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Oxford, 2010Optically Polarized Atoms - Understanding Light-Atom Interactions
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Contents List of acronyms xi PART I INTRODUCTION TO LIGHT–ATOM INTERACTIONS 1 Introduction 3 1.1 Why was this book written? 3 1.2 How to use this book 3 1.3 Relation to other texts 4 1.4 Formalism of quantum mechanics 5 2 Atomic states 8 2.1 Energy states of the hydrogen atom 8 2.2 Angular momentum of the electron in the hydrogen atom 9 2.3 Multielectron atoms 19 2.4 Hyperfine interactions and hyperfine structure of atomic states 26 2.5 Parity of atomic states 27 3 A bit of angularmomentum theory 30 3.1 Classical rotations 30 3.2 Quantummechanical rotations 36 3.3 The angularmomentum operator 39 3.4 Rotations in the Zeeman basis 43 3.5 Addition of angular momenta; Clebsch–Gordan coeÏcients 45 3.6 3 j and 6j symbols 46 3.7 Irreducible tensors and tensor products 49 3.8 The Wigner–Eckart theorem 51 4 Atoms in external electric and magnetic fields 55 4.1 Linear Zeeman eìect 55 4.2 Zeeman eìect in the manifold of hyperfine levels, Breit–Rabi diagrams 58 4.3 Atoms in an electric field: the Stark eìect 62 4.4 Combined eìect of electric and magnetic fields 72 4.5 Atoms in oscillating fields 75 5 Polarized atoms 82 5.1 The density matrix 82 5.2 Rotation of density matrices 88 viii Contents 5.3 Angularmomentum probability surfaces 89 5.4 Angularmomentum probability surfaces and the density matrix: equivalence and symmetries 90 5.5 Temporal evolution of the density matrix: the Liouville equations 92 5.6 Example: alignmenttoorientation conversion 94 5.7 Multipole moments 96 6 Polarized light 109 6.1 The light polarization ellipse 110 6.2 Partially polarized light and unpolarized light 114 6.3 Spin angular momentum of polarized light 116 6.4 Spherical basis for light polarization 118 6.5 The polarization density matrix 121 6.6 Angularmomentum probability surfaces for light 122 6.7 Stokes parameters for partially polarized light 123 7 Atomic transitions 126 7.1 Twolevel system under the action of a periodic perturbation 126 7.2 Selection rules for electricdipole transitions 129 7.3 Probability calculation for electricdipole transitions 133 7.4 Line strength 141 7.5 Highermultipole radiative transitions 144 7.6 Multipole expansion 148 7.7 Twophoton and multiphoton transitions 152 7.8 Visualization of atomic transitions 153 8 Coherence in atomic systems 159 8.1 Dark and bright states 159 8.2 Quantum beats 164 8.3 The Hanle eìect 166 9 Optical pumping 169 9.1 Linear and nonlinear processes; saturation parameters 169 9.2 Optical pumping on closed transitions 173 9.3 Optical pumping on open transitions 183 10 Light–atom interaction observed in transmitted light 186 10.1 Eìect of atoms on transmitted light 186 10.2 Magnetooptical eìects with linearly polarized light 190 10.3 Perturbative approach 213 PART II ADVANCED TOPICS 11 Nonlinear magnetooptical rotation 219 11.1 Nested nonlinear magnetooptical rotation features 219 11.2 Bennettstructure eìects 220 11.3 The role of alignmenttoorientation conversion in nonlinear magnetooptical rotation 221 Contents ix 11.4 Buìergas vapor cells 224 11.5 Antirelaxationcoated cells 225 11.6 Optically thick media 228 11.7 Nonlinear magnetooptical rotation with modulated light 234 12 Perturbative and approximate methods for light–atom interactions 239 12.1 Polarization transfer in spontaneous decay 239 12.2 Perturbative solution of the steadystate density matrix 243 12.3 The opticalfield case 244 12.4 Repopulation and depopulation 246 12.5 Optical excitation 248 12.6 Absorption and optical rotation signals 248 12.7 What kind of atomic polarization can influence the absorption and emission of light? 252 12.8 The broadline approximation 252 13 Polarization eìects in transitions with partially resolved hyperfine structure 257 13.1 Depopulation pumping 259 13.2 Excited state and repopulation pumping 263 13.3 Absorption 266 13.4 Fluorescence 269 13.5 Comparison of diìerent cases 269 14 The eìect of hyperfine splitting on nonlinear magnetooptical rotation 271 14.1 Dopplerfree transit eìect 272 14.2 Dopplerbroadened transit eìect 277 14.3 Wall eìect 280 14.4 Higher nuclear spin and the D2 line 283 14.5 Comparison of quantitative results for diìerent cases 287 15 Coherence eìects revisited 289 15.1 Dark and bright states 289 15.2 Quantum beats 292 15.3 The Hanle eìect 296 16 Collapse and revival in quantum beats 303 17 Nuclear quadrupole resonance and alignmenttoorientation conversion 309 18 Selective addressing of highrank polarization moments 314 18.1 General technique and production and detection of the = 2 and = 4 moments 314 18.2 Production and observation of the = 6 hexacontatetrapole moment 319 18.3 Production and detection of the hexadecapole moment in the Earth’s magnetic field 322 19 Tensor structure of the DCand ACStark polarizabilities 329 20 Photoionization of polarized atoms with polarized light 333 20.1 Photoionization crosssection 334 x Contents 20.2 Formulas for 0,1,2 336 Appendix A Constants, units, and notations 339 Appendix B Units of energy, frequency, and wavelength 342 Appendix C Reference data for hydrogen and the alkali atoms 343 Appendix D Classical rotations 344 D.1 Rotations in the Cartesian basis 344 D.2 The spherical basis 347 Appendix E Nonlinear magnetooptical rotation with hyperfine structure 352 E.1 Perturbation theory with polarization moments 352 E.2 Dopplerfree transit eìect 354 E.3 Dopplerbroadened transit eìect 356 E.4 Wall eìect 357 Appendix F The Atomic Density Matrix software package 358 Bibliography 360 Index 367 |
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