- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Reviews of Modern Physics

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

The quantum-jump approach to dissipative dynamics in quantum optics

M. B. Plenio and P. L. Knight

M. B. Plenio and P. L. Knight

  • Optics Section, Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom

PDF

Rev. Mod. Phys. 70, 101 – Published 1 January, 1998

DOI: https://doi.org/10.1103/RevModPhys.70.101

Abstract

Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schrödinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.

View figure in article

References (241)

  1. Agarwal, G. S., 1974, Quantum Statistical Theories of Spontaneous Emission and their Relation to other Approaches, Springer Tracts in Modern Physics 70 (Springer, Berlin), p. 1.
  2. Agarwal, G. S., S. V. Lawande, and R. D’Souza, 1988a, IEEE J. Quantum Electron. 24, 1413.
  3. Agarwal, G. S., S. V. Lawande, and R. D’Souza, 1988b, Phys. Rev. A 37, 444.
  4. Alsing, P., and H. J. Carmichael, 1991, Quantum Opt. 3, 13.
  5. Arecchi, F. T., A. Schenzle, R. G. De Voe, K. Jungmann, and R. G. Brewer, 1986, Phys. Rev. A 33, 2124.
  6. Autler, S. H., and C. H. Townes, 1955, Phys. Rev. 100, 703.
  7. Barchielli, A., 1986, Phys. Rev. A 34, 1642.
  8. Barchielli, A., 1993, Quantum Opt. 2, 423.
  9. Barchielli, A., and V. P. Belavkin, 1991, J. Phys. A 24, 1495.
  10. Bardou, F., J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, 1994, Phys. Rev. Lett. 72, 203.
  11. Barnett, S. M., and P. L. Knight, 1986, Phys. Rev. A 33, 2444.
  12. Beige, A., and G. C. Hegerfeldt, 1996a, Phys. Rev. A 53, 53.
  13. Beige, A., and G. C. Hegerfeldt, 1996b, Quantum Opt. 8, 999.
  14. Bergquist, J. C., R. B. Hulet, W. M. Itano, and D. J. Wineland, 1986, Phys. Rev. Lett. 57, 1699.
  15. Bergquist, J. C., W. M. Itano, and D. J. Wineland, 1994, in Frontiers in Laser Spectroscopy: Proceedings of the International School of Physics “Enrico Fermi,” Course CXX, edited by T. W. Hänsch and M. Inguscio (North-Holland, Amsterdam), pp. 359–376.
  16. Blatt, R., W. Ertmer, P. Zoller, andJ. J. Hall, 1986, Phys. Rev. A 34, 3022.
  17. Bouwmeester, D., R. J. C. Spreeuw, G. Nienhuis, and J. P. Woerdman, 1994, Phys. Rev. A 49, 4170.
  18. Brun, T. A., 1997, Phys. Rev. Lett. 78, 1833.
  19. Brun, T. A., and N. Gisin, 1996, J. Mod. Opt. 43, 2289.
  20. Brun, T. A., N. Gisin, P. F. O’Mahony, and M. Rigo, 1997, Phys. Lett. A 229, 267.
  21. Brun, T. A., I. C. Percival, and R. Schack, 1996, J. Phys. A 29, 2077.
  22. Brune, M., F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, and S. Haroche, 1996, Phys. Rev. Lett. 76, 1800.
  23. Burt, T. C., and J. Gea-Banacloche, 1996, Quantum Opt. 8, 105.
  24. Calderbank, A. R., and P. W. Shor, 1996, Phys. Rev. A 54, 1098.
  25. Carmichael, H. J., 1993a, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics (Springer, Berlin).
  26. Carmichael, H. J., 1993b, Phys. Rev. Lett. 70, 2273.
  27. Carmichael, H. J., 1994, in Quantum Optics VI, edited by J. D. Harvey and D. F. Walls (Springer, Berlin), p. 219.
  28. Carmichael, H. J., S. Singh, R. Vyas, and P. R. Rice, 1989, Phys. Rev. A 39, 1200.
  29. Castin, Y., J. Dalibard, and K. Mølmer, 1993, in Atomic Physics 13, edited by H. Walther, T. W. Hänsch, and B. Neizert, AIP Conf. Proc. No. 275 (AIP, New York), p. 1143.
  30. Castin, Y., and K. Mølmer, 1995, Phys. Rev. Lett. 74, 3772.
  31. Cirac, J. I., and P. Zoller, 1995, Phys. Rev. Lett. 74, 4091.
  32. Cohen-Tannoudji, C., and J. Dalibard, 1986, Europhys. Lett. 1, 441.
  33. Cohen-Tannoudji, C., J. Dupont-Roc, and G. Grynberg, 1992, Atom-Photon Interactions (Wiley, New York).
  34. Cohen-Tannoudji, C., B. Zambon, and E. Arimondo, 1992a, C. R. Acad. Sci., Ser. II: Mec. Phys., Chim., Sci. Terre Univers 314, 1139.
  35. Cohen-Tannoudji, C., B. Zambon, and E. Arimondo, 1992b, C. R. Acad. Sci., Ser. II: Mec. Phys., Chim., Sci. Terre Univers 314, 1293.
  36. Cohen-Tannoudji, C., B. Zambon, and E. Arimondo, 1993, J. Opt. Soc. Am. B 10, 2107.
  37. Cook, R. J., 1981, Phys. Rev. A 23, 1243.
  38. Cook, R. J., 1988, Phys. Scr. T21, 49.
  39. Cook, R. J., 1990, Prog. Opt. 28, 361.
  40. Cook, R. J., and H. J. Kimble, 1985, Phys. Rev. Lett. 54, 1023.
  41. Coppersmith, D., 1994, IBM Research Report No. RC19642.
  42. Dagenais, M., and L. Mandel, 1978, Phys. Rev. A 18, 2217.
  43. Dalibard, J., Y. Castin, and K. Mølmer, 1992, Phys. Rev. Lett. 68, 580.
  44. Davies, E. B., 1969, Commun. Math. Phys. 15, 277.
  45. Davies, E. B., 1970, Commun. Math. Phys. 19, 83.
  46. Davies, E. B., 1971, Commun. Math. Phys. 22, 51.
  47. Davies, E. B., 1976, Quantum Theory of Open Systems (Academic, New York).
  48. Dehmelt, H. G., 1975, Bull. Am. Phys. Soc. 20, 60.
  49. Dehmelt, H. G., 1982, IEEE Trans Instrum. Meas. IM-31, 83.
  50. Dehmelt, H. G., 1987, Nature (London) 325, 581.
  51. Dicke, R. H., 1981, Am. J. Phys. 49, 925.
  52. Diòsi, L., 1988, J. Phys. A 21, 2885.
  53. Diòsi, L., 1989, Phys. Rev. A 40, 1165.
  54. Diòsi, L., N. Gisin, J. J. Halliwell, and I. C. Percival, 1995, Phys. Rev. Lett. 74, 203.
  55. Dum, R., A. S. Parkins, P. Zoller, and C. W. Gardiner, 1992, Phys. Rev. A 46, 4382.
  56. Dum, R., P. Zoller, and H. Ritsch, 1992, Phys. Rev. A 45, 4879.
  57. Ekert, A., and R. Josza, 1996, Rev. Mod. Phys. 68, 733.
  58. Ekert, A., and P. L. Knight, 1995, Am. J. Phys. 63, 415.
  59. Erber, T., P. Hammerling, G. Hockney, M. Porrati, and S. Putterman, 1989, Ann. Phys. (N.Y.) 190, 254.
  60. Erber, T., and S. Putterman, 1985, Nature (London) 318, 41.
  61. Finn, M. A., G. W. Greenlees, T. W. Hodapp, and D. A. Lewis, 1989, Phys. Rev. A 40, 1704.
  62. Finn, M. A., G. W. Greenlees, and D. A. Lewis, 1986, Opt. Commun. 60, 149.
  63. Frerichs, V., and A. Schenzle, 1991, Phys. Rev. A 44, 1962.
  64. Gardiner, C. W., 1992, Quantum Noise (Springer, Berlin).
  65. Gardiner, C. W., 1993, Phys. Rev. Lett. 70, 2269.
  66. Gardiner, C. W., and A. S. Parkins, 1994, Phys. Rev. A 50, 1792.
  67. Gardiner, C. W., A. S. Parkins, and P. Zoller, 1992, Phys. Rev. A 46, 4363.
  68. Garraway, B. M., M. S. Kim, and P. L. Knight, 1995, Opt. Commun. 117, 560.
  69. Garraway, B. M., and P. L. Knight, 1994a, Phys. Rev. A 49, 1266.
  70. Garraway, B. M., and P. L. Knight, 1994b, Phys. Rev. A 50, 2548.
  71. Garraway, B. M., P. L. Knight, and J. Steinbach, 1995, Appl. Phys. B: Photophys. Laser Chem. 60, 63.
  72. Gell-Mann, M., and J. B. Hartle, 1990, in Complexity, Entropy, and the Physics of Information, Santa Fe Institute Studies in the Science of Complexity, v. VIII, edited by W. Zurek (Addison-Wesley, Reading, PA), p. 425.
  73. Gell-Mann, M., and J. B. Hartle, 1993, Phys. Rev. D 47, 3345.
  74. Ghirardi, G. C., Ph. Pearle, and A. Rimini, 1990, Phys. Rev. A 42, 78.
  75. Ghirardi, G. C., A. Rimini, and T. Weber, 1986, Phys. Rev. D 34, 470.
  76. Gisin, N., 1984, Phys. Rev. Lett. 52, 1657.
  77. Gisin, N., 1989, Helv. Phys. Acta 62, 363.
  78. Gisin, N., 1993, J. Mod. Opt. 40, 2313.
  79. Gisin, N., P. L. Knight, I. C. Percival, R. C. Thompson, and D. C. Wilson, 1993, J. Mod. Opt. 40, 1663.
  80. Gisin, N., and I. C. Percival, 1992, J. Phys. A 25, 5677.
  81. Gisin, N., and I. C. Percival, 1993a, J. Phys. A 26, 2233.
  82. Gisin, N., and I. C. Percival, 1993b, J. Phys. A 26, 2245.
  83. Goetsch, P., and R. Graham, 1993, Ann. Phys. (N.Y.) 3, 706.
  84. Goetsch, P., and R. Graham, 1994, Phys. Rev. A 50, 5242.
  85. Goetsch, P., R. Graham, and F. Haake, 1995, Phys. Rev. A 51, 136.
  86. Granzow, C. M., 1996, Diploma thesis (University of Stuttgart).
  87. Griffiths, R., 1984, J. Stat. Phys. 36, 219.
  88. Grochmalicki, J., and M. Lewenstein, 1989a, Phys. Rev. A 40, 2517.
  89. Grochmalicki, J., and M. Lewenstein, 1989b, Phys. Rev. A 40, 2529.
  90. Haake, F., 1973, in Statistical Treatment of Open Systems by Generalized Master Equations, Springer Tracts of Mod. Physics 66 (Springer, Berlin), p. 98.
  91. Haroche, S., and J. M. Raimond, 1984, Adv. At. Mol. Phys. 20, 347.
  92. Hegerfeldt, G. C., 1993, Phys. Rev. A 47, 449.
  93. Hegerfeldt, G. C., and M. B. Plenio, 1992, Phys. Rev. A 46, 373.
  94. Hegerfeldt, G. C., and M. B. Plenio, 1993, Phys. Rev. A 47, 2186.
  95. Hegerfeldt, G. C., and M. B. Plenio, 1994, Quantum Opt. 6, 15.
  96. Hegerfeldt, G. C., and M. B. Plenio, 1995a, Z. Phys. B 96, 533.
  97. Hegerfeldt, G. C., and M. B. Plenio, 1995b, Phys. Rev. A 52, 3333.
  98. Hegerfeldt, G. C., and M. B. Plenio, 1996, Phys. Rev. A 53, 1164.
  99. Hegerfeldt, G. C., and D. Sondermann, 1996, Quantum Opt. 8, 121.
  100. Hegerfeldt, G. C., and T. S. Wilser, 1991, in Proceedings of the II International Wigner Symposium, edited by H. D. Doebner, W. Scherer, and F. Schroeck (World Scientific, Singapore), p. 104.
  101. Hendriks, B. H. W., and G. Nienhuis, 1988, J. Mod. Opt. 35, 1331.
  102. Herkommer, A. M., H. J. Carmichael, and W. P. Schleich, 1996, Quantum Opt. 8, 189.
  103. Holland, M., and J. Cooper, 1996, private communication.
  104. Holland, M., S. Marksteiner, P. Marte, and P. Zoller, 1996, Phys. Rev. Lett. 76, 3683.
  105. Horvath, G. Z. K., P. L. Knight, and R. C. Thompson, 1997, Contemp. Phys. 38, 25.
  106. Imamoglu, A., 1993, Phys. Rev. A 48, 770.
  107. Imamoglu, A., 1994, Phys. Rev. A 50, 3650.
  108. Itano, W. M., J. C. Bergquist, and D. J. Wineland, 1988, Phys. Rev. A 38, 559.
  109. Itano, W. M., D. J. Heinzen, J. J. Bollinger, and D. J. Wineland, 1990, Phys. Rev. A 41, 2295.
  110. Javanainen, J., 1986a, Phys. Rev. A 33, 2121.
  111. Javanainen, J., 1986b, Phys. Scr. T12, 67.
  112. Javanainen, J., 1986c, J. Opt. Soc. Am. B 3, 98.
  113. Javanainen, J., 1992, Europhys. Lett. 17, 407.
  114. Jayarao, A. S., R. D’Souza, and S. V. Lawande, 1990, Phys. Rev. A 41, 1533.
  115. Kelley, P. L., and W. H. Kleiner, 1964, Phys. Rev. 136, 316.
  116. Kim, M. S., 1987, Ph.D. Thesis (Imperial College, University of London).
  117. Kim, M. S., F. A. M. de Oliveira, and P. L. Knight, 1989, Opt. Commun. 70, 473.
  118. Kim, M. S., and P. L. Knight, 1987, Phys. Rev. A 36, 5265.
  119. Kim, M. S., P. L. Knight, and K. Wodkiewicz, 1987, Opt. Commun. 62, 385.
  120. Kimble, H. J., R. J. Cook, and A. L. Wells, 1986, Phys. Rev. A 34, 3190.
  121. Kimble, H. J., M. Dagenais, and L. Mandel, 1977, Phys. Rev. Lett. 39, 691.
  122. Knight, P. L., and B. M. Garraway, 1996, in Quantum Dynamics of Simple Systems. Proceedings of the Forty Fourth Scottish Universities Summer School in Physics Stirling, edited by G.-L. Oppo, S. M. Barnett, E. Riis, and M. Wilkinson (Institute of Physics, Bristol), p. 199.
  123. Knight, P. L., R. Loudon, and D. T. Pegg, 1986, Nature (London) 323, 608.
  124. Knight, P. L., and P. W. Milonni, 1980, Phys. Rep. 66, 21.
  125. Knight, P. L., and D. T. Pegg, 1982, J. Phys. B 15, 3211.
  126. Kochan, P., and H. J. Carmichael, 1994, Phys. Rev. A 50, 1700.
  127. Köhler, T., 1996, Phys. Rev. A 54, 4544.
  128. Lawande, S. V., Q. V. Lawande, and B. N. Jagatap, 1989, Phys. Rev. A 40, 3434.
  129. Lawande, S. V., B. N. Jagatap, and Q. V. Lawande, 1989, Opt. Commun. 73, 126.
  130. Lawande, Q. V., B. N. Jagatap, and S. V. Lawande, 1990, Phys. Rev. A 42, 4343.
  131. Lax, M., 1963, Phys. Rev. 129, 2342.
  132. Lenstra, D., 1982, Phys. Rev. A 26, 3369.
  133. Lewenstein, M., and J. Javanainen, 1987, Phys. Rev. Lett. 59, 775.
  134. Lewenstein, M., and J. Javanainen, 1988, IEEE J. Quantum Electron. 24, 1403.
  135. Ligare, M., 1988, Phys. Rev. A 37, 3293.
  136. Lindblad, G., 1976, Commun. Math. Phys. 48, 119.
  137. Loudon, R., 1983, The Quantum Theory of Light (Oxford University, New York).
  138. Loudon, R., and P. L. Knight, 1987, J. Mod. Opt. 34, 1.
  139. Lüders, G., 1951, Ann. Phys. (Leipzig) 8, 323.
  140. Mahler, G., and V. A. Weberruβ, 1995, Quantum Networks: Dynamics of Open Nanostructures (Springer, Berlin).
  141. Mandel, L., 1979, Opt. Lett. 4, 205.
  142. Manka, A. S., H. M. Doss, L. M. Narducci, P. Ru, and G.-L. Oppo, 1993, Phys. Rev. A 47, 1378.
  143. Marte, P., R. Dum, R. Taieb, P. D. Lett, and P. Zoller, 1993, Phys. Rev. Lett. 71, 1335.
  144. Marte, P., R. Dum, R. Taieb, and P. Zoller, 1993, Phys. Rev. A 47, 1378.
  145. Meekhof, D. M., C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, 1996, Phys. Rev. Lett. 76, 1796.
  146. Milburn, G. J., 1991, Phys. Rev. A 44, 5401.
  147. Milonni, P. W., 1976, Phys. Rep. 25, 1.
  148. Misra, B., and E. C. G. Sudarshan, 1977, J. Math. Phys. 18, 756.
  149. Mollow, B. R., 1969, Phys. Rev. 188, 1969.
  150. Mollow, B. R., 1972a, Phys. Rev. A 5, 1522.
  151. Mollow, B. R., 1972b, Phys. Rev. A 5, 2217.
  152. Mollow, B. R., 1975, Phys. Rev. A 12, 1919.
  153. Mollow, B. R., 1981, Prog. Opt. XIX, 3.
  154. Mølmer, K., 1994, in Lectures Presented at the Trieste Winter School on Quantum Optics 1994 (International Centre for Theoretical Physics, Trieste).
  155. Mølmer, K., and Y. Castin, 1996, Quantum Opt. 8, 49.
  156. Mølmer, K., Y. Castin, and J. Dalibard, 1993, J. Opt. Soc. Am. B 10, 524.
  157. Moya-Cessa, H., V. Bužek, M. S. Kim, and P. L. Knight, 1993, Phys. Rev. A 48, 3900.
  158. Mu, Y., 1994, Opt. Commun. 110, 334.
  159. Nagourney, W., J. Sandberg, and H. G. Dehmelt, 1986a, Phys. Rev. Lett. 56, 2797.
  160. Nagourney, W., J. Sandberg, and H. G. Dehmelt, 1986b, J. Opt. Soc. Am. B 3, 252.
  161. Nakajima, S., 1958, Prog. Theor. Phys. 20, 948.
  162. Narducci, L. M., G.-L. Oppo, and M. O. Scully, 1990, Opt. Commun. 75, 111.
  163. Narducci, L. M., M. O. Scully, G.-L. Oppo, P. Ru, and J. R. Tredicce, 1990, Phys. Rev. A 42, 1630.
  164. Narozhny, N. B., J. J. Sanchez-Mondragon, and J. H. Eberly, 1981, Phys. Rev. A 23, 236.
  165. Neuhauser, W., M. Hohenstatt, P. Toschek, and H. G. Dehmelt, 1980, Phys. Rev. A 22, 1137.
  166. Nienhuis, G., 1987, Phys. Rev. A 35, 4639.
  167. Omnès, R., 1988, J. Stat. Phys. 53, 893.
  168. Omnès, R., 1989, J. Stat. Phys. 57, 359.
  169. Omnès, R., 1994, The Interpretation of Quantum Mechanics (Princeton University, Princeton, NJ).
  170. Paul, W., 1990, Rev. Mod. Phys. 62, 531.
  171. Paul, W., O. Osberghaus, and E. Fischer, 1958, Ein Ionenkäfig (Forschungsberichte des Wirtschafts- und Verkehrsministeriums, Nordrhein-Westfalen), p. 415.
  172. Pearle, Ph., 1976, Phys. Rev. D 13, 857.
  173. Pegg, D. T., 1980, in Laser Physics, edited by J. D. Harvey and D. F. Walls (Academic, Sydney), p. 33.
  174. Pegg, D. T., and P. L. Knight, 1988a, Phys. Rev. A 37, 4303.
  175. Pegg, D. T., and P. L. Knight, 1988b, J. Phys. D 21, 128.
  176. Pegg, D. T., R. Loudon, and P. L. Knight, 1986a, Nature (London) 323, 608.
  177. Pegg, D. T., R. Loudon, and P. L. Knight, 1986b, Phys. Rev. A 33, 4085.
  178. Percival, I. C., 1994a, J. Phys. A 27, 1003.
  179. Percival, I. C., 1994b, Proc. R. Soc. London, Ser. A 447, 189.
  180. Percival, I. C., 1995, Proc. R. Soc. London, Ser. A 451, 503.
  181. Percival, I. C., 1997, Phys. World 10, 43.
  182. Percival, I. C., and W. T. Strunz, 1997, Proc. R. Soc. London, Ser. A 453, 431.
  183. Piraux, B., R. Bhatt, and P. L. Knight, 1990, Phys. Rev. A 41, 6296.
  184. Plenio, M. B., 1994, Ph.D. thesis (University of Göttingen).
  185. Plenio, M. B., 1996, J. Mod. Opt. 43, 753.
  186. Plenio, M. B., and P. L. Knight, 1996, Phys. Rev. A 53, 2986.
  187. Plenio, M. B., and P. L. Knight, 1997, Proc. R. Soc. London., Ser. A 453, 2017.
  188. Plenio, M. B., P. L. Knight, and R. C. Thompson, 1996, Opt. Commun. 123, 278.
  189. Porrati, M., and S. Putterman, 1987, Phys. Rev. A 36, 929.
  190. Porrati, M., and S. Putterman, 1989, Phys. Rev. A 39, 3010.
  191. Power, W. L., 1995a, Ph.D. thesis (Imperial College, University of London).
  192. Power, W. L., 1995b, J. Mod. Opt. 42, 913.
  193. Power, W. L., and P. L. Knight, 1996, Phys. Rev. A 53, 1052.
  194. Reibold, R., 1992, Physica A 190, 413.
  195. Reibold, R., 1993, J. Phys. A 26, 179.
  196. Rempe, G., and H. Walther, 1987, Phys. Rev. Lett. 58, 353.
  197. Reynaud, S., J. Dalibard, and C. Cohen-Tannoudji, 1988, IEEE J. Quantum Electron. 24, 1395.
  198. Rigo, M., and N. Gisin, 1996, Quantum Opt. 8, 255.
  199. Salama, Y., and N. Gisin, 1993, Phys. Lett. A 181, 269.
  200. Saleh, B., 1978, Photoelectron Statistics, Springer Series in Optical Sciences Vol. 6 (Springer, Berlin).
  201. Sauter, T., R. Blatt, W. Neuhauser, and P. E. Toschek, 1986, Opt. Commun. 60, 287.
  202. Sauter, T., W. Neuhauser, R. Blatt, and P. E. Toschek, 1986a, Phys. Rev. Lett. 57, 1696.
  203. Sauter, T., W. Neuhauser, R. Blatt, and P. E. Toschek, 1986b, J. Opt. Soc. Am. B 3, 252.
  204. Schack, R., T. A. Brun, and I. C. Percival, 1995, J. Phys. A 28, 5401.
  205. Schack, R., T. A. Brun, and I. C. Percival, 1996, Phys. Rev. A 53, 2694.
  206. Schenzle, A., and R. G. Brewer, 1986, Phys. Rev. A 34, 3127.
  207. Schenzle, A., R. G. De Voe, andR. G. Brewer, 1986, Phys. Rev. A 33, 2127.
  208. Schrödinger, E., Br. J. Philos. Sci. III, 1952, August.
  209. Schubert, M., I. Siemers, R. Blatt, W. Neuhauser, and P. E. Toschek, 1992, Phys. Rev. Lett. 68, 3016.
  210. Shor, P. W., 1994, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, Los Alamitos, California, edited by S. Goldwasser (IEEE Computer Society, New York), p. 124.
  211. Shor, P. W., 1996, Phys. Rev. A 52, R2493.
  212. Shore, B. W., and P. L. Knight, 1993, J. Mod. Opt. 40, 1195.
  213. Sondermann, D., 1995a, J. Mod. Opt. 42, 1659.
  214. Sondermann, D., 1995b, in Nonlinear, Deformed and Irreversible Quantum Systems, edited by H. D. Doebner, V. K. Dobrev, and P. Nattermann (World Scientific, Singapore), p. 273.
  215. Spiller, T. P., and J. F. Ralph, 1994, Phys. Lett. A 194, 235.
  216. Srinivas, M. D., 1996, Pramana, J. Phys. 47, 1.
  217. Srinivas, M. D., and E. B. Davies, 1981, Opt. Acta 28, 981.
  218. Srinivas, M. D., and E. B. Davies, 1982, Opt. Acta 29, 235.
  219. Steane, A. M., 1996, Phys. Rev. Lett. 77, 793.
  220. Steinbach, J., B. M. Garraway, and P. L. Knight, 1995, Phys. Rev. A 51, 3302.
  221. Stratonovitch, R. L., 1963, Topics in the Theory of Random Noise (Gordon and Breach, New York), Vol. 1.
  222. Strunz, W. T., 1996a, Phys. Lett. 224, 25.
  223. Strunz, W. T., 1996b, Phys. Rev. A 54, 2664.
  224. Swain, S., 1994, Phys. Rev. Lett. 73, 1493.
  225. Teich, W. G., G. Anders, and G. Mahler, 1989, Phys. Rev. Lett. 62, 1.
  226. Teich, W. G., and G. Mahler, 1992, Phys. Rev. A 45, 3300.
  227. Thompson, R. C., 1996, private communication.
  228. Tian, L., and H. J. Carmichael, 1992, Phys. Rev. A 46, 6801.
  229. Vogel, W., and D.-G. Welsch, 1994, Lectures on Quantum Optics (Akademie, Berlin).
  230. von Neumann, J., 1955, Mathematical Foundations of Quantum Mechanics (Princeton University, Princeton, NJ).
  231. Weisskopf, V., and E. Wigner, 1930, Z. Phys. 63, 54.
  232. Wilser, T. S., 1991, Ph.D. thesis (University of Göttingen).
  233. Wiseman, H. M., 1996, Quantum Opt. 8, 205.
  234. Wiseman, H. M., and G. J. Milburn, 1993a, Phys. Rev. A 47, 642.
  235. Wiseman, H. M., and G. J. Milburn, 1993b, Phys. Rev. A 47, 1652.
  236. Wiseman, H. M., and G. J. Milburn, 1994, Phys. Rev. A 49, 1350.
  237. Yamada, K., and P. R. Berman, 1990, Phys. Rev. A 41, 453.
  238. Yu, T., 1996, Imperial College preprint TP/95-96/44, gr-qc/9605071.
  239. Zoller, P., and C. W. Gardiner, 1995, Lecture Notes of the Les Houches Summer School on Quantum Fluctuations (Elsevier, N.Y.), p. 79.
  240. Zoller, P., M. Marte, and D. F. Walls, 1987, Phys. Rev. A 35, 198.
  241. Zwanzig, R., 1960, Lect. Theor. Phys. (Boulder) 3, 106.

Outline

Information

Rev. Mod. Phys. 70, 101– Published 1 January, 1998

    © 1998 American Physical Society

    Sign In to Your Journals Account

    Filter

    Filter

    Article Lookup

    Enter a citation