Optically Polarized Atoms : Understanding Light-atom Interactions

Optically Polarized Atoms is addressed at upper-level undergraduate and graduate students involved in research in atomic, molecular, and optical Physics. It will also be useful to researchers practicing in this field. It gives an intuitive, yet sufficiently detailed and rigorous introduction to light-atom interactions with a particular emphasis on the symmetry aspects of the interaction, especially those associated with the angular momentum of atoms and light. The book will enable readers to carry out practical calculations on their own, and is richly illustrated with examples drawn from current research topics, such as resonant nonlinear magneto-optical effects. The book comes with a software package for a variety of atomic-physics calculations and further interactive examples that is freely downloadable from the book's web page, as well as additional materials (such as power-point presentations) available to instructors who adopt the text for their courses. Contents......Page 8 List of acronyms......Page 12 PART I: INTRODUCTION TO LIGHT–ATOM INTERACTIONS......Page 14 1.2 How to use this book......Page 16 1.3 Relation to other texts......Page 17 1.4 Formalism of quantum mechanics......Page 18 2.1 Energy states of the hydrogen atom......Page 21 2.2 Angular momentum of the electron in the hydrogen atom......Page 22 2.3 Multielectron atoms......Page 32 2.4 Hyperfine interactions and hyperfine structure of atomic states......Page 39 2.5 Parity of atomic states......Page 40 3.1 Classical rotations......Page 43 3.2 Quantum-mechanical rotations......Page 49 3.3 The angular-momentum operator......Page 52 3.4 Rotations in the Zeeman basis......Page 56 3.5 Addition of angular momenta; Clebsch–Gordan coefficients......Page 58 3.6 3j and 6 j symbols......Page 59 3.7 Irreducible tensors and tensor products......Page 62 3.8 The Wigner–Eckart theorem......Page 64 4.1 Linear Zeeman effect......Page 68 4.2 Zeeman effect in the manifold of hyperfine levels, Breit–Rabi diagrams......Page 71 4.3 Atoms in an electric field: the Stark effect......Page 75 4.4 Combined effect of electric and magnetic fields......Page 85 4.5 Atoms in oscillating fields......Page 88 5.1 The density matrix......Page 95 5.2 Rotation of density matrices......Page 101 5.3 Angular-momentum probability surfaces......Page 102 5.4 Angular-momentum probability surfaces and the density matrix: equivalence and symmetries......Page 103 5.5 Temporal evolution of the density matrix: the Liouville equations......Page 105 5.6 Example: alignment-to-orientation conversion......Page 107 5.7 Multipole moments......Page 109 6 Polarized light......Page 122 6.1 The light polarization ellipse......Page 123 6.2 Partially polarized light and unpolarized light......Page 127 6.3 Spin angular momentum of polarized light......Page 129 6.4 Spherical basis for light polarization......Page 131 6.5 The polarization density matrix......Page 134 6.6 Angular-momentum probability surfaces for light......Page 135 6.7 Stokes parameters for partially polarized light......Page 136 7.1 Two-level system under the action of a periodic perturbation......Page 139 7.2 Selection rules for electric-dipole transitions......Page 142 7.3 Probability calculation for electric-dipole transitions......Page 146 7.4 Line strength......Page 154 7.5 Higher-multipole radiative transitions......Page 157 7.6 Multipole expansion......Page 161 7.7 Two-photon and multi-photon transitions......Page 165 7.8 Visualization of atomic transitions......Page 166 8.1 Dark and bright states......Page 172 8.2 Quantum beats......Page 177 8.3 The Hanle effect......Page 179 9.1 Linear and nonlinear processes; saturation parameters......Page 182 9.2 Optical pumping on closed transitions......Page 186 9.3 Optical pumping on open transitions......Page 196 10.1 Effect of atoms on transmitted light......Page 199 10.2 Magneto-optical effects with linearly polarized light......Page 203 10.3 Perturbative approach......Page 226 PART II: ADVANCED TOPICS......Page 230 11.1 Nested nonlinear magneto-optical rotation features......Page 232 11.2 Bennett-structure effects......Page 233 11.3 The role of alignment-to-orientation conversion in nonlinear magneto-optical rotation......Page 234 11.4 Buffer-gas vapor cells......Page 237 11.5 Antirelaxation-coated cells......Page 238 11.6 Optically thick media......Page 241 11.7 Nonlinear magneto-optical rotation with modulated light......Page 247 12.1 Polarization transfer in spontaneous decay......Page 252 12.2 Perturbative solution of the steady-state density matrix......Page 256 12.3 The optical-field case......Page 257 12.4 Repopulation and depopulation......Page 259 12.6 Absorption and optical rotation signals......Page 261 12.8 The broad-line approximation......Page 265 13 Polarization effects in transitions with partially resolved hyperfine structure......Page 270 13.1 Depopulation pumping......Page 272 13.2 Excited state and repopulation pumping......Page 276 13.3 Absorption......Page 279 13.5 Comparison of diÌerent cases......Page 282 14 The effect of hyperfine splitting on nonlinear magneto-optical rotation......Page 284 14.1 Doppler-free transit effect......Page 285 14.2 Doppler-broadened transit effect......Page 290 14.3 Wall effect......Page 293 14.4 Higher nuclear spin and the D2 line......Page 296 14.5 Comparison of quantitative results for different cases......Page 300 15.1 Dark and bright states......Page 302 15.2 Quantum beats......Page 305 15.3 The Hanle effect......Page 309 16 Collapse and revival in quantum beats......Page 316 17 Nuclear quadrupole resonance and alignmenttoorientation conversion......Page 322 18.1 General technique and production and detection of the k = 2 and k = 4 moments......Page 327 18.2 Production and observation of the k = 6 hexacontatetrapole moment......Page 332 18.3 Production and detection of the hexadecapole moment in the Earth’s magnetic field......Page 335 19 Tensor structure of the DC- and AC-Stark polarizabilities......Page 342 20 Photoionization of polarized atoms with polarized light......Page 346 20.1 Photoionization cross-section......Page 347 20.2 Formulas for 0,1,2......Page 349 Appendix A: Constants, units, and notations......Page 352 Appendix B: Units of energy, frequency, and wavelength......Page 355 Appendix C: Reference data for hydrogen and the alkali atoms......Page 356 D.1 Rotations in the Cartesian basis......Page 357 D.2 The spherical basis......Page 360 E.1 Perturbation theory with polarization moments......Page 365 E.2 Doppler-free transit effect......Page 367 E.3 Doppler-broadened transit effct......Page 369 E.4 Wall effect......Page 370 Appendix F: The Atomic Density Matrix software package......Page 371 Bibliography......Page 373 B......Page 381 D......Page 382 F......Page 383 L......Page 384 O......Page 385 Q......Page 386 S......Page 387 V......Page 388 Z......Page 389 This book is addressed to upper-level undergraduate and graduate students involved in research in atomic, molecular, and optical physics. It will also be useful to researchers practising in this field. It gives an intuitive, yet sufficiently detailed and rigorous introduction to light-atom interactions with a particular emphasis on the symmetry aspects of the interaction, especially those associated with the angular momentum of atoms and light. The book will enable readers to carry out practical calculations on their own, and is richly illustrated with examples drawn from current research topics, such as resonant nonlinear magneto-opticals. The book comes with a software package for a variety of atomic-physics calculations and further interactive examples that is freely downloadable from the book's web page, as well as additional materials (such as power-point presentations) available to instructors who adopt the text for their courses.