Optically Polarized Atoms

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