Preface ........................................................... v Introduction ...................................................... 1 Chapter 1. Coherent Interaction between Atoms and Field ........... 9 1. The Hamiltonian of Atom-Field Interaction .................. 9 2. Light Pressure Force ...................................... 18 2.1. Adiabatic states. Nonresonant potential ............. 24 2.2. Diabatic states. Resonant potential ................. 28 2.3. Atomic density-matrix equation with allowance for a recoil effect ................................. 31 3. The Non-Adiabaticity Operator. Landau-Zener (LZ) Transitions ............................................... 33 Chapter 2. Scattering of Atoms by Light .......................... 45 4. The Classical Picture of Scattering ....................... 45 5. Acceleration of Atoms by Light ............................ 58 6. Diffraction of Atoms ...................................... 68 6.1. Diffraction of a "coherent" atomic beam ............. 68 6.2. Experiment .......................................... 71 6.3. Bragg scattering .................................... 73 6.4. The scattering of atoms by a quantized electromagnetic field ............................... 76 7. The Interference of Atoms ................................. 81 7.1. The interference of atoms scattered by a single standing wave ....................................... 82 7.2. The transfer of the spatial coherence under the Echo conditions ..................................... 85 7.3. Pulse scattering regime ............................. 87 7.4. Nonlinear atomic interferometry ..................... 88 7.5. The Bohm-Aaronov effect ............................. 89 7.6. The interference of atoms in a gas .................. 89 7.7. Combined scattering regime .......................... 91 Chapter 3. Dispersion of Atoms in Light Fields ................... 95 8. Dispersion of Atoms in the Periodic Light Field ........... 95 8.1. Travelling wave ..................................... 96 8.2. Atoms in a standing wave. Symmetry of the problem ............................................. 98 8.3. Dispersion law for a weak field .................... 100 9. A Strong Field Case. The Above-Barrier Motion ............ 103 9.1. The scalar particle in a periodic potential ........ 104 9.2. The influence of the Landau-Zener transitions ...... 105 9.3. The Bloch functions of an atom in a standing-wave field ................................ 108 9.4. Optical characteristics of atoms in a standing-wave field ................................ 109 10. The Under-Barrier Motion of Atoms in a Strong Field ............................................. 113 10.1. The bipotential motion (Δ/2 < ε < V0). Strong coupling approximation (small Δ) ............ 113 10.2. The lifetime of bound states of atoms at large Δ ......................................... 117 10.3. The quasiclassical analysis of the sub- barrier motion ..................................... 122 11. Bipotential Scattering ................................... 130 Chapter 4. Influence of Spontaneous Radiation on Light Pressure Force ....................................... 141 12. Equation for the Atomic Density Matrix ................... 142 13. The Light Pressure Force and the Hysteresis Phenomenon ............................................... 150 13.1. Light pressure force in the travelling wave ........ 152 13.2. Light pressure force in the standing wave .......... 153 13.3. Peculiarities of the perturbation theory in the field of a standing wave ....................... 155 13.4. Strong field. Quasistationary approximation ........ 161 13.5. Strong field. Quasiclassical approximation. LZ-transitions ..................................... 168 13.6. Friction force for fast atoms ...................... 176 14. Light Pressure Force and Spectrum of Resonance Fluorescence ............................................. 178 14.1. Atomic correlation matrix with allowance for recoil ......................................... 178 14.2. Spectrum resonance fluorescence in the field of a travelling wave ............................... 183 14.3. Relationship between the light pressure force and spectrum of resonance fluorescence ............. 186 14.4. Spectrum of resonance fluorescence in the field of a standing wave ........................... 189 15. Cooling and Velocity Bunching of Atoms in the Light Field .............................................. 194 15.1. Deceleration of atoms in the intense standing wave ...................................... 194 15.2. Cooling of atoms by the spontaneous light pressure force ..................................... 196 15.3. Coooling of trapped ions by the light field ........ 196 15.4. Bunching of atoms in the velocity space ............ 201 16. Interference Phenomena and the Effect of Rectification of the Radiation Force ..................... 212 16.1. Interference phenomena in the monochromatic field .............................................. 212 16.2. Interference phenomena in a weak bichromatic field .............................................. 217 16.3. Bichromatic fields of finite amplitude ............. 219 Chapter 5. Kinetics of Atoms in Light Fields .................... 227 17. Kinetics of Atoms in the Travelling Wave Field ........... 228 17.1. The Fokker-Planck kinetic equation ................. 228 17.2. Slow bunching in velocities of atoms in the travelling wave field .......................... 231 17.3. Rapid velocity bunching in the presence of magnetic field .................................. 235 17.4. Influence of the light pressure on the nonlinear susceptibility of resonance atoms ........ 236 18. Kinetics of Atoms in a Weak Standing-Wave Field .......... 241 18.1. Kinetic equation in linear approximation in the field strength ................................. 241 18.2. Evolution of the velocity distribution in a weak standing-wave field ......................... 247 18.3. Viscous confinement in a field of the three orthogonal standing waves .......................... 253 18.4. Nonlinear susceptibility of resonance atoms in a standing-wave field ........................... 254 19. Kinetic Equation for Slow Atoms in a Standing-Wave Field .................................................... 256 19.1. Derivation of the kinetic equation ................. 257 19.2. Properties of the kinetic coefficients ............. 260 19.3. Light pressure force in a laser beam of finite radius ...................................... 264 20. Scattering of Atoms by a Standing Wave in the Kinetic Regime ........................................... 267 21. Cooling and Localization of Atoms in a Strong Standing Light Wave ...................................... 276 21.1. Stationary solution of the kinetic equation ........ 277 21.2. Effective temperature of the untrapped particles .......................................... 279 21.3. One-dimensional lattice of cooled atoms and the channelling phenomenon ......................... 281 21.4. Three-dimensional lattice of cooled atom ........... 285 21.5. Lifetime of atoms in the light-wave grating ........ 288 21.6. Viscous confinement in a saturating field .......... 289 22. Localization of Atoms in Strong Fields ................... 291 22.1. Motion of atoms in the focus of a laser beam ....... 292 22.2. Localization of atoms by light and magnetic fields .................................... 295 22.3. Localization of atoms in a bichromatic field ....... 297 23. Kinetics of Fast Atoms in a Standing Light Wave .......... 299 23.1. Kinetics of atoms under strong hysteresis .......... 300 23.2. Fokker-Planck equation for fast atoms .............. 302 23.3. Strong field. Bipotential kinetics ................. 306 24. Diffraction, Diffusion and Potential Scattering Atoms in a Standing-Light Wave Field ..................... 308 24.1. Basic equations .................................... 309 24.2. The case of large detunings. Spatial correlation of spontaneous and induced transitions ............. 311 24.3. Diffraction scattering ............................. 315 24.4. Incoherent scattering .............................. 317 24.5. Statistics of scattered photons .................... 320 25. Polarization Effects in the Resonance Light Pressure ................................................. 320 25.1. Equation for the density matrix .................... 321 25.2. Magnetization of atoms by the linearly polarized wave ..................................... 326 26. Density Effects .......................................... 330 26.1. Atomic collisions in a light field ................. 330 26.2. The interaction of atoms in a light field .......... 333 Appendix I. Diffraction of Atoms from a Standing-Wave Field with Smooth Temporal Envelope ............... 337 Appendix II. Effects of Spontaneous Relaxation in the Transfer of Spatial Coherence under the Echo Conditions .... 341 Appendix III. General Form of the Dispersion Law for Atoms in a Standing-Wave Field .................... 347 Appendix IV. Dispersion of an Atom in a Strong Standing Wave under Small Detunings from Resonance .............. 353 Appendix V. Solution of the Bloch Equations Near the Standing-Wave Nodes ............................... 363 References ...................................................... 367 Subject Index ................................................... 375