Optically Pumped Atoms

✍ Scribed by William Happer, Yuan-Yu Jau, Thad Walker

• Publisher: Wiley-VCH
• Year: 2010
• Tongue: English
• Leaves: 249
• Category: Library

✦ Synopsis

This ready reference covers the most important facts about optical pumping and spin relaxation of atoms. The authors show that systematic use of Liouville space together with modern scientific computing software makes it practical to analyze the full, multilevel system of optically pumped atoms. Sections of MATLAB codes included in the text allow the reader to assemble quite sophisticated codes for modelling various optical-pumping phenomena. The text assumes that the reader has a basic understanding of quantum mechanics, atomic physics, optics, magnetic resonance, and the mathematics of physics and chemistry.

✦ Table of Contents

Contents......Page 2
Preface......Page 12
Index to Codes......Page 14
1 Introduction......Page 16
2.1 Electronic Energies......Page 30
2.2 Valence-Electron Wave Functions......Page 33
2.3 Hyperfine Structure......Page 35
3.1.1 Kronecker Products......Page 40
3.1.2 Angular Momentum Matrices......Page 42
3.2 Energy States......Page 43
3.3 Zero-Field States......Page 45
4 Density Matrix and Liouville Space......Page 48
4.2 Ground State, Excited State, and Optical Coherence......Page 50
4.3.1 Column-Vector Transforms......Page 51
4.3.2 Row-Vector Transforms......Page 52
4.3.3 Expectation Values......Page 53
4.4.1 Transposition Matrix......Page 54
4.4.2 Evolution Matrices......Page 55
4.5 Eigendecomposition of G......Page 56
4.5.1 Nullspace......Page 57
4.5.2 Critical Damping......Page 58
4.6.1 Flat and Sharp Superoperators......Page 59
4.6.2 Square Matrices......Page 61
4.6.4 O-Dot Superoperators......Page 62
5.1 The Electric Field of Light......Page 64
5.2.1 Spherical Tensors......Page 65
5.2.2 Hermitian Conjugates......Page 66
5.2.3 Addition of Angular Momentum......Page 67
5.2.5 Identities for and †......Page 68
5.2.7 Energy Basis......Page 71
5.3 Spontaneous Emission......Page 72
5.4 Electric Dipole Interaction......Page 73
5.5 Rotating Coordinate System......Page 74
5.6 Net Evolution......Page 77
5.6.2 Normalization......Page 79
5.7 Optical Bloch Equations......Page 80
5.8 Liouville Space......Page 81
5.8.1 Transients......Page 83
5.8.2 Steady State......Page 84
5.8.3 Steady State Versus Detuning......Page 85
6 Quasi-Steady-State Optical Pumping......Page 88
6.1 Ground-State Evolution......Page 89
6.2 Excited-State Evolution......Page 91
6.3 Collisions......Page 92
6.5 Identities......Page 93
6.6 Net Evolution......Page 95
6.7 Negligible Stimulated Emission......Page 96
6.8 High-Pressure Pumping......Page 97
6.8.1 Liouville Space......Page 99
6.9 Spectral Width of Pumping Light......Page 102
6.9.1 Gaussian Spectral Profiles......Page 103
6.9.2 Plasma Dispersion Function......Page 104
6.10 Doppler Broadening......Page 105
7 Modulation......Page 108
7.2 Modulated Light......Page 109
7.2.2 Lower Pressure......Page 110
7.2.3 Modulated Optical Pumping Matrices......Page 111
7.3 Secular Approximation......Page 112
7.4 Attenuation of Modulated Coherence in Passingthrough the Excited State......Page 115
7.5.1 Isolated Magnetic Resonances......Page 117
7.5.2 Zeeman Magnetic Resonances......Page 118
7.5.3 Push–Pull Pumping......Page 121
8.1 Induced Electric Dipole Moment......Page 124
8.2 Absorption Cross Section......Page 126
8.3 Small Magnetic Fields......Page 127
8.4 Evolution of a Beam in Space and Time......Page 129
8.5 First-Order Propagation Equation......Page 130
8.6 Propagation of Weak Probe Light......Page 131
8.7 Faraday Rotation......Page 132
8.8 Specific Absorption......Page 133
8.9 Fluorescent Light......Page 134
9.1 Mean Force......Page 136
9.2 Forces from Monochromatic Light......Page 138
9.3 Forces in Magneto-Optical Traps......Page 139
9.3.1 Repump Lasers......Page 145
9.4 Pointing Probability......Page 147
9.5 Momentum Space......Page 150
9.6 Evolution in Spin-Momentum Space......Page 153
9.8 Compactification......Page 155
9.8.1 Compactified pq Space......Page 156
9.8.2 Compactification within a Tile......Page 158
9.9.1 Momentum-Space Displays......Page 162
9.9.2 Position-Space Displays......Page 164
9.10 Momentum Diffusion......Page 166
9.11 Momentum Diffusion Due to Spontaneous Emission......Page 167
9.12 Momentum Diffusion from Pumping......Page 168
10 Relaxation of Polarized Atoms......Page 174
10.1 S-Matrix......Page 175
10.2 Collisions in the Gas......Page 178
10.3 Weak Collisions......Page 179
10.4 Relative Power Spectrum......Page 181
10.5 Sudden Collisions......Page 182
10.6 Strong Collisions......Page 183
10.7 Hyperfine-Shift Interaction......Page 186
10.8 Spin–Rotation Interaction......Page 190
10.8.1 Binary Collisions......Page 191
10.9 Spin Exchange between Alkali-Metal Atoms and Noble Gas Atoms......Page 193
10.9.1 Binary Collisions......Page 196
10.9.2 Spin Temperature......Page 199
10.9.3 Experimental Measurements......Page 201
10.10 Spatial Diffusion......Page 204
10.11 Adsorption on the Walls......Page 209
10.12.1 Partial-Wave Analysis......Page 213
10.12.2 Semiclassical Calculation of Partial-Wave Cross Sections......Page 222
10.13 Pressure Dependence of Relaxation in the Dark......Page 223
10.14 Collisions of Excited Atoms......Page 227
11.1 Electronic Multipoles......Page 234
11.2 Projection Operators in Terms of S or J......Page 236
11.3 Recoupling Example......Page 238
References......Page 240
Index......Page 246