Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

The semiclassical theory of laser cooling

Stig Stenholm

Stig Stenholm

  • Research Institute for Theoretical Physics, University of Helsinki, SF-00170 Helsinki, Finland

Rev. Mod. Phys. 58, 699 – Published 1 July, 1986

DOI: https://doi.org/10.1103/RevModPhys.58.699

Abstract

This paper reviews the basic theory of the mechanical action of light in resonant interaction with atoms. At present the main application is laser cooling, but the approach is applicable to a broader range of phenomena. It is based on an adiabatic elimination philosophy, which turns out to give the lowest-order quantum corrections to the behavior found when the photon momentum goes to zero. Hence it is called a semiclassical theory. In this manner a subjective but consistent approach can be presented; other treatments are incorporated or mentioned at the appropriate places. Both the classical and the quantum-mechanical approach are discussed. Those readers who wish to obtain only a heuristic overview of the phenomena can concentrate on Sec. III, which treats both the photon momentum effects and their connection with photon counting statistics. The detailed theoretical treatment utilizes Wigner functions and Fokker-Planck techniques. The ensuing theory is applied both to the cooling of free particles and trapped ones. The paper ends with an extensive bibliography, where the author lists most papers of interest for research into the mechanical manifestations of light. For completeness, many papers are included that are not explicitly mentioned in the text.

References (309)

  1. Abov, Yu. G., S. P. Borovlev, V. V. Vasilev, V. V. Vladimirskii, and E. N. Mospan, 1983, "Measurement of the time of storage of ultracold neutrons in a magnetic trap," Yad. Fiz. 38, 122
  2. Aminoff, C.-G., and S. Stenholm, 1976, "Recoil effects in quantum electronics II: Saturated absorber spectroscopy," J. Phys. B 9, 1039
  3. André, J., A. Teboul, F. Vedel, and M. Vedel, 1981, "A simplified model for computing temperature of a dilute population of laser cooled stored ions," J. Phys. (Paris) Colloq. C8-42, 315
  4. Andreev, S. V., V. I. Balykin, V. S. Letokhov, and V. G. Minogin, 1981, "Radiative slowing and reduction of energy spread of a beam of sodium atoms to 1.5 K in an oppositely directed laser beam," Pis'ma Zh. Eksp. Teor. Fiz. 34, 463
  5. Andreev, S. V., V. I. Balykin, V. S. Letokhov, and V. G. Minogin, 1982, "Radiative slowing down and monochromatization of a beam of sodium atoms in a counterpropagating laser beam," Zh. Eksp. Teor. Fiz. 82, 1429
  6. Argyres, P. N., 1966, "Theory of the method of kinetic equations for quantum systems and elementary applications," in Lectures in Theoretical Physics, Vol. VIII A,...Summer Institute...Boulder, 1965, edited by W. E. Brittin (University of Colorado, Boulder), p. 183
  7. Arimondo, E., A. Bambini, and S. Stenholm, 1981, "Quasiclassical theory of laser-induced atomic-beam dispersion," Phys. Rev. A 24, 898
  8. Arimondo, E., H. Lew, and T. Oka, 1979a, "Deflection of a Nabeam by resonant standing wave radiation," in Laser Spectroscopy IV, edited by H. Walter and K. W. Rothe (Springer, Berlin), p. 56
  9. Arimondo, E., H. Lew, and T. Oka, 1979b, "Deflection of a Nabeam by resonant standing-wave radiation," Phys. Rev. Lett. 43, 753
  10. Ashkin, A., 1970a, "Acceleration and trapping of particles by radiation pressure," Phys. Rev. Lett. 24, 156
  11. Ashkin, A., 1970b, "Atomic beam deflection by resonance-radiation pressure," Phys. Rev. Lett. 25, 1321
  12. Ashkin, A., 1972, "The pressure of laser light," Sci. Am. 226, 63
  13. Ashkin, A., 1978, "Trapping of atoms by resonance radiation pressure," Phys. Rev. Lett. 40, 729
  14. Ashkin, A., 1980, "Applications of laser radiation pressure," Science 210, 1081
  15. Ashkin, A., 1984, "Stable radiation-pressure particle traps using alternating light beams," Opt. Lett. 9, 454
  16. Ashkin, A., and J. M. Dziedzic, 1971, "Optical levitation by radiation pressure," Appl. Phys. Lett. 19, 283
  17. Ashkin, A., and J. M. Dziedzic, 1973, "Radiation pressure on a free liquid surface," Phys. Rev. Lett. 30, 139
  18. Ashkin, A., and J. M. Dziedzic, 1974, "Stability of optical levitation by radiation pressure," Appl. Phys. Lett. 24, 586
  19. Ashkin, A., and J. M. Dziedzic, 1975, "Optical levitation of liquid drops by radiation pressure," Science 187, 1073
  20. Ashkin, A., and J. M. Dziedzic, 1976a, "Observation of a new nonlinear photoelectric effect using optical levitation," Phys. Rev. Lett. 36, 267
  21. Ashkin, A., and J. M. Dziedzic, 1976b, "Optical levitation in high vacuum," Appl. Phys. Lett. 28, 333
  22. Ashkin, A., and J. M. Dziedzic, 1977a, "Feedback stabilization of optically levitated particles," Appl. Phys. Lett. 30, 202
  23. Ashkin, A., and J. M. Dziedzic, 1977b, "Observation of resonances in the radiation pressure on dielectric spheres," Phys. Rev. Lett. 38, 1351
  24. Ashkin, A., and J. M. Dziedzic, 1980, "Observation of light scattering from nonspherical particles using optical levitation," Appl. Opt. 19, 660
  25. Ashkin, A., and J. M. Dziedzic, 1981, "Observation of optical resonances of dielectric spheres by light scattering," Appl. Opt. 20, 1803
  26. Ashkin, A., and J. M. Dziedzic, 1985, "Observation of radiation-pressure trapping of particles by alternating light beams," Phys. Rev. Lett. 54, 1245
  27. Ashkin, A., and J. P. Gordon, 1979, "Cooling and trapping of atoms by resonance radiation pressure," Opt. Lett. 4, 161
  28. Ashkin, A., and J. P. Gordon, 1983, "Stability of radiation-pressure particle traps: an optical Earnshaw theorem," Opt. Lett. 8, 511
  29. Askar'yan, G. A., 1962, "Effects of the gradient of a strong electromagnetic beam on electrons and atoms," Zh. Eksp. Teor. Fiz. 42, 1567
  30. Bagayev, S. N., L. S. Vasilenko, V. G. Goldort, A. K. Dmitriyev, A. S. Dyshkov, and V. P. Chebotaev, 1977, "A tunable laser at λ=3.39 μm with line width of 7 Hz used in investigating a hyperfine structure of the F2(2) line of methane," Appl. Phys. 13, 291
  31. Baklanov, E. V., 1975a, "Field shift of the center of the Lamb dip taking into account the recoil effect," Opt. Spectrosc. 38, 352
  32. Baklanov, E. V., 1975b, "Influence of field on the Lamb dip centre shift with account of recoil effect," Opt. Commun. 13, 54
  33. Baklanov, E. V., V. P. Chebotaev, and E. A. Titov, 1981, "Optical absorption resonances of trapped particles," Appl. Phys. 25, 81
  34. Baklanov, E. V., and B. Ya. Dubetskii, 1976, "Fokker-Planck equation for gas atoms resonantly interacting with a light wave," Opt. Spectrosc. 41, 1
  35. Baklanov, E. V., and E. A. Titov, 1980, "Intensity of a linear resonance of the absorption by trapped particles," Kvant. Elektron. (Moscow) 7, 1834
  36. Balazs, N. L., and B. K. Jennings, 1984, "Wigner's function and other distribution functions in mock phase space," Phys. Rep. 104, 347
  37. Balykin, V. I., 1980, "Cyclic interaction of Na atoms with circularly polarized laser radiation," Opt. Commun. 33, 31
  38. Balykin, V. I., V. S. Letokhov, and V. G. Minogin, 1981, "Radiative redistribution of the velocities of free sodium atoms by resonance laser radiation," Zh. Eksp. Teor. Fiz. 80, 1779
  39. Balykin, V. I., V. S. Letokhov, and V. G. Minogin, 1984, "On the possibility of highly selective detection of rare isotopic atoms by means of resonant laser light pressure," Appl. Phys. B 33, 247
  40. Balykin, V. I., V. S. Letokhov, V. G. Minogin, Yu. V. Rozhdestvensky, and A. I. Sidorov, 1985, "Radiative collimation of atomic beams through two-dimensional cooling of atoms by laser radiation pressure," J. Opt. Soc. Am. B2, 1776
  41. Balykin, V. I., V. S. Letokhov, V. G. Minogin, and T. V. Zueva, 1984, "Collimation of atomic beams by resonant laser radiation pressure," Appl. Phys. B 35, 149
  42. Balykin, V. I., V. S. Letokhov, and V. I. Mushin, 1979, "Observation of the cooling of free sodium atoms in a resonance laser field with a scanning frequency," Pis'ma Zh. Eksp. Teor. Fiz. 29, 614
  43. Balykin, V. I., V. S. Letokhov, and V. I. Mushin, 1980, "Cooling of sodium atoms by resonant laser emission," Zh. Eksp. Teor. Fiz. 78, 1376
  44. Balykin, V. I., V. S. Letokhov, and A. I. Sidorov, 1984a, "Formation of an intense steady flux of cold atoms by the laser slowing of an atomic beam," Zh. Eksp. Teor. Fiz. 86, 2019
  45. Balykin, V. I., V. S. Letokhov, and A. I. Sidorov, 1984b, "Intense stationary flow of cold atoms formed by laser deceleration of atomic beam," Opt. Commun. 49, 248
  46. Balykin, V. I., Letokhov, and A. I. Sidorov, 1984, "Radiative collimation of an atomic beam by two-dimensional cooling by a laser beam," Pis'ma Zh. Eksp. Teor. Fiz. 40, 251
  47. Bambini, A., and S. Stenholm, 1979, "Quantum description of free-electrons in the laser," Opt. Commun. 30, 391
  48. Berman, P. R., and S. Stenholm, 1978, "Heating and cooling using collisionally aided fluorescence," Opt. Commun. 24, 155
  49. Bernhardt, A. F., 1976, "Isotope separation by laser deflection of an atomic beam," Appl. Phys. 9, 19
  50. Bernhardt, A. F., D. E. Duerre, J. R. Simpson, and L. L. Wood, 1974, "Separation of isotopes by laser deflection of atomic beam I. Barium," Appl. Phys. Lett. 25, 617
  51. Bernhardt, A. F., D. E. Duerre, J. R. Simpson, and L. L. Wood, 1976a, "High resolution spectroscopy using photodeflection," Opt. Commun. 16, 166
  52. Bernhardt, A. F., D. E. Duerre, J. R. Simpson, and L. L. Wood, 1976b, "Multifrequency radiation pressure laser isotope separation," Opt. Commun. 16, 169
  53. Bernhardt, A. F., and B. W. Shore, 1981, "Coherent atomic deflection by resonant standing waves," Phys. Rev. A 23, 1290
  54. Bjorkholm, J. E., A. Ashkin, and D. B. Pearson, 1975, "Observation of resonance radiation pressure on an atomic vapor," Appl. Phys. Lett. 27, 534
  55. Bjorkholm, J. E., and R. R. Freeman, 1980, "Resonance-radiation pressure on atoms: New perspectives," Comments At. Mol. Phys. 10, 31
  56. Bjorkholm, J. E., R. R. Freeman, A. Ashkin, and D. B. Pearson, 1978, "Observation of focusing of neutral atoms by the dipole force of resonance radiation pressure," Phys. Rev. Lett. 41, 361
  57. Bjorkholm, J. E., R. R. Freeman, A. Ashkin, and D. B. Pearson, 1980, "Experimental observation of the influence of the quantum fluctuations of resonance radiation pressure," Opt. Lett. 5, 111
  58. Bjorkholm, J. E., R. R. Freeman, and D. B. Pearson, 1981, "Efficient transverse deflection of neutral atomic beams using spontaneous resonance-radiation pressure," Phys. Rev. A 23, 491
  59. Blatt, R., W. Ertmer, and J. L. Hall, 1984, "Cooling of an atomic beam with frequency-sweep techniques," Prog. Quantum Electron. 8, 237
  60. Blatt, R., U. Schelting, and G. Werth, 1979, "On the sensitivity of ion traps for spectroscopic applications," Appl. Phys. 20, 295
  61. Bloch, C., 1958, "Sur la théorie des perturbations des états liés," Nucl. Phys. 6, 329
  62. Bogoliubov, N. N., 1967, "Perturbation theory for a degenerate level," in Bogoliubov, Lectures on Quantum Statistics (Gordon and Breach, New York), Vol. I, Part 4.5
  63. Bollinger, J. J., J. D. Prestage, W. M. Itano, and D. J. Wineland, 1985, "Laser-cooled atomic frequency standard," Phys. Rev. Lett. 54, 1000
  64. Bollinger, J. J., and D. J. Wineland, 1984, "Strongly coupled nonneutral ion plasma," Phys. Rev. Lett. 53, 348
  65. Bordé, C. J., 1977, "Progress in understanding sub-Doppler line shapes," in Laser Spectroscopy III, edited by J. L. Hall and J. L. Carlsten (Springer, Berlin), p. 121
  66. Bordé, C. J., G. Camy, and B. Decomps, 1979, "Measurement of the recoil shift of saturation resonances of I2127 at 5145 Å," Phys. Rev. A 20, 254
  67. Bothe, W., and H. Geiger, 1925, "Experimentelles zur Theorie von Bohr, Kramers und Slater," Naturwissenschaften 13, 440
  68. Botin, A. P. and A. P. Kazantsev, 1975, "Scattering of atoms by light," Zh. Eksp. Teor. Fiz. 68, 2075
  69. Botin, A. P., A. P. Kazantsev, and V. S. Smirnov, 1976, "Quantized motion of atoms and molecules in electromagnetic fields," Zh. Eksp. Teor. Fiz. 71, 122
  70. Carlsten, J. L., and A. Szöke, 1976, "Spectral resolution of near-resonant Rayleigh scattering and collision-induced resonance fluorescence," Phys. Rev. Lett. 36, 667
  71. Carlsten, J. L., A. Szöke, and M. G. Raymer, 1977, "Collisional redistribution and saturation of near-resonance scattered light," Phys. Rev. A 15, 1029
  72. Casagrande, F., E. Eschenezi, and L. S. Lugiato, 1984, "Fluctuation theory in quantum-optical systems. II. Rigorous adiabatic elimination by the hierarchy method," Phys. Rev. A 29, 239
  73. Chang, S., and S. S. Lee, 1985, "Optical torque exerted on a homogeneous sphere levitated in the circularly polarized fundamental laser beam," J. Opt. Soc. Am. B2, 1853
  74. Channell, P. J., 1981, "Laser cooling of heavy-ion beams," J. Appl. Phys. 52, 3791
  75. Chebotaev, V. P., Yu. Dubetsky, A. P. Kazantsev, and V. P. Yakovlev, 1985, "Interference of atoms in separated optical fields," J. Opt. Soc. Am. B2, 1791
  76. Chu, S., L. Hallberg, J. E. Bjorkholm, A. Cable, and A. Ashkin, 1985, "Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure," Phys. Rev. Lett. 55, 48
  77. Cohen-Tannoudji, C., 1977, "Interaction of atoms with strong electromagnetic fields," in Frontiers in Laser Spectroscopy, edited by R. Balian, S. Haroche, and S. Liberman (North-Holland, Amsterdam), p. 4
  78. Cohen-Tannoudji, C., B. Diu, and F. Laloe, 1977, Quantum Mechanics, Complement HIII (Hermann/Wiley, Paris)
  79. Compagno, G., J. S. Peng, and F. Persico, 1982a, "Deflection and internal dynamics of atoms dressed by a resonant standing wave," Phys. Lett. A 88, 285
  80. Compagno, G., J. S. Peng, and F. Persico, 1982b, "Self-consistent potential for a two-level atom in a standing-wave field," Phys. Rev. A 26, 2065
  81. Compton, A. H., 1925, "On the mechanism of x-ray scattering," Proc. Natl. Acad. Sci. U.S.A. 11, 303
  82. Compton, A. H., and A. W. Simon, 1925, "Directed quanta of scattered x rays," Phys. Rev. 26, 289
  83. Cook, R. J., 1978, "Theory of atomic motion in a resonant electromagnetic wave," Phys. Rev. Lett. 41, 1788
  84. Cook, R. J., 1979, "Atomic motion in resonant radiation: An application of Ehrenfest's theorem," Phys. Rev. A 20, 224
  85. Cook, R. J., 1980a, "Theory of resonance radiation pressure," Phys. Rev. A 22, 1078
  86. Cook, R. J., 1980b, "Photon statistics in resonance fluorescence from laser deflection of an atomic beam," Opt. Commun. 35, 347
  87. Cook, R. J., 1980c, "Quantum mechanical fluctuations of the resonance-radiation force," Phys. Rev. Lett. 44, 976
  88. Cook, R. J., 1981, "Photon number statistics in resonance fluorescence," Phys. Rev. A 23, 1243
  89. Cook, R. J., and A. F. Bernhardt, 1978, "Deflection of atoms by a resonant standing electromagnetic wave," Phys. Rev. A 18, 2533
  90. Cook, R. J., and R. K. Hill, 1982, "An electromagnetic mirror for neutral atoms," Opt. Commun. 43, 258
  91. Corney, A., 1977, Atomic and Laser Spectroscopy (Clarendon, Oxford), Chap. 5
  92. Cross, W. G., and N. F. Ramsey, 1950, "The conservation of energy and momentum in Compton Scattering," Phys. Rev. 80, 929
  93. Dalibard, J., and C. Cohen-Tannoudji, 1985a, "Atomic motion in laser light: Connection between semiclassical and quantum descriptions," J. Phys. B 18, 1661
  94. Dalibard, J., and C. Cohen-Tannoudji, 1985b, "Dressed atom approach to atomic motion in laser light: The dipole force revisited," J. Opt. Soc. Am. B2, 1707
  95. Dalibard, J., S. Reynaud, and C. Cohen-Tannoudji, 1983, "Proposals of stable optical traps for neutral atoms," Opt. Commun. 47, 395
  96. Dalibard, J., S. Reynaud, and C. Cohen-Tannoudji, 1984, "Potentialities of a new σ+σ laser configuration for radiative cooling and trapping," J. Phys. B 17, 4577
  97. Dehmelt, H. G., 1967, "Radiofrequency spectroscopy of stored ions I: Storage," Adv. At. Mol. Phys. 3, 53
  98. Dehmelt, H. G., 1969, "Radiofrequency spectroscopy of stored ions II: Spectroscopy," Adv. At. Mol. Phys. 5, 109
  99. Dehmelt, H. G., 1976, "Entropy reduction by motional sideband excitation," Nature (London) 262, 777
  100. Dehmelt, H. G., 1981a, "Stored ion spectroscopy," in Advances in Laser Spectroscopy, NATO Advanced Science Institute Series B, Vol. 95 (San Miniato, Italy), edited by F. T. Arecchi, F. Strumia, and H. Walther (Plenum, New York/London), p. 153
  101. Dehmelt, H. G., 1981b, "Coherent spectroscopy on single atomic system at rest in free space II," J. Phys. (Paris) Colloq. C8-42, Suppl. 12, 299
  102. Dehmelt, H. G., 1982, "Mono-ion oscillator as potential ultimate laser frequency standard," IEEE Trans. Instrum. Meas. IM-31, 83
  103. Delone, G. A., V. A. Grinchuk, S. D. Kuzmichev, M. L. Nagaeva, A. P. Kazantsev, and G. F. Surdutovich, 1980, "The Kapitza-Dirac resonance effect," Opt. Commun. 33, 149
  104. Djen, N., and W. T. Whitney, 1981, "Laser cooling by spontaneous anti-Stokes scattering," Phys. Rev. Lett. 46, 236
  105. Drullinger, R. E., and D. J. Wineland, 1979, "Laser cooling of ions bound to a Penning trap," in Laser Spectroscopy IV, edited by H. Walther and K. W. Rothe (Springer, Berlin), p. 66
  106. Drullinger, R. E., D. J. Wineland, and J. C. Bergquist, 1980, "High resolution optical spectra of laser cooled ions," Appl. Phys. 22, 365
  107. Einstein, A., 1917, "Quantentheorie der Strahlung," Phys. Z. 18, 121
  108. Ekstrom, P., and D. Wineland, 1980, "The isolated electron," Sci. Am. 243, 90
  109. Ertmer, W., R. Blatt, and J. L. Hall, 1984, "Some candidate atoms and ions for frequency standard using laser radiation cooling," Prog. Quantum Electron. 8, 249
  110. Ertmer, W., R. Blatt, J. L. Hall, and M. Zhu, 1985, "Laser manipulation of atomic beam velocities: Demonstration of stopped atoms and velocity reversal," Phys. Rev. Lett. 54, 996
  111. Evenson, K. M., D. A. Jennings, F. R. Peterson, J. S. Wells, and R. E. Drullinger, 1984, "Optical frequency synthesis spectroscopy," Prog. Quantum Electron. 8, 143
  112. Fiordilino, E., and M. H. Mittelman, 1984, "Forces on atoms in a standing-wave laser field," Phys. Rev. A 30, 177
  113. Frisch, R., 1933, "Experimenteller Nachweis des Einsteinischen Straklungsrückstosses," Z. Phys. 86, 42
  114. Gaponov, A. V., and M. A. Miller, 1958, "Potential wells for charged particles in a high-frequency electromagnetic field," Zh. Eksp. Teor. Fiz. 34, 242
  115. Gardiner, C. W., 1983, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, Berlin)
  116. Gardiner, C. W., 1984, "Adiabatic elimination in stochastic systems. I. Formulation of methods and application to few-variable systems," Phys. Rev. A 29, 2814
  117. Gardiner, C. W., and M. L. Steyn-Ross, 1984, "Adiabatic elimination in stochastic systems. II. Application to reaction diffusion and hydrodynamic-like systems," Phys. Rev. A 29, 2823
  118. Giacobino, E., and P. R. Berman, 1984, "Cooling of vapors using collisionally aided radiative excitation," Prog. Quantum Electron. 8, 215
  119. Giacobino, E., M. Tawil, P. R. Berman, O. Redi, and H. H. Stroke, 1983, "Production of "hot" excited-state atoms in collisionally aided radiative transitions," Phys. Rev. A 28, 2555
  120. Goela, J. S., and R. K. Thareja, 1982a, "Heating or cooling of gases with tunable laser radiation," Opt. Commun. 40, 254
  121. Goela, J. S., and R. K. Thareja, 1982b, "Cooling or heating of gases through energy transfer using lasers," Opt. Commun. 42, 417
  122. Gordon, J. P., 1984, "The motion of atoms in a radiative trap," Prog. Quantum Electron. 8, 177
  123. Gordon, J. P., and A. Ashkin, 1980, "Motion of atoms in a radiation trap," Phys. Rev. A 21, 1606
  124. Gould, P. L., G. A. Ruff, and D. E. Pritchard, 1986, "Diffraction of atoms by light: The near-resonant Kapitza-Dirac effect," Phys. Rev. Lett. 56, 827
  125. Gozzini, A., F. Maccarone, F. Mango, I. Longo, and S. Barbarino, 1985, "Light pressure bistability at microwave frequencies," J. Opt. Soc. Am. B2, 1841
  126. Grabert, H., 1982, Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer Tracts in Modern Physics, Vol. 95 (Springer, Berlin)
  127. Greene, G. L., 1984, "Trapping of low energy neutrons," Prog. Quantum Electron. 8, 257
  128. Grinchuk, V. A., A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, 1981a, "Scattering of atoms by a short standing-light-wave pulse," Pis'ma Zh. Eksp. Teor. Fiz. 34, 395
  129. Grinchuk, V. A., A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, 1984, "Scattering of atoms by the forces of stimulated radiation pressure," Zh. Eksp. Teor. Fiz. 86, 100
  130. Grinchuk, V. A., E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, and G. I. Surdutovich, 1985, "Scattering of atoms by coherent interaction with light," J. Opt. Soc. Am. B2, 1805
  131. Grinchuk, V. A., E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, and V. P. Yakovlev, 1981b, "Scattering of an atomic beam by a short light pulse," Phys. Lett. A 86, 136
  132. Haake, F., and M. Lewenstein, 1983a, "Adiabatic expansion for the single-mode laser," Phys. Rev. A 27, 1013
  133. Haake, F., and M. Lewenstein, 1983b, "Adiabatic drag and initial slip in random processes," Phys. Rev. A 28, 3606
  134. Haken, H., 1977, Synergetics. An Introduction (Springer, Berlin)
  135. Hall, J. L., C. J. Bordé, and K. Uehara, 1976, "Direct optical resolution of the recoil effect using saturated absorber spectroscopy," Phys. Rev. Lett. 37, 1339
  136. Hänsch, T., and A. Schawlow, 1975, "Cooling of gases by laser radiation," Opt. Commun. 13, 68
  137. Hemmer, P. R., S. Ezekiel, and C. C. Leiky, 1984, "Stabilization of a microwave oscillator using a resonance Raman transition in a sodium beam," Prog. Quantum Electron. 8, 161
  138. Hemmer, P. R., F. Y. Wu, and S. Ezekiel, 1981, "Influence of atomic recoil on power-broadened lineshapes in 2-level atoms," Opt. Commun. 38, 105
  139. Hillary, M., R. F. O'Connell, M. O. Scully, and E. P. Wigner, 1984, "Distribution functions in physics: Fundamentals," Phys. Rep. 106, 121
  140. Itano, W. M., and D. J. Wineland, 1981, "Laser cooling double resonance spectroscopy of stored ions," in Laser Spectroscopy V, edited by D. R. W. McKellar, T. Oka, and B. P. Stoicheff (Springer, Berlin), p. 360
  141. Itano, W. M., and D. J. Wineland, 1982, "Laser cooling of ions stored in harmonic and Penning traps," Phys. Rev. A 25, 35
  142. Jacquinot, D., S. Liberman, J. L. Picque, and J. Pinard, 1973, "High resolution spectroscopic application of atomic beam deflection by resonant light," Opt. Commun. 8, 163
  143. Javanainen, J., 1980a, "Light pressure cooling of trapped ions in three dimensions," Appl. Phys. 23, 175
  144. Javanainen, J., 1980b, "Separation of atomic beams by light pressure," Appl. Phys. 21, 263
  145. Javanainen, J., 1980c, "Low intensity fluorescence from a trapped ion," Opt. Commun. 34, 375
  146. Javanainen, J., 1981a, "Light-induced motion of trapped ions I: Low-intensity limit," J. Phys. B 14, 2519
  147. Javanainen, J., 1981b, "Light-induced motion of trapped ions II: Arbitrary intensity," J. Phys. B 14, 4191
  148. Javanainen, J., 1982, "Theory of resonance-light pressure," Acta Phys. Pol. A 61, 271
  149. Javanainen, J., 1985, "Light-induced motion of trapped ions III: Expansion around the recoilless solution," J. Phys. B 18, 1549
  150. Javanainen, J., M. Kaivola, U. Nielsen, O. Poulsen, and E. Riis, 1985, "Laser cooling of a fast ion beam," 1985, J. Opt. Soc. Am. B2, 1768
  151. Javanainen, J., M. Lindberg, and S. Stenholm, 1984, "Laser cooling of trapped ions: Dynamics of the final stages," J. Opt. Soc. Am. B1, 111
  152. Javanainen, J., and S. Stenholm, 1980a, "Broad band resonant light pressure I: Basic equations," Appl. Phys. 21, 35
  153. Javanainen, J., and S. Stenholm, 1980b, "Broad band resonant light pressure II: Cooling of gases," Appl. Phys. 21, 163
  154. Javanainen, J., and S. Stenholm, 1980c, "Laser cooling of trapped particles I: The heavy particle limit," Appl. Phys. 21, 283
  155. Javanainen, J., and S. Stenholm, 1981a, "Laser cooling of trapped particles II: The fast particle limit," Appl. Phys. 24, 71
  156. Javanainen, J., and S. Stenholm, 1981b, "Laser cooling of trapped particles III: The Lamb-Dicke limit," Appl. Phys. 24, 151
  157. Kaneko, K., 1981, "Adiabatic elimination by the eigenfunction expansion method," Prog. Theor. Phys. 66, 129
  158. Kazantsev, A. P., 1973, "Acceleration of atoms by a resonance field," Zh. Eksp. Teor. Fiz. 63, 1628
  159. Kazantsev, A. P., 1974, "The acceleration of atoms by light," Zh. Eksp. Teor. Fiz. 66, 1599
  160. Kazantsev, A. P., 1975, "Recoil effect in a strong resonant field," Zh. Eksp. Teor. Fiz. 67, 1660
  161. Kazantsev, A. P., 1978, "Resonance light pressure," Usp. Fiz. Nauk. 124, 113
  162. Kazantsev, A. P., V. S. Smirnov, G. I. Surdutovich, D. O. Chudesnikov, and V. P. Yakovlev, 1985, "Kinetic phenomena of atomic motion in a light field," J. Opt. Soc. Am. B2, 1731
  163. Kazantsev, A. P., and V. P. Sokolov, 1980, "Stimulated Coulomb interaction of neutral atoms," Opt. Acta 27, 269
  164. Kazantsev, A. P., and G. I. Surdutovich, 1975, "The Kapitza-Dirac effect for atoms in a strong resonant field," Pis'ma Zh. Eksp. Teor. Fiz. 21, 346
  165. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1980, "On the quantum theory of resonance scattering of atoms by light," Pis'ma Zh. Eksp. Teor. Fiz. 31, 542
  166. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1981a, "Motion of atoms and molecules in a resonant light field," Zh. Eksp. Teor. Fiz. 80, 541
  167. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1981b, "The motion of atoms and molecules in a resonance light field," J. Phys. (Paris) 42, 1231
  168. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1981c, "The scattering of slow atoms by light," Appl. Phys. 25, 165
  169. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1982, "Intersection of the quasi-energetical terms of an atom in the field of a standing light wave," Opt. Commun. 43, 180
  170. Kazantsev, A. P., G. I. Surdutovich, and V. P. Yakovlev, 1983, "Atomic dispersion in a light field," Zh. Eksp. Teor. Fiz. 85, 852
  171. Kazantsev, A. P., G. I. Surdutovich, V. P. Yakovlev, and D. O. Chudesnikov, 1985, "On the quantum theory of the scattering of atoms by a standing light wave," Opt. Commun. 52, 311
  172. Klein, M. J., 1952, "The ergodic theorem in quantum statistical mechanics," Phys. Rev. 87, 111
  173. Kol'chenko, A. P., S. G. Rautian, and R. I. Sokolovskii, 1969, "Interaction of an atom with a strong electromagnetic field with the recoil effect taken into consideration," Zh. Eksp. Teor. Fiz. 55, 1864
  174. Krasnov, I. V., and N. Ya. Shaparev, 1975, "Separation of gases by resonant electromagnetic fields," Pis'ma Zh. Tekh. Fiz. 1, 875
  175. Krasnov, I. V., and N. Ya. Shaparev, 1976, "Cooling of atoms by resonant radiation and separation of isotopes," Pis'ma Zh. Tekh. Fiz. 2, 769
  176. Krasnov, I. V., and N. Ya. Shaparev, 1977, "A possible use of the radiation pressure in a gas for spectroscopic purpose," Kvant. Elektron. (Moscow) 4, 176
  177. Krasnov, I. V., and N. Ya. Shaparev, 1978, "Manifestation of the resonance radiation pressure in a gas," Opt. Commun. 27, 239
  178. Krasnov, I. V., and N. Ya. Shaparev, 1979, "Phasing of atomic velocities in the field of a travelling electromagnetic wave," Zh. Eksp. Teor. Fiz. 77, 899
  179. Kubo, R., 1957, "Statistical-mechanical theory of irreversible processes I. General theory and simple application to magnetic and conduction problems," J. Phys. Soc. Jpn. 12, 570
  180. Lakkaraju, H. S., and H. A. Schuessler, 1982, "Motional sideband resonances in the microwave spectrum of stored ions," J. Appl. Phys. 53, 3967
  181. Lam, J. F., and P. R. Berman, 1976, "Effect of recoil on resonance fluorescence," Phys. Rev. A 14, 1683
  182. Lax, M., 1950, "Removal of degeneracy in any order," Phys. Rev. 79, 200
  183. Lebedev, P., 1901, "Untersuchungen über die Druckkräfte des Lichtes," Ann. Phys. (Leipzig) 6, 433
  184. Lebedev, P., 1910a, "The pressure of light on gases. An experimental study for the theory of comets' tails," Astrophys. J. 31, 385
  185. Lebedev, P. N., 1910b, "Die Druckkräfte des Lichtes auf Gase," Ann. Phys. (Leipzig) 32, 411
  186. Lenstra, D., 1982, "Photon number statistics in resonance fluorescence," Phys. Rev. A 26, 3369
  187. Letokhov, V. S., 1968, "Narrowing of the Doppler width in a standing light wave," Pis'ma Zh. Eksp. Teor. Fiz. 7, 348
  188. Letokhov, V. S., 1977, "Laser methods of γ spectroscopy without Doppler broadening," Comments At. Mol. Phys. 6, 117
  189. Letokhov, V. S., and V. P. Chebotaev, 1977, Nonlinear Laser Spectroscopy (Springer, Berlin), Sec. 10.2.2
  190. Letokhov, V. S., and V. G. Minogin, 1977, "Quantum motions of ultracooled atoms in resonant laser field," Phys. Lett. A 61, 370
  191. Letokhov, V. S., and V. G. Minogin, 1978a, "Quantum motion of atoms in the resonant field of a standing light wave," Zh. Eksp. Teor. Fiz. 74, 1318
  192. Letokhov, V. S., and V. G. Minogin, 1978b, "Trapping and storage of atoms in a laser field," Appl. Phys. 17, 99
  193. Letokhov, V. S., and V. G. Minogin, 1979, "Cooling, trapping and storage of atoms by resonant laser fields," J. Opt. Soc. Am. 69, 413
  194. Letokhov, V. S., and V. G. Minogin, 1980, "Possibility of accumulation and storage of cold atoms in magnetic traps," Opt. Commun. 35, 199
  195. Letokhov, V. S., and V. G. Minogin, 1981a, "Laser cooling of atoms and its application in frequency standards," J. Phys. (Paris) Colloq. C8-42, 347
  196. Letokhov, V. S., and V. G. Minogin, 1981b, "Laser radiation pressure on free atoms," Phys. Rep. 73, 1
  197. Letokhov, V. S., V. G. Minogin, and B. D. Pavlik, 1976, "Cooling and trapping of atoms and molecules by a resonant laser field," Opt. Commun. 19, 72
  198. Letokhov, V. S., V. G. Minogin, and B. D. Pavlik, 1977, "Cooling and capture of atoms and molecules by a resonant light field," Zh. Eksp. Teor. Fiz. 72, 1328
  199. Letokhov, V. S., and B. D. Pavlik, 1976, "Spectral line narrowing in a gas by atoms trapped in a standing light wave," Appl. Phys. 9, 229
  200. Levin, G. A., 1980, "A new way of gas cooling by light," Opt. Commun. 35, 61
  201. Lindberg, M., 1984, "Steady state of a laser-cooled trapped ion in the Lamb-Dicke limit," J. Phys. B 17, 2129
  202. Lindberg, M., and S. Stenholm, 1984, "The master equation for laser cooling of trapped particles," J. Phys. B 17, 3375
  203. Löwdin, P.-O., 1951, "A note on the quantum-mechanical perturbation theory," J. Chem. Phys. 19, 1396
  204. Mandel, L., 1979a, "Distribution of atomic momentum in resonance fluorescence," J. Opt. (Paris) 10, 51
  205. Mandel, L., 1979b, "Sub-Poissonian photon statistics in resonance fluorescence," Opt. Lett. 4, 205
  206. Melik-Barkhudarov, T. K., 1982, "Dynamics of an atom in a field of quantized radiation and an elliptically polarized wave," Zh. Eksp. Teor. Fiz. 83, 1241
  207. Meystre, P., E. M. Wright, I. McCullen, and E. Wignes, 1985, "Theory of radiation pressure driven interferometers," J. Opt. Soc. Am. B2, 1830
  208. Migdall, A. L., J. V. Prodan, W. D. Phillips, T. H. Bergeman, and H. J. Metcalf, 1985, "First observation of magnetically trapped neutral atoms," Phys. Rev. Lett. 54, 2596
  209. Minogin, V. G., 1980a, "Deceleration and monochromatization of atomic beams by laser radiation pressure," Opt. Commun. 34, 265
  210. Minogin, V. G., 1980b, "Kinetic equation for atoms interacting with laser radiation," Zh. Eksp. Teor. Fiz. 79, 2044
  211. Minogin, V. G., 1981, "Kinetic theory of the scattering of atoms by a resonant standing light wave," Zh. Eksp. Teor. Fiz. 80, 2231
  212. Minogin, V. G., 1982a, "The theory of the radiative atomic trap," Kvant. Elektron. (Moscow) 9, 505
  213. Minogin, V. G., 1982b, "Resonance light pressure in the field of partially coherent laser radiation," Opt. Spectrosc. 53, 73
  214. Minogin, V. G., 1982c, "Single-ion oscillator with radiative cooling," Usp. Fiz. Nauk. 137, 173
  215. Minogin, V. G., 1982d, "Local velocity distribution of atoms in a light wave in resonance with an atomic transition," Zh. Tekh. Fiz. 52, 1905
  216. Minogin, V. G., 1985, "Resonance-radiation pressure on atoms in symmetric light fields," Opt. Lett. 10, 179
  217. Minogin, V. G., and J. Javanainen, 1982, "A tetrahedral light pressure trap for atoms," Opt. Commun. 43, 119
  218. Minogin, V. G., V. S. Letokhov, and T. V. Zueva, 1981, "Hydrodynamical equations for atomic motion in a resonant light wave," Opt. Commun. 38, 225
  219. Minogin, V. G., and Yu. V. Rozhdestvenskii, 1983a, "Motion of a multilevel atom in resonance light fields," Opt. Spectrosc. 54, 369
  220. Minogin, V. G., and Yu. V. Rozhdestvenskii, 1983b, "Resonance radiation pressure on interstellar gas," Sov. Astron. AJ 27, 403
  221. Minogin, V. G., and Yu. V. Rozhdestvensky, 1984, "Dynamics of a three-level atom in a resonant light field," Appl. Phys. B 34, 161
  222. Minogin, V. G., and O. T. Serimaa, 1979, "Resonant light pressure force in a strong laser wave," Opt. Commun. 30, 373
  223. Mittleman, M. H., K. Rubin, R. H. Callender, and J. I. Gersten, 1977, "Deflection of laser-excited atoms by an electric field," Phys. Rev. A 16, 583
  224. Moskowitz, P. E., P. L. Gould, S. R. Atlas, and D. E. Pritchard, 1983, "Diffraction of an atomic beam by standingwave radiation," Phys. Rev. Lett. 51, 370
  225. Moskowitz, P. E., P. L. Gould, and D. E. Pritchard, 1985, "Deflection of atoms by standing wave radiation," J. Opt. Soc. Am. B2, 1784
  226. Moyal, J. E., 1949, "Quantum mechanics as a statistical theory," Proc. Cambridge Philos. Soc. 45, 99
  227. Mulser, P., 1985, "Radiation pressure on macroscopic bodies," J. Opt. Soc. Am. B2, 1814
  228. Nebenzahl, I., and A. Szöke, 1974, "Deflection of atomic beams by resonance radiation using stimulated emission," Appl. Phys. Lett. 25, 327
  229. Neuhauser, W., M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, 1978a, "Optical-sideband cooling of visible atom cloud confined in parabolic well," Phys. Rev. Lett. 41, 233
  230. Neuhauser, W., M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, 1978b, "Visual observation and optical cooling of electrodynamically contained ions," Appl. Phys. 17, 123
  231. Neuhauser, W., M. Hohenstatt, P. E. Toschek, and H. G. Dehmelt, 1980, "Localized visible Ba+ mono-ion-oscillator," Phys. Rev. A 22, 1137
  232. Neuhauser, W., M. Hohenstatt, P. E. Toschek, and H. Dehmelt, 1981, "Resonance fluorescence from single ions at rest," in Spectral Line Shapes, Proceedings 5th International Conference..., edited by P. Wende (de Gruyter, Berlin/New York), p. 1045
  233. Nichols, E. F., and G. F. Hull, 1901, "A preliminary communication on the pressure of heat and light radiation," Phys. Rev. 13, 307
  234. Nichols, E. F., and G. F. Hull, 1903, "The pressure due to radiation," Phys. Rev. 17, 26 ibid.17, 91
  235. Pawula, R. F., 1967, "Approximation of the linear Boltzmann equation by the Fokker-Planck equation," Phys. Rev. 162, 186
  236. Pearson, D. B., R. R. Freeman, J. E. Bjorklund, and A. Ashkin, 1980, "Focusing and defocusing of neutral atomic beams using resonance-radiation pressure," Appl. Phys. Lett. 36, 99
  237. Pearson, D. B.R. R. FreemanJ. E. BjorklundA. AshkinPhillips, W. D., 1984, Ed., "Laser-cooled and trapped atoms, a workshop on spectroscopic applications of slow atomic beams," Prog. Quantum Electron. 8, 115
  238. Phillips, W. D., and H. J. Metcalf, 1982, "Laser deceleration of an atomic beam," Phys. Rev. Lett. 48, 596
  239. Phillips, W. D., J. V. Prodan, and H. J. Metcalf, 1983, "Laser cooling of free neutral atoms in an atomic beam," in Laser Spectroscopy VI, edited by H. P. Weber and W. Lüthy (Springer, Berlin), p. 162
  240. Phillips, W. D., J. V. Prodan, and H. J. Metcalf, 1985, "Laser cooling and electromagnetic trapping of neutral atoms," J. Opt. Soc. Am. B2, 1751
  241. Picque, J. L., 1979, "Radiation-induced modifications of the atomic momentum distribution in a traveling-wave resonance light field," Phys. Rev. A 19, 1622
  242. Picque, J. L., and J. L. Vialle, 1972, "Atomic-beam deflection and broadening by recoils due to photon absorption or emission," Opt. Commun. 5, 402
  243. Power, E. A., and S. Zienau, 1959, "Coulomb gauge in nonrelativistic quantum electrodynamics and the shape of spectral lines," Philos. Trans. R. Soc. London 251, 427
  244. Prichard, D. E., 1983, "Cooling neutral atoms in a magnetic trap for precision spectroscopy," Phys. Rev. Lett. 51, 1336
  245. Prichard, D. E., and P. L. Gould, 1985, "Experimental possibilities for observation of unidirectional momentum transfer of atoms from standing wave light," J. Opt. Soc. Am. B2, 1799
  246. Prodan, J., A. Migdall, W. D. Phillips, I. So, H. Metcalf, and J. Dalibard, 1985, "Stopping atoms with laser light," Phys. Rev. Lett. 54, 992
  247. Prodan, J. V., W. D. Phillips, and H. Metcalf, 1982, "Laser production of a very slow monoenergetic atomic beam," Phys. Rev. Lett. 49, 1148
  248. Pusep, A. Yu., 1976, "Acceleration of atoms by strong resonance field," Zh. Eksp. Teor. Fiz. 70, 851
  249. Pusep, A. Yu., A. B. Doktorov, and A. I. Burshtein, 1977, "Effect of coherent radiation on the translational motion of atoms," Zh. Eksp. Teor. Fiz. 72, 98
  250. Ramsey, N. F., 1983, "History of atomic clocks," J. Res. Natl. Bur. Stand. 88, 301
  251. Risken, H., 1984, The Fokker-Planck Equation, Methods of Solution and Applications (Springer, Berlin)
  252. Roosen, G., and Ch. Imbert, 1978, "The TEM01 mode laser beam—a powerful tool for optical levitation of various types of spheres," Opt. Commun. 26, 432
  253. Savolainen, J., and S. Stenholm, 1972, "The Hamiltonian of quantum electronics," Am. J. Phys. 40, 667
  254. Schieder, R., H. Walther, and L. Wöste, 1972, "Atomic beam deflection by the light of a tunable dye laser," Opt. Commun. 5, 337
  255. Schlicher, R. R., W. Becker, J. Bergou, and M. O. Scully, 1984, "Interaction Hamiltonian in quantum optics or: p·A vs. E·r revisited," in Quantum Electrodynamics and Quantum Optics, edited by A. O. Barut (Plenum, New York), p. 405
  256. Schrödinger, E., 1927, "Über den Compton effekt," Anns. Phys. (Leipzig) 82, 257
  257. Shapiro, V. E., 1976, "Cooling of matter by a high frequency resonance field," Zh. Eksp. Teor. Fiz. 70, 1463
  258. Shirley, J. H., 1980, "Recoil effects on Doppler-free lineshapes in non-linear spectroscopy," J. Phys. B 13, 1537
  259. Shirley, J. H., and S. Stenholm, 1977, "New quantum representation for treating recoil effects in non-linear spectroscopy," J. Phys. A 10, 613
  260. Short, R., and L. Mandel, 1983, "Observation of sub-Poissonian photon statistics," Phys. Rev. Lett. 51, 384
  261. Singh, S., 1983, "Antibunching, sub-Poissonian photon statistics and finite band width effects in resonance fluorescence," Opt. Commun. 44, 254
  262. Smirnov, D. F., and I. V. Sokolov, 1976, "Intensity-fluctuation spectrum of spontaneous radiation," Zh. Eksp. Teor. Fiz. 70, 2098
  263. Smirnov, D. F., and A. S. Troshin, 1977, "Intensity fluctuation spectrum of the nonlinear resonance fluorescence of an atomic system," Zh. Eksp. Teor. Fiz. 72, 2055
  264. Smirnov, D. F., and A. S. Troshin, 1979, "Possibility of observing negative time pair correlation of photons in nonlinear resonance fluorescence," Zh. Eksp. Teor. Fiz. 76, 1254
  265. Smirnov, D. F., and A. S. Troshin, 1981, "Distribution of photocounts in nonlinear resonance fluorescence," Zh. Eksp. Teor. Fiz. 81, 1597
  266. Stenholm, S., 1974, "Recoil effects in quantum electronics: The nonlinear molecular response," J. Phys. B 7, 1235
  267. Stenholm, S., 1978a, "Redistribution of molecular velocities by optical processes," Appl. Phys. 15, 287
  268. Stenholm, S., 1978b, "Theoretical foundations of laser spectroscopy," Phys. Rep. 43, 151
  269. Stenholm, S., 1983, "Distribution of photons and atomic momentum in resonance fluorescence," Phys. Rev. A 27, 2513
  270. Stenholm, S., 1984a, "Statistical mechanics of light-induced forces," J. Opt. Soc. Am. B1, 658
  271. Stenholm, S., 1984b, "Quantum fluctuations as corrections to slowly varying quantities," in Quantum Electrodynamics and Quantum Optics, edited by A. O. Barut (Plenum, New York), p. 263
  272. Stenholm, S., 1985, "Dynamics of trapped particle cooling in the Lamb-Dicke limit," J. Opt. Soc. Am. B2, 1743
  273. Stenholm, S., and A. Bambini, 1981, "Single-particle theory of the free-electron laser in a moving frame," IEEE J. Quantum Electron. QE-17, 1363
  274. Stenholm, S., and J. Javanainen, 1978, "Velocity redistribution by standing waves," Appl. Phys. 16, 159
  275. Stenholm, S., V. G. Minogin, and V. S. Lethokov, 1978, "Resonant light pressure due to a strong standing wave," Opt. Commun. 25, 107
  276. Tanguy, C., S. Reynaud, and C. Cohen-Tannoudji, 1984, "Deflection of an atomic beam by a laser wave: transition between diffractive and diffusive regimes," J. Phys. B 17, 4623
  277. Tanguy, C., S. Reynaud, M. Matsuoka, and C. Cohen-Tannoudji, 1983, "Deflection profiles of a monoenergetic atomic beam crossing a standing light wave," Opt. Commun. 44, 249
  278. Tatarskii, V. I., 1983, "The Wigner representation in quantum mechanics," Usp. Fiz. Nauk. 139, 587
  279. Titulaer, U. M., 1978, "A systematic solution procedure for the Fokker-Planck equation of a Brownian particle in the high friction case," Physica A 91, 321
  280. Titulaer, U. M., 1980a, "The Chapman-Enskog procedure as a form of degenerate perturbation theory," Physica A 100, 234
  281. Titulaer, U. M., 1980b, "Corrections to the Smoluchowski equation in the presence of hydrodynamic interactions," Physica A 100, 251
  282. Toschek, P. E., 1984, "Atomic particles in traps," in New Trends in Atomic Physics, Les Houches Session 38...1982, edited by Grynberg and R. Stora (North-Holland, Amsterdam), Vol. II, p. 381
  283. Toschek, P. E., and W. Neuhauser, 1980, "Einzelne Ionen für die Doppler-freie Spektroskopie," Phys. B1. 36, 198
  284. Toschek, P. E., and W. Neuhauser, 1981, "Spectroscopy of localized and cooled ions," in Atomic Physics, edited by D. Kleppner and F. M. Pipkin (Plenum, New York), Vol. 7 p. 529
  285. Ujihara, K., 1985, "Resonances and mirror confinement in a 3-mirror phase-conjugate resonator," J. Opt. Soc. Am. B2, 1846
  286. van Dyck, R. S., Jr., P. B. Schwinberg, and H. G. Dehmelt, 1977, "Precise measurements of axial, magnetron, cyclotron and spin-cyclotron beat frequencies on an isolated 1-meV electron," Phys. Rev. Lett. 38, 310
  287. van Kampen, N. G., 1981, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam)
  288. van Kampen, N. G., 1985, "Elimination of fast variables," Phys. Rep. 124, 70
  289. Vorobev, F. A., S. G. Rautian, and R. I. Sokolovskii, 1969, "The effect of recoil in the interaction of an atom with a strong field," Opt. Spectrosc. 27, 398
  290. Wang, Y., 1981, "Laser cooling of gas atoms by optical frequency shifts," Chinese Phys. 2, 227
  291. Wang, Y., 1983, "Monoenergetic atomic beam deflection by resonant light pressure," Chinese Phys. 3, 463
  292. Wang, Y., R. Zhou, Z. Zhou, W. Cai, G. Ni, S. Zhou, C. Wang, and W. Zheng, 1984, "Deflection of sodium atomic beam by resonance light pressure of multi-laser-beam," Sci. Sin. (Series A) 27, 881
  293. Wigner, E. P., 1932, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749
  294. Wineland, D. J., J. C. Bergquist, W. M. Itano, and R. E. Drullinger, 1980, "Double-resonance and optical-pumping experiments on electromagnetically confined, laser-cooled ions," Opt. Lett. 5, 245
  295. Wineland, D. J., J. J. Bollinger, W. M. Itano, and J. D. Prestage, 1985, "Angular momentum of trapped atomic particles," J. Opt. Soc. Am. B2, 1721
  296. Wineland, D. J., and H. Dehmelt, 1975, Bull. Am. Phys. Soc. 20, 637
  297. Wineland, D. J., R. E. Drullinger, and F. L. Walls, 1978a, "Radiation-pressure cooling of bound resonant absorbers," Phys. Rev. Lett. 40, 1639
  298. Wineland, D. J., P. Ekstrom, and H. Dehmelt, 1978b, "Monoelectron oscillator," Phys. Rev. Lett. 31, 1279
  299. Wineland, D. J., and W. M. Itano, 1979, "Laser cooling of atoms," Phys. Rev. A 20, 1521
  300. Wineland, D. J., and W. M. Itano, 1981, "Spectroscopy of single Mg+ ion," Phys. Lett. A 82, 75
  301. Wineland, D. J., W. M. Itano, and R. S. van Dyck, Jr., 1983, "High resolution spectroscopy of stored ions," Adv. At. Mol. Phys. 19, 135
  302. Wing, W. H., 1980, "Electrostatic trapping of neutral atomic particles," Phys. Rev. Lett. 45, 631
  303. Wing, W. H., 1985, "On neutral particle trapping in quasistatic electromagnetic fields," Prog. Quantum Electron. 8, 181
  304. Wuerker, R. F., H. Shelton, and R. V. Langmuir, 1959, "Electrodynamic containment of charged particles," J. Appl. Phys. 30, 342
  305. Zhelnov, B. L., A. P. Kazantsev and G. I. Surdutovich, 1977, "Scattering of atoms by an electromagnetic field," Kvant. Elektron. (Moscow) 4, 893
  306. Zhukova, N. I., and A. P. Kazantsev, 1978, "Cooling and heating of atoms colliding in an optical field," Pis'ma Zh. Eksp. Teor. Fiz. 27, 636
  307. Zueva, T. V., V. S. Letokhov, and V. G. Minogin, 1981, "Theory of the deceleration of atomic beams by resonant laser radiation," Zh. Eksp. Teor. Fiz. 81, 84
  308. Zueva, T. V., and V. G. Minogin, 1981, "Optimum slowing of atoms by a resonant laser beam," Pis'ma Zh. Tekh. Fiz. 7, 953
  309. Zwanzig, R., 1960, "Ensemble method in the theory of irreversibility," J. Chem. Phys. 33, 1338

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation