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Rydberg Atoms in Strong Static Fields

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Springer Handbook of Atomic, Molecular, and Optical Physics

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Abstract

Semiclassical approximations provide a connection between quantum mechanics and classical mechanics. That relationship is problematic when classical orbits are chaotic. Highly excited states of atoms have provided a laboratory for the study of this relationship. When classical trajectories are orderly, corresponding quantum spectra and wave-functions display the same type of order. When they are chaotic, the quantum spectrum is very complex, but short closed classical orbits are connected to the large-scale structure of the density of states and the absorption spectrum.

This chapter is restricted to a discussion of Rydberg atoms in strong static fields. Related information on atoms in strong fields, on Rydberg atoms, and on the interaction of atoms with strong laser fields can be found elsewhere in the book.

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References

  1. Hilborn, R.C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2nd edn. Oxford Univ. Press, Oxford, New York (2000)

    MATH  Google Scholar 

  2. Jackson, E.A.: Perspectives of Nonlinear Dynamics. Cambridge Univ. Press, Cambridge (1990)

    MATH  Google Scholar 

  3. Haake, F.: Quantum Signatures of Chaos, 2nd edn. Springer Series in Synergetics, vol. 54. Springer, Berlin, Heidelberg, New York (2013)

    MATH  Google Scholar 

  4. Gutzwiller, M.C.: Chaos in Classical and Quantum Mechanics. Interdisciplinary Applied Mathematics, vol. 1. Springer, Berlin, Heidelberg, New York (2013)

    MATH  Google Scholar 

  5. Berggren, K.: Quantum Chaos Y2K: Proceedings of Nobel Symposium 116, Bäckaskog Castle, Sweden, June 13–17, 2000. World Scientific, Singapore (2001)

    MATH  Google Scholar 

  6. Bayfield, J.E.: Phys. Rep. 51, 317 (1979)

    ADS  Google Scholar 

  7. Delos, J., Knudson, S., Noid, D.: Phys. Rev. A 30, 1208 (1984)

    ADS  Google Scholar 

  8. Delande, D., Gay, J.: Comments At. Mol. Phys. 19, 35 (1986)

    Google Scholar 

  9. Casati, G., Chirikov, B.V., Shepelyansky, D.L., Guarneri, I.: Phys. Rep. 154, 77 (1987)

    ADS  Google Scholar 

  10. Hasegawa, H.: Prog. Theor. Phys. Suppl. 98, 198 (1989)

    ADS  Google Scholar 

  11. Friedrich, H., Wintgen, D.: Phys. Rep. 183, 37 (1989)

    MathSciNet  ADS  Google Scholar 

  12. Lu, K.T., Tomkins, F.S., Garton, W.R.S.: Proc. R. Soc. A 362, 421 (1978)

    ADS  Google Scholar 

  13. Holle, A., Main, J., Wiebusch, G., Rottke, H., Welge, K.: Phys. Rev. Lett. 61, 161 (1988)

    ADS  Google Scholar 

  14. Main, J., Wiebusch, G., Holle, A., Welge, K.: Phys. Rev. Lett. 57, 2789 (1986)

    ADS  Google Scholar 

  15. Waterland, R., Delos, J., Du, M.: Phys. Rev. A 35, 5064 (1987)

    ADS  Google Scholar 

  16. Raithel, G., Fauth, M., Walther, H.: Phys. Rev. A 44, 1898 (1991)

    ADS  Google Scholar 

  17. Freund, S., Ubert, R., Flöthmann, E., Welge, K., Wang, D., Delos, J.: Phys. Rev. A 65, 53408 (2002)

    ADS  Google Scholar 

  18. Connerade, J., Zhan, M., Rao, J., Taylor, K.: J. Phys. B 32, 2351 (1999)

    ADS  Google Scholar 

  19. Bartsch, T., Main, J., Wunner, G.: Phys. Rev. A 67, 063411 (2003)

    ADS  Google Scholar 

  20. Von Milczewski, J., Uzer, T.: Phys. Rev. E 55, 6540 (1997)

    ADS  Google Scholar 

  21. Gallagher, T.F.: Rydberg Atoms. Cambridge Monographs on Atomic, Molecular and Chemical Physics, vol. 3. Cambridge Univ. Press, Cambridge (2005)

    Google Scholar 

  22. Friedrich, H.: Theoretical Atomic Physics, 3rd edn. Springer, Berlin, Heidelberg (2006)

    MATH  Google Scholar 

  23. Rao, J., Taylor, K.: J. Phys. B 30, 3627 (1997)

    ADS  Google Scholar 

  24. Knudson, S., Delos, J., Bloom, B.: J. Chem. Phys. 83, 5703 (1985)

    MathSciNet  ADS  Google Scholar 

  25. Knudson, S.K., Delos, J.B., Noid, D.W.: J. Chem. Phys. 84, 6886 (1986)

    ADS  Google Scholar 

  26. Delos, J.B.: Adv. Chem. Phys. 65, 161 (1986)

    Google Scholar 

  27. Littlejohn, R.G.: J. Stat. Phys. 68, 7 (1992)

    ADS  Google Scholar 

  28. Maslov, V.P., Fedoriuk, M.V.: Semi-Classical Approximations in Quantum Mechanics. D. Reidel Publishing Company, Dordrecht (1981)

    Google Scholar 

  29. Solov’ev, E.: Sov. Phys. JETP 55, 1017 (1982)

    ADS  Google Scholar 

  30. Herrick, D.R.: Phys. Rev. A 26, 323 (1982)

    MathSciNet  ADS  Google Scholar 

  31. Noid, D.W., Marcus, R.A.: J. Chem. Phys. 62, 2119 (1975)

    ADS  Google Scholar 

  32. Keller, J.B.: Ann. Phys. 4, 180 (1958)

    ADS  Google Scholar 

  33. Stone, A.D.: Phys. Today 58, 37 (2005)

    Google Scholar 

  34. Berry, M.V.: Les Houches Lect. Ser. 36, 171 (1983)

    Google Scholar 

  35. Berry, M.V.: In: The Wave-Particle Dualism: A Tribute to Louis de Broglie on his 90th Birthday, p. 231. D. Reidel Publishing Company, Dordrecht, Boston, Lancaster (1984)

    Google Scholar 

  36. Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer, New York (1978)

    Google Scholar 

  37. Arnold, V., Avez, A.: Ergodic Problems of Classical Mechanics. Benjamin Inc., New York (1968)

    MATH  Google Scholar 

  38. Moser, J.K.: Stable and Random Motions in Dynamical Systems. Princeton Univ. Press, Princeton (1973)

    MATH  Google Scholar 

  39. Hansen, K.T.: Phys. Rev. E 51, 1838 (1995)

    ADS  Google Scholar 

  40. Courtney, M., Kleppner, D.: Phys. Rev. A 53, 178 (1996)

    ADS  Google Scholar 

  41. Chernov, N., Markarian, R.: Chaotic Billiards. American Mathematical Society, Providence (2006)

    MATH  Google Scholar 

  42. Doron, E., Smilansky, U.: Nonlinearity 5, 1055 (1992)

    MathSciNet  ADS  Google Scholar 

  43. Sridhar, S., Hogenboom, D., Willemsen, B.A.: J. Stat. Phys. 68, 239 (1992)

    ADS  Google Scholar 

  44. Berry, M.V.: R. Soc. Lond. Proc. Ser. A 413, 183 (1987)

    ADS  Google Scholar 

  45. Du, M., Delos, J.: Phys. Rev. A 38, 1896 (1988)

    ADS  Google Scholar 

  46. Du, M., Delos, J.: Phys. Rev. A 38, 1913 (1988)

    ADS  Google Scholar 

  47. Bogomol’nyi, E.: Sov. Phys. JETP 69, 275 (1989)

    ADS  Google Scholar 

  48. Main, J., Wiebusch, G., Welge, K., Shaw, J., Delos, J.: Phys. Rev. A 49, 847 (1994)

    ADS  Google Scholar 

  49. Gao, J., Delos, J.B.: Phys. Rev. A 49, 869 (1994)

    ADS  Google Scholar 

  50. Spellmeyer, N., Kleppner, D., Haggerty, M.R., Kondratovich, V., Delos, J.B., Gao, J.: Phys. Rev. Lett. 79, 1650 (1997)

    ADS  Google Scholar 

  51. Haggerty, M., Delos, J.: Phys. Rev. A 61, 53406 (2000)

    ADS  Google Scholar 

  52. Jensen, R.V., Flores-Rueda, H., Wright, J.D., Keeler, M.L., Morgan, T.J.: Phys. Rev. A 62, 53410 (2000)

    ADS  Google Scholar 

  53. Keeler, M.L.: Phys. Rev. A 77, 34503 (2008)

    ADS  Google Scholar 

  54. Karremans, K., Vassen, W., Hogervorst, W.: Phys. Rev. A 60, 4764 (1999)

    ADS  Google Scholar 

  55. Courtney, M., Jiao, H., Spellmeyer, N., Kleppner, D., Gao, J., Delos, J.B.: Phys. Rev. Lett. 74, 1538 (1995)

    ADS  Google Scholar 

  56. Mao, J., Delos, J.: Phys. Rev. A 45, 1746 (1992)

    ADS  Google Scholar 

  57. Sadovskii, D.A., Shaw, J.A., Delos, J.B.: Phys. Rev. Lett. 75, 2120 (1995)

    ADS  Google Scholar 

  58. Sadovskii, D.A., Delos, J.B.: Phys. Rev. E 54, 2033 (1996)

    ADS  Google Scholar 

  59. Shaw, J.A., Robicheaux, F.: Phys. Rev. A 58, 3561 (1998)

    ADS  Google Scholar 

  60. Kips, A., Vassen, W., Hogervorst, W.: Phys. Rev. A 59, 2948 (1999)

    ADS  Google Scholar 

  61. Gao, J., Delos, J.B.: Phys. Rev. A 56, 356 (1997)

    ADS  Google Scholar 

  62. Wang, D., Delos, J.: Phys. Rev. A 63, 43409 (2001)

    ADS  Google Scholar 

  63. Main, J., Wunner, G.: Phys. Rev. A 55, 1743 (1997)

    ADS  Google Scholar 

  64. Haggerty, M., Spellmeyer, N., Kleppner, D., Delos, J.: Phys. Rev. Lett. 81, 1592 (1998)

    ADS  Google Scholar 

  65. Peters, A.D., Jaffé, C., Delos, J.B.: Phys. Rev. Lett. 73, 2825 (1994)

    ADS  Google Scholar 

  66. Shaw, J.A., Robicheaux, F.: Phys. Rev. A 58, 1910 (1998)

    ADS  Google Scholar 

  67. Bartsch, T., Main, J., Wunner, G.: J. Phys. A 32, 3013 (1999)

    MathSciNet  ADS  Google Scholar 

  68. Bartsch, T., Main, J., Wunner, G.: Ann. Phys. 277, 19 (1999)

    ADS  Google Scholar 

  69. Bartsch, T., Main, J., Wunner, G.: Phys. Rev. A 66, 033404 (2002)

    ADS  Google Scholar 

  70. Fabčič, T., Main, J., Bartsch, T., Wunner, G.: J. Phys. B 38, 219 (2005)

    ADS  Google Scholar 

  71. Kondratovich, V., Delos, J.B., Spellmeyer, N., Kleppner, D.: Phys. Rev. A 62, 043409 (2000)

    ADS  Google Scholar 

  72. Gao, J., Delos, J.B.: Phys. Rev. A 46, 1455 (1992)

    ADS  Google Scholar 

  73. Dando, P.A., Monteiro, T.S., Delande, D., Taylor, K.T.: Phys. Rev. Lett. 74, 1099 (1995)

    ADS  Google Scholar 

  74. Dando, P.A., Monteiro, T.S., Delande, D., Taylor, K.T.: Phys. Rev. A 54, 127 (1996)

    ADS  Google Scholar 

  75. Matzkin, A., Monteiro, T.S.: Phys. Rev. Lett. 87, 143002 (2001)

    ADS  Google Scholar 

  76. Beims, M., Kondratovich, V., Delos, J.: Phys. Rev. A 62, 43401 (2000)

    ADS  Google Scholar 

  77. Johnson, B.R., Kinsey, J.L.: Phys. Rev. Lett. 62, 1607 (1989)

    ADS  Google Scholar 

  78. Farantos, S.C.: Laser Chem. 13, 87 (1993)

    Google Scholar 

  79. Farantos, S.C.: Int. Rev. Phys. Chem. 15, 345 (1996)

    Google Scholar 

  80. Prosmiti, R., Farantos, S.C.: J. Chem. Phys. 118, 8275 (2003)

    ADS  Google Scholar 

  81. Jaffé, C., Farrelly, D., Uzer, T.: Phys. Rev. Lett. 84, 610 (2000)

    ADS  Google Scholar 

  82. Jaffé, C., Uzer, T.: Ann. N. Y. Acad. Sci. 1017, 39 (2004)

    ADS  Google Scholar 

  83. Jaffé, C., Ross, S.D., Lo, M.W., Marsden, J., Farrelly, D., Uzer, T.: Phys. Rev. Lett. 89, 11101 (2002)

    ADS  Google Scholar 

  84. Uzer, T., Jaffe, C., Palacian, J., Yanguas, P., Wiggins, S.: Nonlinearity 15, 957 (2002)

    MathSciNet  ADS  Google Scholar 

  85. Jaffé, C., Farrelly, D., Uzer, T.: Phys. Rev. A 60, 3833 (1999)

    ADS  Google Scholar 

  86. Müller, S., Heusler, S., Braun, P., Haake, F.: New J. Phys. 9, 12 (2007)

    ADS  Google Scholar 

  87. Jensen, R.: Chaos 1, 101 (1991)

    MathSciNet  ADS  Google Scholar 

  88. Main, J., Wunner, G.: Phys. Rev. Lett. 69, 586 (1992)

    ADS  Google Scholar 

  89. Tiyapan, A., Jaffé, C.: J. Chem. Phys. 103, 5499 (1995)

    ADS  Google Scholar 

  90. Hansen, K.T., Güttler, S.: J. Phys. A 30, 3421 (1997)

    MathSciNet  ADS  Google Scholar 

  91. Stania, G., Walther, H.: Phys. Rev. Lett. 95, 194101 (2005)

    ADS  Google Scholar 

  92. Mandelbrot, B.B.: The Fractal Geometry of Nature. W.H. Freeman Company, New York (1982)

    MATH  Google Scholar 

  93. Keen, L., Devaney, R.L., Alligood, K.T.: Chaos and Fractals: The Mathematics Behind the Computer Graphics. American Mathematical Society, Providence (1989)

    Google Scholar 

  94. Barnsley, M.F.: Fractals Everywhere, 2nd edn. Academic Press, Massachusetts (1993)

    MATH  Google Scholar 

  95. Falconer, K.: Fractals: A Very Short Introduction. Oxford Univ. Press, Oxford (2013)

    MATH  Google Scholar 

  96. Mitchell, K., Handley, J., Tighe, B., Delos, J., Knudson, S.: Chaos 13, 880 (2003)

    MathSciNet  ADS  Google Scholar 

  97. Mitchell, K., Handley, J., Delos, J., Knudson, S.: Chaos 13, 892 (2003)

    MathSciNet  ADS  Google Scholar 

  98. Mitchell, K.A., Delos, J.B.: Physica D 221, 170 (2006)

    MathSciNet  ADS  Google Scholar 

  99. Mitchell, K.A.: Physica D 238, 737 (2009)

    MathSciNet  ADS  Google Scholar 

  100. Mitchell, K., Handley, J., Tighe, B., Flower, A., Delos, J.: Phys. Rev. Lett. 92, 73001 (2004)

    ADS  Google Scholar 

  101. Mitchell, K., Handley, J., Tighe, B., Flower, A., Delos, J.: Phys. Rev. A 70, 43407 (2004)

    ADS  Google Scholar 

  102. Delos, J., Mitchell, K.: Few-Body Syst. 38, 181 (2006)

    ADS  Google Scholar 

  103. Mitchell, K.A., Delos, J.B.: Physica D 229, 9 (2007)

    MathSciNet  ADS  Google Scholar 

  104. Burke, K., Mitchell, K.A.: 2010 Annual Meeting of the California-Nevada Section of the APS, Vol. 55 (2010)

    Google Scholar 

  105. Wang, L., Yang, H., Liu, X., Liu, H., Zhan, M., Delos, J.: Phys. Rev. A 82, 22514 (2010)

    ADS  Google Scholar 

  106. Shan-Hong, D., Song, G., Yong-Ping, L., Xue-You, X., Sheng-Lu, L.: Chin. Phys. B 19, 040511 (2010)

    Google Scholar 

  107. Topçu, T.Ü., Robicheaux, F.: Abstract 5005. In: APS 37th Meeting of the Division of Atomic, Molecular and Optical Physics 2006 (2006)

    Google Scholar 

  108. Hansen, P., Mitchell, K.A., Delos, J.B.: Phys. Rev. E 73, 66226 (2006)

    ADS  Google Scholar 

  109. Novick, J., Keeler, M.L., Giefer, J., Delos, J.B.: Phys. Rev. E 85, 016205 (2012)

    ADS  Google Scholar 

  110. Novick, J., Delos, J.B.: Phys. Rev. E 85, 016206 (2012)

    ADS  Google Scholar 

  111. Mitchell, K.A., Steck, D.A.: Phys. Rev. A 76, 31403 (2007)

    ADS  Google Scholar 

  112. Ivory, M.K., Byrd, T.A., Pyle, A.J., Das, K.K., Mitchell, K.A., Aubin, S., Delos, J.B.: Phys. Rev. A 90, 023602 (2014)

    ADS  Google Scholar 

  113. Byrd, T.A., Das, K.K., Mitchell, K.A., Aubin, S., Delos, J.B.: Phys. Rev. E 90, 052107 (2014)

    ADS  Google Scholar 

  114. Byrd, T.A., Delos, J.B.: Phys. Rev. E 89, 022907 (2014)

    ADS  Google Scholar 

  115. Budyansky, M.V., Uleysky, M.Y., Prants, S.V.: J. Exp. Theor. Phys. 99, 1018 (2004)

    ADS  Google Scholar 

  116. Budyansky, M., Prants, S.: In: Proceedings of the 2005 International Conference of Physics and Control, p. 556. (2005)

    Google Scholar 

  117. Collins, P., Ezra, G.S., Wiggins, S.: Phys. Rev. E 86, 056218 (2012)

    ADS  Google Scholar 

  118. Avron, J., Herbst, I., Simon, B.: Ann. Phys. 114, 431 (1978)

    ADS  Google Scholar 

  119. Schmelcher, P., Cederbaum, L.S.: arXiv preprint physics/9909045 (1999)

    Google Scholar 

  120. Schmelcher, P., Cederbaum, L.: Int. J. Quantum Chem. 40, 371 (1991)

    Google Scholar 

  121. Schmelcher, P.: Phys. Rev. A 64, 063412 (2001)

    ADS  Google Scholar 

  122. Melezhik, V., Schmelcher, P.: Phys. Rev. Lett. 84, 1870 (2000)

    ADS  Google Scholar 

  123. Schmelcher, P., Cederbaum, L.: Struct. Bonding 86, 27 (1997)

    Google Scholar 

  124. Ruder, H., Wunner, G., Herold, H., Geyer, F.: Atoms in Strong Magnetic Fields: Quantum Mechanical Treatment and Applications in Astrophysics and Quantum Chaos. Springer, Berlin (1994)

    Google Scholar 

  125. Friedrich, H., Eckhardt, B.: Classical, Semiclassical and Quantum Dynamics in Atoms. Springer, Berlin, Heidelberg (2014)

    MATH  Google Scholar 

  126. Friedrich, H.: Theoretical Atomic Physics, 4th edn. Springer, Berlin (2017)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Butterfly Dynamics LLC, Williamsburg, VA, USA

    John B. Delos

  2. Mathematical Sciences, Loughborough University, Leicestershire, UK

    Thomas Bartsch

  3. School of Physics, Georgia Institute of Technology, Atlanta, GA, USA

    Turgay Uzer

Authors
  1. John B. Delos
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  2. Thomas Bartsch
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  3. Turgay Uzer
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Correspondence to John B. Delos .

Editor information

Editors and Affiliations

  1. Dept. of Physics, University of Windsor, N9B 3P4, Windsor, ON, Canada

    Gordon W. F. Drake

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Delos, J.B., Bartsch, T., Uzer, T. (2023). Rydberg Atoms in Strong Static Fields. In: Drake, G.W.F. (eds) Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-73893-8_16

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