The Theory of Coherent Atomic Excitation (two-volume set)

Contents ......Page 4
I. BASIC PRINCIPLES AND DEFINITIONS ......Page 20
1. Introduction and Definitions ......Page 22
1.1 Atoms and Excitation ......Page 23
1.2 Selective Excitation: Isotope Separation ......Page 46
1.3 Probabilities and States ......Page 53
1.4 Radiation Intensity; Photons ......Page 61
1.5 Plane Waves and Polarization ......Page 68
1.6 Time Averages: Partial Polarization ......Page 79
1.7 The Spectrum ......Page 90
1.8 Spectral Line Profiles ......Page 97
1.9 Coherent Radiation ......Page 107
2. Elementary Atoms ......Page 112
2.1 The Boltzmann (Thermodynamic) Atom ......Page 113
2.2 The Einstein (Radiative Rate Equation) Atom ......Page 125
2.3 Cross Sections ......Page 134
2.4 Radiative Excitation Cross Sections ......Page 139
2.5 Interruption Cross Sections ......Page 149
2.6 Collisional-Radiative Rate Equations ......Page 153
2.7 The Rabi (Oscillatory) Atom ......Page 161
2.8 The Field-Atom Interaction: Multipoles ......Page 165
2.9 Basic Parameters: Scales of Length and Time ......Page 180
II. TWO-STATE ATOMS ......Page 204
3. The Schrodinger Atom ......Page 206
3.1 The Schrédinger Picture of Quantum Dynamics ......Page 207
3.2 The Two-State Schrodinger Atom ......Page 213
3.3 The Interaction Energy ......Page 220
3.4 Steady Interactions: Ma jorana Population Oscillations ......Page 228
3.5 Dressed States and Initial Conditions ......Page 235
3.6 Slowly Varying Interactions: Adiabatic States ......Page 239
3.7 Complex-Exponential Oscillatory Interactions; Pictures ......Page 243
3.8 Real-Valued Oscillatory Interactions ......Page 249
3.9 The Two-State Rotating-Wave Approximation ......Page 254
3.10 Analytic RWA Solutions with Loss ......Page 259
3.11 Alternative Atomic Hamiltonians ......Page 271
4. Beyond the Rotating-W ave Approximation ......Page 282
4.1 Degeneracy: Strong Fields ......Page 283
4.2 The Floquet Hamiltonian ......Page 287
4.3 Quasistatic States: The Dynamic Stark Effect ......Page 296
4.4 Weak Resonant Excitation: Saturation ......Page 303
4.5 Time-Dependent Perturbation Theory: Broadband Excitation ......Page 309
4.6 Intense-Field Excitation and Ionization ......Page 317
5. Pulsed Excitation ......Page 322
5.1 Pulse Shape Effects ......Page 323
5.2 Multiple Pulses: Phase Observations ......Page 328
5.3 Analytic Pulse Shapes ......Page 332
5.4 Exponential Pulses: Bessel Functions ......Page 336
5.5 The Hyperbolic Secant Pulse: Hypergeometric Functions ......Page 339
5.6 Chirped Pulses: Parabolic Cylinder Functions ......Page 344
6. Statistical Atoms ......Page 350
6.1 Initial Conditions: Pure and Mixed States ......Page 351
6.2 Operator Expectation Values; The Statistical Matrix ......Page 354
6.3 The Liouville Equation ......Page 364
6.4 The Reduced Density Matrix; Relaxation; Motion ......Page 370
7. The Heisenberg Atom ......Page 384
7.1 Classical Dynamics; Expectation Values ......Page 385
7.2 Quantum Dynamics; Operators and Uncertainties ......Page 392
7.3 The Schrddinger-Heisenberg Connection ......Page 399
7.4 The Heisenberg Picture of Quantum Dynamics ......Page 404
7.5 The Unbound Electron in a Uniform Electric Field ......Page 409
7.6 The Two-State Heisenberg Atom; Multistate Atoms ......Page 420
8. The Bloch and Lorentz Atoms ......Page 432
8.1 The Bloch Variables; Damping ......Page 433
8.2 The Lorentz Atom ......Page 440
8.3 Laplace Transform Solutions; Susceptibility ......Page 447
8.4 The RWA Optical Bloch Equations ......Page 455
8.5 The Feynman-Vernon-Hellwarth (Vector) Atom ......Page 466
8.6 Transform Solutions to the Bloch Equations ......Page 473
8.7 The Rate Equation Limit ......Page 478
8.8 Significance of the Rabi Frequency ......Page 482
8.9 Limitations of the Two-State Schrbdinger Equation ......Page 485
III. PHOTONS AND RADIATION ......Page 490
9. Free Fields: Photons ......Page 492
9.1 Maxwell Equations and Free Electromagnetic Fields ......Page 493
9.2 Standing Waves; Quantization ......Page 498
9.3 Energy States; Photons ......Page 507
9.4 Travelling Waves ......Page 512
9.5 Basis Fields ......Page 514
9.6 Radiation Modes ......Page 523
9.7 Fock States; The Density Matrix ......Page 539
9.8 Thermal Fields ......Page 542
9.9 Photon Phase ......Page 547
9.10 Single-Mode Phase-Increment Representation ......Page 551
9.11 Single-Mode Coherent States ......Page 557
9.12 Alternative Pictures of Quantum Electrodynamics ......Page 566
9.13 What Is a Photon? ......Page 569
9.14 The Hamiltonian of Interacting Radiation and Charges ......Page 573
9.15 The Multipole Form for Hamiltonian Electrodynamics ......Page 582
10. Photon-Atom Dynamics ......Page 600
10.1 Photon-Number States and the RWA ......Page 601
10.2 Photons and Floquet Theory ......Page 609
10.3 Dressed Photon-Atom States ......Page 617
10.4 Depicting Dressed States; Dynamic Stark Shifts ......Page 622
10.5 Constructing Field-Atom Eigenstates ......Page 632
10.6 Spontaneous Emission Dynamics ......Page 637
10.7 Cavity Electrodynamics: The Jaynes-Cummings Atom ......Page 656
10.8 Conservation of Energy in Population Oscillations ......Page 669
11. The Scattered Field Spectrum ......Page 674
11.1 Radiation Power; The Atomic Emission Spectrum ......Page 675
11.2 The Source Field; The Retarded Solution ......Page 681
11.3 Time-Dependent Spectra; The Field Autocorrelation ......Page 687
11.4 The Atomic Autocorrelation Function ......Page 694
11.5 The Schr6dinger Picture of Emission ......Page 696
11.6 The Heisenberg Picture of Emission ......Page 702
12. Propagation ......Page 710
12.1 Radiative Transport Equations ......Page 711
12.2 Wave Equations ......Page 722
12.3 Fourier Expansions for Radiation ......Page 733
12.4 Plane-Wave Envelope Propagation Equations ......Page 744
12.5 Phase and Intensity Equations: Absorption Coefficient ......Page 754
12.6 The Two-State Maxwell-Bloch Equations; Rate Equations ......Page 760
12.7 Coherence in Two-State Propagation; Transients ......Page 766
12.8 Pulse-Mode Expansions ......Page 776
12.9 Multistate Excitation; Numerical Integration ......Page 787
IV. MULTISTATE ATOMS ......Page 794
13. Three-State Atoms ......Page 796
13.1 The Three-State Rotating-Wave Approximation ......Page 797
13.2 Three-State Analytic Solutions; Dressed States ......Page 806
13.3 The Three-State Ladder ......Page 811
13.4 Virtual States ......Page 828
13.5 Rate Equations and Virtual Levels ......Page 833
13.6 A Three-State Example: Circular Polarization ......Page 837
13.7 The Lambda System: Population Trapping ......Page 843
13.8 The Vee System: Quantum Beats; Quantum Jumps ......Page 857
13.9 D0ppler Detuning; Doppler-Free Excitation ......Page 863
13.10 The Three-State Heisenberg Atom; SU(3) Matrices ......Page 871
14. The N-State Formalism ......Page 878
14.1 The N-State Model ......Page 879
14.2 The Global Rotating-Wave Approximation ......Page 885
14.3 The Time-Evolution Operator ......Page 895
14.4 Exponential and Eigenvector Methods ......Page 901
14.5 Long-Time Average Populations ......Page 910
14.6 Laplace Transform Technique ......Page 915
14.7 The Resolvent ......Page 918
14.8 The Effective Hamiltonian ......Page 921
14.9 Induced Moments: The Raman Hamiltonian ......Page 931
14.10 Multistate Heisenberg Equations: Matrix Expansions ......Page 947
15. The N-State Ladder ......Page 956
15.1 Analytic Solutions: The Driven Harmonic Oscillator ......Page 957
15.2 Other Analytic Solutions for Unbounded N ......Page 968
15.3 Eigenvector Solutions: Dressed States and Quasienergies ......Page 975
15.4 Finite-N Ladders ......Page 984
15.5 Short-Time Behavior: Population Flow ......Page 989
15.6 Multilevel Rate Equations: Population Equilibration ......Page 993
15.7 Excitation Ladders With Loss ......Page 1000
15.8 Long-Time Periodicities ......Page 1002
15.9 Resonant-Ladder Time Averages ......Page 1009
15.10 Anharmonic Ladders ......Page 1010
15.11 Multiphoton Resonances ......Page 1017
15.12 Standing Waves: Atomic Deflection ......Page 1028
16. Continuum Processes ......Page 1048
16.1 Quasicontinuum Excitation ......Page 1049
16.2 Fano States ......Page 1068
16.3 Continuum Excitation ......Page 1072
16.4 Continuum Discretization ......Page 1078
16.5 Multiple Continuua ......Page 1082
17. Transition Rates ......Page 1092
17.1 Time-Dependent Perturbation Theory ......Page 1093
17.2 Two-State Perturbation Theory: Rabi Oscillations ......Page 1098
17.3 Rate Coefficients: The Golden Rule ......Page 1100
17.4 Radiative Transitions: Single-Photon Rates ......Page 1106
17.5 Two-Photon Transitions: Raman Processes ......Page 1115
17.6 Multiphoton Transition Rates ......Page 1121
V. ANGULAR MOMENTUM AND COMPLEX ATOMS ......Page 1128
18. Angular Momentum and Periodicities ......Page 1130
18.1 Quantum Theory of Angular Momentum ......Page 1131
18.2 Matrix Representations: Spin ......Page 1136
18.3 Differential Representations: Spherical Harmonics ......Page 1144
18.4 Angular Momentum and Rotations ......Page 1147
18.5 The Rotation Matrix ......Page 1152
18.6 The N-State Spin-I Analog ......Page 1162
18.7 Two-State Behavior in N-State Systems ......Page 1177
19. Angular Momentum States: Coupling ......Page 1192
19.1 Angular Momentum Coupling; Correlation ......Page 1193
19.2 Multiple Coupling and Recoupling ......Page 1209
19.3 Photon States: Plane Waves and Spin ......Page 1217
19.4 Photon States: Spherical Waves and Vector Harmonics ......Page 1223
19.5 Multipole Fields ......Page 1231
19.6 Rutherford—Kepler Runge-Lenz Hydrogen: Orbits ......Page 1245
19.7 The Bohr-Pauli Hydrogen Atom ......Page 1255
19.8 Multi-Electron Atomic Wavefunctions; Antisymmetrization ......Page 1247
19.9 Single-Electron Orbitals ......Page 1279
19.10 Spectroscopic Notation; Excited States ......Page 1293
20. Angular Momentum Interactions ......Page 1304
20.1 Euclidean Vectors; Scalar and Vector Products ......Page 1305
20.2 Tensors; Irreducible Tensors......Page 1310
20.3 Coupled Irreducible Tensors ......Page 1322
20.4 Interactions and Tensors; Tensor Invariants ......Page 1328
20.5 Tensor Operators: The Wigner-Eckart Theorem ......Page 1338
20.6 Reduced Matrix Elements and Racah Algebra ......Page 1349
20.7 Multipole Transitions; Spontaneous Emission with Sublevels ......Page 1357
20.8 The Rabi Frequency in an Angular Momentum Basis ......Page 1367
20.9 The Rabi Frequency: Geometric Factor; Multiplet Strength ......Page 1375
20.10 The Transition Moment: Length, Velocity and Acceleration ......Page 1378
20.11 Degenerate Two-Level Systems; Inaccessible Sublevels ......Page 1381
20.12 Degenerate Multi-Step Ladders ......Page 1386
20.13 Polarization Choices ......Page 1391
20.14 Electrostatic Energies ......Page 1401
20.15 Atomic Hartree-Fock Equations ......Page 1409
21. Linkage Patterns and Static Interactions ......Page 1418
21.1 Fine and Hyperfine Structure ......Page 1419
21.2 Effects of Hyperfine Structure on Coherent Excitation ......Page 1427
21.3 Two-Level Linkages ......Page 1433
21.4 Branched Excitation Ladders ......Page 1436
21.5 Zeeman Splittings ......Page 1445
21.6 Angular Distribution of Zeeman Radiation ......Page 1448
21.7 The Zeeman Pattern of Hyperfine Components ......Page 1456
21.8 Heisenberg Equations with Angular Momentum ......Page 1459
21.9 Coupled Basis Operators: State Multipoles ......Page 1466
21.10 Example: Two-Level Raman System ......Page 1484
VI. INCOHERENCE ......Page 1498
22. Incoherence ......Page 1500
22.1 Homogeneous and Inhomogeneous Incoherence ......Page 1501
22.2 D0ppler Averages ......Page 1503
22.3 Intensity Optimization: Pulse Compression ......Page 1511
22.4 Orientation Averages ......Page 1521
22.5 Rate Equation Limit of the Schrbdinger Equation ......Page 1526
22.6 Bloch Equations and Rate Equations ......Page 1528
22.7 Rate Equation Behavior; Failures of Rate Equations ......Page 1534
23. Fluctuations and Interruptions ......Page 1546
23.1 Stochastic Differential Equations ......Page 1548
23.2 Gaussian Markov Processes: O-U, W-L and Brownian ......Page 1562
23.3 Applications of Gaussian Processes; Radiation Spectra ......Page 1570
23.4 Multiplicative White Noise ......Page 1578
23.5 Poisson (Jump) Processes ......Page 1583
23.6 Interrupted Excitation; Monte Carlo Method ......Page 1593
23.7 Marginal Averages: The Burshtein Equation ......Page 1597
23.8 Markov Processes and Atomic Equations ......Page 1601
23.9 Properties of the Burshtein Equation ......Page 1605
23.10 Application of the Burshtein Equation ......Page 1610
APPENDICES ......Page 1624
A Mathematical Preliminaries: Vectors, Matrices and Groups ......Page 1626
B Fourier Analysis; The Dirac Delta; Density of Modes ......Page 1649
C Laplace Transforms ......Page 1661
D Special Functions and Classical Polynomials ......Page 1667
E Numerical Integration ......Page 1679
F The Classical Nonrelativistic Lagrangian ......Page 1684
G Probability and Stochastic Processes ......Page 1688
H Electromagnetic Units ......Page 1701
Author Index ......Page 1710
Subject Index ......Page 1728