T. van de Meerakker, et al, Phys. Rev. Lett., 91, 243001 (2003);
[26] M. R. Tarbutt, 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] J.D.Weinstein, et al, Nature, 395, 148 (1998);
[30] R.deCarvalho, 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] S. A. Rangwala, et al, Phys. Rev., A. 67,043406 (2003);
[35] T. Junglen, et al, Eur.Phys.J.D., 31,365 (2004);
[36] R. Fulton, et al, Phys. Rev. Lett., 93,243004 (2004);
[37] R. Fulton, 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 (2000);
[41] Jacqueline van Veldhoven, et al, Phys. Rev., Lett. 94, 083001(2005);
[42] Jacqueline van Veldhoven, et al, Phys.Rev.A., 73, 063408 (2006);
[43] Daniel P. Katz, J. Chem. Phys., 107, 8491 (1997);
[44] Floris M.H. Crompvoets, et al, nature, 411,174 (2001);
[45] Floris M. H. Crompvoets, et al, Phys. Rev. A., 69,063406 (2004);
[46] Rienk T.Jongma et al, Chem.Phys.Lett. 270, 304 (1997);
[47] D DeMille, et al, Eur.phys.J.D., 31, 375 (2004);
[48] T. Takekoshi et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[49]T. Rieger, et al, Phys. Rev. Lett., 95,173002 (2005);
[1] T. Takekoshi, et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[2] J.D.Weinstein, 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);
[10] T. Takekoshi et al, Phys. Rev. Lett., 81(23), 5105 (1998);
[11] D DeMille, et al, Eur. phys.J.D., 31 375 (2004);
[12] 郭硕鸿，电动力学，高等教育出版社(1984)；
[13] 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)；
[14] 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)；
[15] 黄流兴，牛胜利，蒙特卡罗方法及其应用，陕西科技出版社(2004)；
[16] Yong Xia, et al, Applied Physics B., 81(4), 459 (2005);
[17] Lianzhong Deng, et al, Chin Phys Lett., 22(8), 1887 (2005);
[18] Hendrick L. Bethlem, et al, Physical Chemistry., 22, 73 (2003);
[1] K. S. Johnson, et al, Phys. Rev.Lett., 81(6), 1137 (1998);
[2] J. Denschlag, et al, Phys. Rev.Lett, 82(10), 2014 (1999);
[3] D. Muller, et al, Phys. Rev.Lett, 83(25), 5194 (1999);
[4] J. Denschlag, et al, Appl. Phys, B 69,291 (1999);
[5] J. H. Thywissen, et al, Eur. Phys. J, D 7, 361 (1999);
[6] N. H. Dekker, et al, Phys. Rev.Lett, 84(6), 1124 (2000);
[7] D. Cassettari, et al, Appl. Phys, B70, 721 (2000);
[8] D. Cassettari, et al, Phys. Rev.Lett, 85(26), 5483 (2000);
[9] D. Muller, et al, Opt. Lett, 25(18), 1382 (2000);
[10] Y. Xia, et al, Chin. Phys. Lett, 20(5), 674 (2003);
[11] E. Andersson, et al, Phys. Rev. Lett, 88(10), 100401 (2002);
[12] J. Schmiedmayer, Eur. Phys. J, D 4, 57 (1998);
[13] J. H. Thywissen, et al, Phys. Rev.Lett, 83(19), 3762 (1999);
[14] R.Folman, et al, Phys. Rev.Lett, 84(20), 4749 (2000);
[15] W. Hansel, et al, Nature, 413,498 (2001);
[16] D. E. Pritchard, Phys. Rev.Lett, 51,1336 (1995);
[17] W. Hansel, et al, Nature 413,498 (2001);
[18] J. Reichel, et al, Appl. Phys, B 74,469 (2002);
[19] M. P. AJones, et al, Phys. Rev.Lett, 91,080401 (2002);
[20] Philipp Treutlein, et al, Phys. Rev.Lett, 92,203005 (2004);
[21] D. DeMille, Phys. Rev.Lett, 88,067901 (2002);
[22] P.Rable, et al, Phys. Rev.Lett, 97,033003 (2006);
[23] A.Andre, et al, Nature Physics, 2, 636 (2006);