Method of multiple scales in quantum optics

Physics Reports

Volumn 375, Issue 5, 2003, Pages 327-410

  Janowicz, Maciej ^a  

^a INSTITUTE OF PHYSICS   (Poland)

Author keywords

Anharmonic oscillator; Cavity quantum electrodynamics; Method of multiple scales; Quantum optics; Resonance fluorescence; Spontaneous emmision

Indexed keywords

EID: 0037312788     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(02)00551-3     Document Type: Review

References (125)

1. J. Kevorkian, J.D. Cole, Perturbation Methods in Applied Mathematics, Springer, New York, 1981.
2. J. Kevorkian, J.D. Cole, Multiple Scale and Singular Perturbation Methods, Springer, New York, 1996.
3. A.H. Nayfeh, Perturbation Methods, Wiley-Interscience, New York, 1973.
4. A.H. Nayfeh, Introduction to Perturbation Theory, Wiley, New York, 1981.
5. A.H. Nayfeh, D.T. Mook, Nonlinear Oscillations, Wiley, New York, 1979.
6. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Singapore, 1978.
7. M. Van Dyke, Perturbation Methods in Fluid Dynamics, Academic Press, New York, 1964.
8. J. Ackerhalt, K. Rza̧zewski, Phys. Rev. A 12 (1975) 2549.
9. E.T. Jaynes, F.W. Cummings, Proc. IEEE 51 (1963) 89.
10. P.L. Knight, P.W. Milonni, Phys. Rep. 66C (1980) 21.
11. P.S. Lee, Y.C. Lee, C.T. Chang, Phys. Rev. A 8 (1973) 1722.
12. P.S. Lee, Y.C. Lee, Phys. Rev. A 8 (1973) 1727.
13. Y.C. Lee, P.S. Lee, Phys. Rev. B 10 (1974) 344.
14. K.C. Liu, Y.C. Lee, Y. Shan, Phys. Rev. B 11 (1975) 978.
15. Y.C. Lee, D.S. Chuu, W.N. Mei, Phys. Rev. Lett. 69 (1992) 1081.
16. G.L. Brooks, L.M. Scarfone, Phys. Rev. A 26 (1982) 3268.
17. J. Wong, J.C. Garrison, T.H. Einwohner, Phys. Rev. A 13 (1976) 674.
18. J.C. Garrison, T.H. Einwohner, J. Wong, Phys. Rev. A 14 (1976) 731.
19. J. Wong, J.C. Garrison, T.H. Einwohner, Phys. Rev. A 16 (1977) 213.
20. Ch. Szwaj, S. Bielawski, D. Derozier, Th. Erneux, Phys. Rev. Lett. 80 (1998) 3968.
21. J.C. Celet, D. Dangoisse, P. Glorieux, G. Lythe, Th. Erneux, Phys. Rev. Lett. 81 (1998) 975.
22. A. Kossakowski, Z. Phys. B 56 (1984) 247.
23. A. Kossakowski, Z. Phys. B 56 (1984) 257.
24. J. Lega, P.K. Jakobsen, J.V. Moloney, A.C. Newell, Phys. Rev. A 49 (1994) 4201.
25. Th. Erneux, in: R. Binder, P.Blood, M. Osinski (Eds.), Physics and Simulations of Optoelectronic Devices VIII, Proc. SPIE 3944 (2000) 588.
26. Th. Erneux, in: B. Krauskopf, D. Lenstra (Eds.), Fundamental Issues of Nonlinear Laser Dynamics, AIP, New York, AIP Conf. Proc. 548 (2000) 54.
27. S. Stenholm, Phys. Rev. A 47 (1993) 2523.
28. J. Mizerski, W. Miklaszewski, S. Stenholm, J. Opt. Soc. Am. B 8 (1991) 509.
29. M.W. Janowicz, J.M.A. Ashbourn, Phys. Rev. A 55 (1997) 2348.
30. M. Janowicz, Phys. Rev. A 57 (1998) 4784.
31. M. Janowicz, Phys. Rev. A 57 (1998) 5016.
32. C.M. Bender, T. Wu, Phys. Rev. 184 (1969) 1231.
33. F.T. Hioe, D. MacMillen, E.W. Montroll, Phys. Rep. 43 (1978) 305.
34. P.M. Stevenson, Phys. Rev. D 30 (1984) 1712.
35. C.M. Bender, L.M.A. Bettencourt, Phys. Rev. Lett. 77 (1996) 4114.
36. C.M. Bender, L.M.A. Bettencourt, Phys. Rev. D 54 (1996) 7710.
37. E. Fermi, Rend. Lincei 5 (1927) 795.
38. M.D. Crisp, E.T. Jaynes, Phys. Rev. 179 (1969) 1253.
39. P.W. Milonni, Phys. Rep. 25 (1976) 1.
40. W.H. Louisell, Quantum Statistical Properties of Radiation, Wiley, New York, 1973.
41. J.A. Abate, Opt. Commun. 10 (1974) 269.
42. R.E. Grove, F.Y. Wu, S. Ezekiel, Phys. Rev. A 15 (1977) 227.
43. D. Meschede, H. Walther, G. Müller, Phys. Rev. Lett. 54 (1985) 551.
44. W. Zakowicz, W. Rza̧zewski, J. Phys. A 7 (1974) 869.
45. K. Rza̧zewski, W. Zakowicz, J. Phys. A 9 (1976) 1159.
46. E.A. Power, S. Zienau, Phil. Trans. R. Soc. London 251 (1959) 427.
47. E.A. Power, T. Thirunamachandran, Am. J. Phys. 46 (1978) 370.
48. E.A. Power, T. Thirunamachandran, Phys. Rev. A 28 (1983) 2649.
49. I. Białynicki-Birula, in: A.O. Barut (Ed.), Quantum Electrodynamics and Quantum Optics, Plenum Press, New York, 1984.
50. L. Allen, J.H. Eberly, K. Rza̧zewski, Optical Resonance, PWN, Warszawa 1981. This is the Polish translation of the book by L. Allen and J.H. Eberly, Optical Resonance and Two-Level Atoms with additions ofthe translator K. Rza̧zewski.
51. R.H. Dicke, Phys. Rev. 93 (1954) 99.
52. V.F. Weisskopf, E.P. Wigner, Z. Phys. 63 (1930) 54.
53. W. Heitler, Quantum Theory ofRadiation, Clarendon, Oxford, 1954.
54. M. Wilkens, Z. Białynicka-Birula, P. Meystre, Phys. Rev. A 45 (1992) 477.
55. S. Stenholm, Phys. Scr. T 12 (1986) 56.
56. B.M. Garraway, P.L. Knight, Phys. Rev. A 54 (1996) 3592.
57. B.M. Garraway, Phys. Rev. A 55 (1997) 2290.
58. B.M. Garraway, Phys. Rev. A 55 (1977) 4636.
59. M.W. Noel, W.M. Griffith, T.F. Gallagher, Phys. Rev. A 58 (1998) 2265.
60. M. Janowicz, Phys. Rev. A 61 (2000) 025802.
61. B.W. Shore, The Theory of Coherent Atomic Excitations, Wiley, New York, 1990.
62. C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications, Wiley, New York, 1992.
63. A.J. Lichtenberg, M.A. Liebermann, Regular and Chaotic Dynamics, Springer, Berlin, 1992.
64. M. Wilkens, K. Rza̧zewski, Phys. Rev. A 40 (1989) 3164.
65. B.R. Mollow, Phys. Rev. 188 (1968) 1969.
66. H.J. Carmichael, D. Walls, J. Phys. B 9 (1976) 1199.
67. H.J. Kimble, L. Mandel, Phys. Rev. A 13 (1976) 2123.
68. C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10 (1977) 345.
69. G.Yu. Kryuchkov, Opt. Commun. 54 (1985) 19.
70. H.S. Freedhoff, Z. Chen, Phys. Rev. A 41 (1990) 6013;
71. H.S. Freedhoff, Z. Chen, Phys. Rev. A 46 (1992) 7328.
72. S.P. Tewari, M.K. Kumari, Phys. Rev. A 41 (1990) 5273.
73. G.S. Agarwal, Y. Zhu, D.J. Gauthier, T.W. Mossberg, J. Opt. Soc. Am. B 8 (1991) 1163.
74. Z. Ficek, H.S. Freedhoff, Phys. Rev. A 48 (1993) 3092.
75. Z. Ficek, H.S. Freedhoff, Phys. Rev. A 53 (1996) 4275.
76. Z. Ficek, T. Rudolph, Phys. Rev. A 60 (1999) R4245.
77. G.S. Agarwal, W. Harshawardhan, Phys. Rev. A 50 (1997) R4465.
78. W. Harshawardhan, G.S. Agarwal, Phys. Rev. A 55 (1997) 2165.
79. B.M. Garraway, N.V. Vitanov, Phys. Rev. A 55 (1997) 4418.
80. M. Janowicz, Phys. Rev. A 44 (1991) 3144.
81. V.N. Smelyanskiy, R.S. Conti, G.W. Ford, Phys. Rev. A 55 (1997) 2186.
82. C. Cohen-Tannoudji, in: R. Balian, S. Haroche, S. Liberman (Eds.), Atoms in Strong Resonant Fields, Les Houches 1975 Frontiers in Laser Spectroscopy, Vol. 1, North-Holland, Amsterdam, 1977.
83. J.H. Eberly, K. Wódkiewicz, J. Opt. Soc. Am. 67 (1977) 1252.
84. N.B. Narozhny, J.J. Sanchez-Mondragon, J.H. Eberly, Phys. Rev. A 23 (1981) 236.
85. J.J Sanchez-Mondragon, N.B Narozhny, J.H. Eberly, Phys. Rev. Lett. 51 (1983) 550.
86. H.-I. Yoo, J.H. Eberly, Phys. Rep. 118 (1985) 239.
87. P.L. Knight, P.M. Radmore, Phys. Rev. A 26 (1982) 676.
88. G. Rempe, H. Walther, N. Klein, Phys. Rev. Lett. 58 (1987) 353.
89. S. Yu, H. Rauch, Y. Chang, Phys. Rev. A 52 (1995) 2585.
90. L. Davidovich, M. Brune, J.M. Raimond, S. Haroche, Phys. Rev. A 53 (1996) 1295.
91. C. Gerry, J.H. Eberly, Phys. Rev. A 42 (1991) 6805.
92. M. Alexanian, S.K. Bose, Phys. Rev. A 52 (1995) 2218.
93. N.N. Bogoliubov, Yu.A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York, 1961.
94. S.J.D. Phoenix, P.L. Knight, J. Opt. Soc. Am. B 7 (1996) 116.
95. G.T. Moore, J. Math. Phys. 11 (1970) 2679.
96. S.A. Fulling, P.C.W. Davies, Proc. R. Soc. London Ser. A 348 (1976) 393.
97. M. Razavy, J. Terning, Phys. Rev. D 31 (1985) 307.
98. G. Barton, C. Eberlein, Ann. Phys. (NY) 227 (1993) 393.
99. C. Eberlein, Phys. Rev. Lett. 76 (1996) 3842.
100. C. Eberlein, Phys. Rev. A 53 (1996) 2772.
101. V.V. Dodonov, A.B. Klimov, V.I. Man'ko, Phys. Lett. A 149 (1990) 225.
102. V.V. Dodonov, A.B. Klimov, D.E. Nikonov, J. Math. Phys. 34 (1993) 2742.
103. V.V. Dodonov, A.B. Klimov, Phys. Rev. A 53 (1996) 2664.
104. V.V. Dodonov, Phys. Lett. A 213 (1996) 219.
105. V.V. Dodonov, Phys. Lett. A 207 (1995) 126.
106. G. Barton, A. Calogeracos, Ann. Phys. (NY) 238 (1995) 227.
107. A. Calogeracos, G. Barton, Ann. Phys. (NY) 238 (1995) 268.
108. P.A. Maia Neto, J. Phys. A 27 (1994) 2167.
109. S.A. Fulling, Aspects of Quantum Field Theory in Curved Space-Time, Cambridge University Press, Cambridge, 1989.
110. C.K. Law, Phys. Rev. A 49 (1994) 433.
111. C.K. Law, Phys. Rev. A 51 (1995) 2537.
112. A.S. Parkin, D.F. Walls, Phys. Rep. 303 (1998) 1.
113. C.J. Pethick, H. Smith, Bose-Einstein Condensation in Dilute Gases, Cambridge University Press, Cambridge, 2000.
114. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Rev. Mod. Phys. 71 (1999) 463.
115. A. Leggett, Rev. Mod. Phys. 73 (2001) 307.
116. G.J. Milburn, J. Corney, E.M. Wright, D.F. Walls, Phys. Rev. A 55 (1997) 4318.
117. S. Raghavan, A. Smerzi, S. Fantoni, S.R. Shenoy, Phys. Rev. A 59 (1999) 620.
118. M. Holthaus, S. Stenholm, Eur. Phys. J. B 20 (2001) 451.
119. M. Holthaus, Phys. Rev. A 64 (2001) 011601.
120. G.L. Salmond, C.A. Holmes, G.J. Milburn, Phys. Rev. A 65 (2002) 033623.
121. J. Anglin, Phys. Rev. Lett. 79 (1997) 6.
122. J. Ruostekoski, D.F. Walls, Phys. Rev. A 58 (1998) R50.
123. C. Sparrow, The Lorenz Equations: Bifurcations, Chaos and Strange Attractors, Springer, New York, 1982.
124. N. Guckenheimer, P. Holmes, Nonlinear Oscilltions, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York, 1983.
125. A.C. Newell, J.V. Moloney, Nonlinear Optics, Addison-Wesley, Redwood City, 1992.