Coherent states in a Rydberg atom: Classical mechanics

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 55, Issue 3, 1997, Pages 2203-2221

  Lee, Ernestine ^a   Brunello, Andrea F ^a,b   Farrelly, David ^a  

^a UTAH STATE UNIVERSITY   (United States)

^b STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001058891     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.55.2203     Document Type: Article

References (127)

1. E. Rutherford, Philos. Mag. 21, 669 (1911).
2. E. Nagaoka, Philos. Mag. 7, 445 (1904).
3. M. Born, The Mechanics of the Atom, 2nd ed., translated by J. W. Fisher (Ungar, New York, 1960), pp. 130–241.
4. M. Nauenberg, C. Stroud and J. A. Yeazell, Sci. Am. 270, 44 (1994).
5. G. Raithel, M. Fauth and H. Walther, Phys. Rev. A 47, 419 (1991).
6. J. A. Yeazell and C. R. Stroud, Phys. Rev. A 43, 5153 (1991).
7. T. F. Gallagher, Rydberg Atoms (Cambridge University Press, Cambridge, 1994).
8. L. S. Brown, Am. J. Phys. 41, 525 (1973).
9. D. R. Snieder, Am. J. Phys. 51, 801 (1983).
10. J. Mostowski, Lett. Math. Phys. 2, 1 (1977).
11. C. C. Gerry, Phys. Rev. A 33, 6 (1986);
12. B. R. Johnson, Phys. Rev. A 35, 1412 (1987).
13. D. Bhaumik, B. Dutta-Roy and G. Gosh, J. Phys. A 19, 1353 (1986).
14. S. Nandy and C. S. Shastry, J. Phys. A 22, 1005 (1989).
15. M. Nauenberg, Phys. Rev. A 40, 1133 (1989).
16. J. C. Gay, D. Delande and A. Bommier, Phys. Rev. A 39, 6587 (1989).
17. D. S. McAnnally and A. J. Bracken, J. Phys. A 23, 2027 (1990).
18. Z. D. Gaeta and C. R. Stroud, Phys. Rev. A 42, 6308 (1990).
19. C. Lena, D. Delande and J. C. Gay, Europhys. Lett. 15, 697 (1991).
20. J. R. Klauder, J. Phys. A 29, L293 (1996).
21. G. Alber and P. Zoller, Phys. Rep. 199, 231 (1991).
22. L. Marmet, H. Held, G. Raithel, J. A. Yeazell and H. Walther, Phys. Rev. Lett. 72, 3779 (1994).
23. J. Wals, Phys. Rev. Lett. 72, 3783 (1994).
24. W. M. Zhang, D. H. Feng and R. Gilmore, Rev. Mod. Phys. 62, 867 (1990).
25. E. Schrödinger, Naturwissenschaften 14, 664 (1926).
26. E. Schrödinger, in Letters in Wave Mechanics, edited by K. Prizibram (Philosophical Library, New York, 1967).
27. P. Kustaanheimo and E. Stiefel, J. Reine Angew. Math. 218, 204 (1965).
28. A. Deprit, A. Elipe, and S. Ferrer, Celest. Mech. and Dynam. Astron., 58, 151 (1994).
29. A. O. Barut and B. W. Xu, Helv. Phys. Acta. 66, 712 (1993).
30. J. A. Yeazell and C. R. Stroud, Phys. Rev. Lett. 60, 1494 (1988).
31. R. J. Brecha, G. Raithel, C. Wagner and H. Walther, Opt. Commun. 102, 257 (1993).
32. P. Nussenzveig, F. Bernardot, M. Brune, J. Hare, J. M. Raimond, S. Haroche and W. Gavlik, Phys. Rev. A 48, 3991 (1993).
33. M. Mallalieu and C. R. Stroud, Phys. Rev. A 49, 2329 (1994).
34. M. Mallalieu and C. R. Stroud, Phys. Rev. A 51, 1827 (1995).
35. Z. D. Gaeta, M. W. Noel and C. R. Stroud, Phys. Rev. Lett. 73, 636 (1994).
36. J. A. Yeazell, M. Mallalieu and C. R. Stroud, Phys. Rev. Lett. 61, 1938 (1988).
37. J. A. Yeazell, M. Mallalieu and C. R. Stroud, Phys. Rev. A 40, 5040 (1989).
38. C. Raman, C. W. S. Conover, C. I. Sukenik and P. H. Bucksbaum, Phys. Rev. Lett. 76, 2436 (1996).
39. D. W. Schumaker, J. H. Hoogenraad, D. Pinkos and P. H. Bucksbaum, Phys. Rev. A 52, 4719 (1996).
40. M. W. Noel and C. R. Stroud, Phys. Rev. Lett. 75, 1252 (1995).
41. R. G. Hulet and D. Kleppner, Phys. Rev. Lett. 51, 1430 (1983).
42. W. A. Molander, C. R. Stroud and J. A. Yeazell, J. Phys. B 19, L461 (1986).
43. C. H. Cheng, C. Y. Lee and T. F. Gallagher, Phys. Rev. Lett. 73, 3078 (1994).
44. J. Hare, M. Gross and P. Goy, Phys. Rev. Lett. 73, 3078 (1994).
45. S. B. Hansen, Phys. Rev. Lett. 71, 1522 (1993).
46. K. S. Mogensen, Phys. Rev. A 51, 4038 (1995).
47. A. Bommier, D. Delande, and J. C. Gay, Atoms in Strong Fields, edited by C. A. Nicolaides et al (Plenum, New York, 1990).
48. R. J. Glauber, Phys. Rev. 130, 2529 (1963).
49. D. Farrelly and T. Uzer, Phys. Rev. Lett. 74, 1720 (1995).
50. I. Bialynicki-Birula, M. Kalin-acuteski and J. H. Eberly, Phys. Rev. Lett. 73, 1777 (1994).
51. P. Fu, T. J. Scholz, J. M. Hettema and T. F. Gallagher, Phys. Rev. Lett. 64, 511 (1990).
52. C. H. Cheng, C. Y. Lee and T. F. Gallagher, Phys. Rev. Lett. 73, 3078 (1994).
53. M. Nauenberg, Phys. Rev. Lett. 64, 2731 (1990).
54. M. Nauenberg, Europhys. Lett. 13, 611 (1990).
55. P. Kappertz and M. Nauenberg, Phys. Rev. A 47, 4749 (1993).
56. J. A. Griffiths and D. Farrelly, Phys. Rev. A 45, R2678 (1992).
57. K. Rzazewski and B. Piraux, Phys. Rev. A 47, R1612 (1993).
58. A. Peregrine-Smew, D. Farrelly and T. Uzer, Phys. Rev. A 51, 4293 (1995).
59. D. Farrelly, P. Bellomo and T. Uzer, Phys. Rev. Lett. 74, 3495 (1995).
60. G. W. Hill, Am. J. Math. 1, 5 (1878).
61. V. Szebehely, Theory of Orbits: The Restricted Problem of Three Bodies (Academic, New York, 1967).
62. R. Abraham and J. E. Marsden, Foundations of Mechanics, 2nd ed. (Addison-Wesley, Redwood City, CA, 1987), pp. 675–688.
63. D. Farrelly, E. Lee and T. Uzer, Phys. Rev. Lett. 75, 972 (1995).
64. I. Bialynicki-Birula, M. Kalin-acuteski and J. H. Eberly, Phys. Rev. Lett. 75, 973 (1995).
65. J. Zakrzewski, R. Gebarowski and D. Delande, Phys. Rev. A 54, 691 (1996).
66. M. Kalin-acuteski, J. H. Eberly and Bialynicki-Birula, Phys. Rev. A 52, 2460 (1995).
67. M. Kalin-acuteski and J. H. Eberly, Phys. Rev. A 53, 1715 (1996).
68. M. Kalin-acuteski, J. H. Eberly and Bialynicki-Birula, Phys. Rev. A 52, 4285 (1995).
69. D. Delande, J. Zakrzewski and A. Buchleitner, Europhys. Lett. 32, 107 (1995).
70. J. Zakrzewski, D. Delande and A. Buchleitner, Phys. Rev. Lett. 75, 4015 (1995).
71. A. Buchleitner, B. Grémand and D. Delande, J. Phys. B 55, 1622 (1985).
72. A. Maquet, S. I. Chu and W. P. Reinhardt, Phys. Rev. A 27, 2946 (1983).
73. D. Farrelly, E. Lee and T. Uzer, Phys. Lett. A 204, 359 (1995).
74. E. Lee, A. F. Brunello and D. Farrelly, Phys. Rev. Lett. 75, 3641 (1994).
75. A. F. Brunello, T. Uzer and D. Farrelly, Phys. Rev. Lett. 76, 2874 (1996). The contour plots of eigenstates shown in this Letter and also those for the Trojan states in 68 (i.e., at the maximum) seem to adopt the shape of the level curves of the underlying ZVS.
76. W. Paul, Rev. Mod. Phys. 62, 531 (1992).
77. F. M. Penning, Rev. Mod. Phys. 3, 873 (1936).
78. H. Dehmelt, Rev. Mod. Phys. 62, 525 (1992).
79. L. S. Brown and G. Gabrielese, Rev. Mod. Phys. 58, 2335 (1986).
80. J. Schmiedmayer, Z. Phys. D 60, 169 (1995).
81. J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol, Phys. Rev. Lett. 63, 364 (1989).
82. R. Blümel, J. M. Chen, E. Peik, W. Quint, W. Schleich, and H. Walther, 334, 309 (1988).
83. D. Farrelly and J. E. Howard, Phys. Rev. A 48, 851 (1993);
84. D. Farrelly and J. E. Howard, Phys. Rev. A 49, 1494 (1994).
85. J. E. Howard and D. Farrelly, Phys. Lett. A 178, 62 (1993).
86. C. W. Clark, E. Korevaar and M. G. Littman, Phys. Rev. Lett. 54, 320 (1985).
87. C. Nessman and W. P. Reinhardt, Phys. Rev. A 35, 3269 (1987).
88. G. Raithel, M. Fauth and H. Walther, Phys. Rev. A 44, 1898 (1991).
89. G. Wiebusch, J. Main, K. Kruger, H. Rottke, A. Holle and K. H. Welge, Phys. Rev. Lett. 62, 2821 (1989).
90. G. Raithel and H. Walther, Phys. Rev. A 49, 1646 (1993).
91. J. Main and G. Wunner, Phys. Rev. Lett. 44, 1898 (1992).
92. M. J. Gourlay, T. Uzer and D. Farrelly, Phys. Rev. A 47, 3113 (1993).
93. D. Farrelly, Phys. Lett. A 191, 265 (1994).
94. J. C. Gay, L. R. Pendrill and B. Cagnac, Phys. Lett. A 72, 315 (1979).
95. L. A. Burkova, I. E. Dzyaloshinskii, G. F. Drukarev and B. S. Monozon, Zh. Eksp. Teor. Fiz. 71, 526 (1976) [Sov. Phys. JETP 44, 276 (1976)].
96. S. K. Bhattacharya and A. R. P. Rau, Phys. Rev. A 26, 2315 (1982).
97. L. I. Gorkov and I. E. Dzyaloshinski, Zh. Eksp. Teor. Fiz. 53, 717 (1967) [Sov. Phys. JETP 26, 449 (1968)].
98. O. Dippel, P. Schmelcher and L. S. Cederbaum, Phys. Rev. A 49, 4415 (1994).
99. C. Cerjan, E. Lee, D. Farrelly, and T. Uzer, 55, 2222 (1997).
100. A. Deprit, in The Big Bang and George Lemaitre, edited by A. Berger (Reidel, Dordrecht, 1984), pp. 151–180.
101. K. Weierstrass, in Weierstrass: Mathematische Werke, reprinted (Olms and Johnson, Hildesheim, 1967), Vol. 1, pp. 233–246; R. S. MacKay, in Nonlinear Phenomena and Chaos, edited by S. Sarkar (Hilger, Bristol, 1986), pp. 254–270.
102. R. Greenberg and D. R. Davis, Am. J. Phys. 46, 1068 (1978).
103. A. Deprit, Astron. J. 71, 77 (1966).
104. A. Deprit and A. Deprit-Bartholomé, Astron. J. 72, 173 (1966).
105. A. Deprit and A. Delie, Icarus 4, 242 (1965).
106. A. Bohr and B. R. Mottelson, Nuclear Structure (Benjamin, Reading, MA, 1975), Vol. II, pp. 84–88.
107. K. F. Liu and G. Ripka, Nucl. Phys. A 293, 333 (1977).
108. D. Glas, U. Mosel and P. G. Zint, Z. Phys. 285, 83 (1978).
109. M. A. Z. Habeeb, J. Phys. G 13, 651 (1987).
110. D. Farrelly, T. Uzer, P. E. Raines, J. P. Skelton and J. A. Milligan, Phys. Rev. A 45, 4738 (1992).
111. N. N. Bogoliubov, Lectures on Quantum Systems, Vol. I, Quantum Statistics (Gordon and Breach, New York, 1967).
112. S. V. Tyablikov, Methods in the Quantum Theory of Magnetism (Plenum, New York, 1967).
113. M. S. Krishnan, Jr. and T. Carrington, J. Chem. Phys. 94, 461 (1991).
114. J. E. Howard and R. S. MacKay, J. Math. Phys. (N.Y.) 28, 1036 (1987).
115. A. Deprit (private communication).
116. V. Lanchares, M. Iñarrea, J. P. Salas, E. Lee, and D. Farrelly (unpublished).
117. M. J. Rakovic-acute and S. I. Chu, Phys. Rev. A 50, R5077 (1994).
118. M. J. Rakovic-acute and S. I. Chu, Physica D 81, 271 (1995).
119. M. J. Rakovic-acute and S. I. Chu, Phys. Rev. A 52, 1358 (1995).
120. D. Apostolakis, E. G. Floratos, and N. D. Vlachos (unpublished).
121. M. J. Rakovic-acute, T. Uzer, and D. Farrelly (unpublished).
122. T. Zuo, A. D. Bandrauk, M. Ivanov and P. B. Corkum, Phys. Rev. A 51, 3991 (1995).
123. M. Murison, Ph.D. thesis, University of Wisconsin, 1988 (unpublished).
124. I. Dzyaloshinskii, Phys. Lett. A 165, 69 (1992).
125. D. Baye, N. Clerbaux and M. Vincke, Phys. Lett. A 166, 135 (1992).
126. B. R. Johnson, J. O. Hirschfelder and K. H. Yang, Rev. Mod. Phys. 55, 109 (1988).
127. P. Schmelcher, J. Phys. B 25, 2697 (1992).