目錄
1 早期原子物理學(xué) 1
1.1 導(dǎo)引 1
1.2 氫原子光譜 1
1.3 Bohr理論 3
1.4 相對(duì)論效應(yīng) 5
1.5 Moseley和原子數(shù) 7
1.6 輻射衰變 11
1.7 愛(ài)因斯坦A系數(shù)和B系數(shù) 11
1.8 Zeeman效應(yīng) 13
1.8.1 Zeeman效應(yīng)的實(shí)驗(yàn)觀察 17
1.9 原子單位總結(jié) 18
習(xí)題 19
2 氫原子 22
2.1 Schrodinger方程 22
2.1.1 角向方程的解 23
2.1.2 徑向方程的解 26
2.2 躍遷 29
2.2.1 選擇定則 30
2.2.2 對(duì)θ的積分 32
2.2.3 宇稱 32
2.3 精細(xì)結(jié)構(gòu) 34
2.3.1 電子的自旋 35
2.3.2 自旋軌道相互作用 36
2.3.3 氫原子的精細(xì)結(jié)構(gòu) 38
2.3.4 Lamb位移 40
2.3.5 精細(xì)能級(jí)之間的躍遷 41
進(jìn)一步閱讀 42
習(xí)題 42
3 氦原子 45
3.1 氦原子的基態(tài) 45
3.2 氦原子的激發(fā)態(tài) 46
3.2.1 自旋本征態(tài) 51
3.2.2 氦原子中的躍遷 52
3.3 氦原子中的積分估計(jì) 53
3.3.1 基態(tài) 53
3.3.2 激發(fā)態(tài)：直接積分 54
3.3.3 激發(fā)態(tài)：交換積分 55
進(jìn)一步閱讀 56
習(xí)題 58
4 堿金屬 60
4.1 殼層結(jié)構(gòu)和周期表 60
4.2 量子數(shù)虧損 61
4.3 中心場(chǎng)近似 64
4.4 Schrodinger方程的數(shù)值解 68
4.4.1 自洽解 70
4.5 自旋軌道相丘作用：量子方法 71
4.6 堿金屬的精細(xì)結(jié)構(gòu) 73
4.6.1 精細(xì)結(jié)構(gòu)躍遷的相對(duì)強(qiáng)度 74
進(jìn)一步閱讀 75
習(xí)題 76
5 L-S耦合方式 80
5.1 L-S耦合方式的精細(xì)結(jié)構(gòu) 83
5.2 j-j偶合方式 84
5.3 居間耦合：不同耦合方式之間的躍遷 86
5.4 L-S耦合方式的選擇定則 90
5.5 Zeeman效應(yīng) 90
5.6 93
進(jìn)一步閱讀 94
習(xí)題 94
6 超精細(xì)結(jié)構(gòu)和同位素移位 97
6.1 超精細(xì)結(jié)構(gòu) 97
6.1.1 s電子的超精細(xì)結(jié)構(gòu) 97
6.1.2 氫微波激射器 100
6.1.3 l≠0時(shí)的超精細(xì)結(jié)構(gòu) 101
6.1.4 超精細(xì)結(jié)構(gòu)與精細(xì)結(jié)構(gòu)的比較 l02
6.2 同位素移位 105
6.2.1 質(zhì)量效應(yīng) 105
6.2.2 體積移位 106
6.2.3 原子揭示的原子核信息 108
6.3 Zeeman效應(yīng)和超精細(xì)結(jié)構(gòu) 108
6.3.1 弱場(chǎng)下的Zeeman效應(yīng)，μBB<A 109
6.3.2 強(qiáng)場(chǎng)下的Zeeman效應(yīng)，μBB>A 110
6.3.3 111
6.4 超精細(xì)結(jié)構(gòu)的測(cè)量 112
6.4.1 原子束技術(shù) 114
6.4.2 原子鐘 118
進(jìn)一步閱讀 119
習(xí)題 120
7 原子與輻射的相互作用 123
7.1 方程的建立 123
7.1.1 振蕩電場(chǎng)的擾動(dòng) 124
7.1.2 旋波近似 125
7.2 愛(ài)因斯坦B系數(shù) 126
7.3 與單色輻射的相互作用 127
7.3.1 π脈沖與π/2脈沖 128
7.3.2 Bloch矢量和Bloch球面 128
7.4 Ramsey條紋 132
7.5 輻射阻尼 134
7.5.1 經(jīng)典偶極輻射阻尼 135
7.5.2 光Bloch球面 137
7.6 光吸收截面 138
7.6.1 純輻射展寬截面 141
7.6.2 飽和強(qiáng)度 142
7.6.3 功率展寬 143
7.7 交流Stark效應(yīng)/光頻移 144
7.8 145
7.9 146
進(jìn)一步閱讀 147
習(xí)題 148
8 無(wú)Doppler激光光譜 151
8.1 譜線的Doppler展寬 151
8.2 交叉束技術(shù) 153
8.3 飽和吸收光譜 155
8.3.1 飽和吸收光譜的原理 156
8.3.2 飽和吸收光譜的穿越共振 159
8.4 雙光子光譜 163
8.5 激光光譜的校準(zhǔn)168
8.5.1 相對(duì)頻率的校準(zhǔn) 168
8.5.2 絕對(duì)校準(zhǔn) 169
8.5.3 光頻梳 171
進(jìn)一步閱讀 175
習(xí)題 175
9 原子冷卻與捕陷 178
9.1 散射力 179
9.2 減慢原子束 182
9.2.1 啁啾冷卻 184
9.3 光學(xué)黏膠技術(shù) 185
9.3.1 Doppler冷卻的極限 188
9.4 磁光阱 190
9.5 偶極力導(dǎo)論 194
9.6 偶極力理論 197
9.6.1 光學(xué)品格 201
9.7 Sisyphus冷卻技術(shù) 203
9.7.1 概論 203
9.7.2 Sisyphus冷卻 204
9.7.3 Sisyphus冷卻機(jī)制的極限 207
9.8 Raman躍遷 208
9.8.1 Raman躍遷的速度選擇 208
9.8.2 Raman冷卻 210
9.9 原子噴泉 211
9.10 總結(jié) 213
習(xí)題 214
10 磁捕陷、蒸發(fā)冷卻和Bose-Einstein凝聚 218
10.1 磁捕陷的原理 218
10.2 磁捕陷 220
10.2.1 徑向約束 220
10.2.2 軸向約束 221
10.3 蒸發(fā)冷卻 224
10.4 Bose-Einstein凝聚 226
10.5 捕陷原子蒸氣中的Bose-EinsLein凝聚 228
10.5.1 散射長(zhǎng)度 229
10.6 種Bose-Einstein凝聚體 234
10.7 Bose凝聚氣體的性質(zhì) 239
10.7.1 聲速 239
10.7.2 消退長(zhǎng)度 240
10.7.3 Bose-Einstein凝聚的相干性 240
10.7.4 原子激光 242
10.8 總結(jié) 242
習(xí)題 243
11 原子干涉 246
11.1 楊氏雙縫實(shí)驗(yàn) 247
11.2 原子的衍射光柵 249
11.3 三光柵干涉儀 251
11.4 旋轉(zhuǎn)的測(cè)量 251
11.5 光對(duì)原子的衍射 253
11.5.1 Raman躍遷干涉測(cè)量技術(shù) 255
11.6 總結(jié) 257
進(jìn)一步閱讀 258
習(xí)題 258
12 離子阱 259
12.1 電場(chǎng)中離子的受力 259
12.2 Earnshaw定理 260
12.3 Paul阱 261
12.3.1 旋轉(zhuǎn)馬鞍上小球的平衡 262
12.3.2 交流場(chǎng)中的有效勢(shì) 262
12.3.3 線性Paul阱 262
12.4 緩沖氣冷卻 266
12.5 激光冷卻捕陷離子 267
12.6 量子跳躍 269
12.7 Penning阱和Paul阱 271
12.7.1 Penning阱 272
12.7.2 離子的質(zhì)譜 274
12.7.3 電子的反常磁矩 274
12.8 電子束離子阱 275
12.9 解析側(cè)帶冷卻 277
12.10 離子阱總結(jié) 279
進(jìn)一步閱讀 279
習(xí)題 280
13 量子計(jì)算 282
13.1 量子比特及其性質(zhì) 283
13.1.1 糾纏 284
13.2 量子邏輯門(mén) 287
13.2.1 設(shè)計(jì)CNOT門(mén) 287
13.3 量子并行算法 289
13.4 量子計(jì)算機(jī)綜述 291
13.5 退相干和量子糾錯(cuò) 291
13.6 總結(jié) 293
進(jìn)一步閱讀 294
習(xí)題 294
附錄A 微擾理論 298
A.1 微擾理論的數(shù)學(xué) 298
A.2 相近頻率經(jīng)典振子的相互作用 299
附錄B 靜電能的計(jì)算 302
附錄C 磁偶極躍遷 305
附錄D 飽和吸收的線形 307
附錄E Raman躍遷和雙光子躍遷 310
E.1 Raman躍遷 310
E.2 雙光子躍遷 313
附錄F Bose-Einstein凝聚有關(guān)統(tǒng)計(jì)力學(xué)知識(shí) 315
F.1 光子的統(tǒng)計(jì)力學(xué) 315
F.2 Bose-Einstein凝聚 316
F.2.1 諧振阱中的Bose-Einstein凝聚 318
參考文獻(xiàn) 319
索引 326
Contents
1 Early atomic physics 1
1.1 Introduction 1
1.2 Spectrum of atomic hydrogen 1
1.3 Bohr's theory 3
1.4 Relathristic effects 5
1.5 Moseley and the atomic number 7
1.6 Radiative decay 11
1.7 Einstein A and B coefficients 11
1.8 The Zeeman effect 13
1.8.1 Experimental obserxfation of the Zeeman effect 17
1.9 Summary of atomic units 18
Exercises 19
2 The hydrogen atom 22
2.1 The Schrodinger equation 22
2.1.1 Solution of the angular equation 23
2.1.2 Solution of the radial equation 26
2.2 Transitions 29
2.2.1 Selection rules 30
2.2.2 Integration with respect to θ 32
2.2.3 Parity 32
2.3 Fine structure 34
2.3.1 Spin of the electron 35
2.3.2 The spin-orbit interaction 36
2.3.3 The fine structure of hydrogen 38
2.3.4 The Lamb shift 40
2.3.5 Transitions between fine-structure levels 41
Further reading 42
Exercises 42
3 Helium 45
3.1 The ground state of helium 45
3.2 Excited states of helium 46
3.2.1 Spin eigenstates 51
3.2.2 Transitions in helium 52
3.3 Evaluation of the integrals in helium 53
3.3.1 Ground state 53
3.3.2 Excited states：the direct integral 54
3.3.3 Excited states：the exchange integral 55
Further reading 56
Exercises 58
4 The alkalis 60
4.1 Shell structure and the periodic table 60
4.2 The quantum defect 61
4.3 The central-field approximation 64
4.4 Numerical solution of the Schrodinger equation 68
4.4.1 Self-consistent solutions 70
4.5 The spin-orbit interaction：a quantum mechanical approach 71
4.6 Fine structure in the alkalis 73
4.6.1 Relative intensities of fine-structure transitions 74
Further reading 75
Exercises 76
5 The LS-coupling scheme 80
5.1 Fine structure in the /S-coupling scheme 83
5.2 The jj-coupling scheme 84
5.3 Intermediate coupling：the transition between coupling schemes 86
5.4 Selection rules in the /S-coupling scheme 90
5.5 The Zeeman effect 90
5.6 Summary 93
Further reading 94
Exercises 94
6 Hyperfine structure and isotope shift 97
6.1 Hyperfine structure 97
6.1.1 Hyperfine structure for s-electrons 97
6.1.2 Hydrogenmaser 100
6.1.3 Hyperfine structure for l≠0 101
6.1.4 Comparison of hyperfine and fine structures 102
6.2 Isotope shift 105
6.2.1 Mass effects 105
6.2.2 Volume shift 106
6.2.3 Nuclear information from atoms 108
6.3 Zeeman effect and hyperfine structure 108
6.3.1 Zeeman effect of a weak field，μBB<A 109
6.3.2 Zeeman effect of a strong field，μBB>A 110
6.3.3 Intermediate field strength 111
6.4 Measurement of hyperfine structure 112
6.4.1 The atomic-beam technique 114
6.4.2 Atomic clocks 118
Further reading 119
Exercises 120
7 The interaction of atoms with radiation 123
7.1 Setting up the equations 123
7.1.1 Perturbation by an oscillating electric field 124
7.1.2 The rotating-wave approximation 125
7.2 The Einstein B coefficients 126
7.3 Interaction with monochromatic radiation 127
7.3.1 The concepts ofπ-pulses and π/2-pulses 128
7.3.2 The Bloch vector and Bloch sphere 128
7.4 Ramsey fringes 132
7.5 Radiative damping 134
7.5.1 The damping of a classical dipole 135
7.5.2 The optical Bloch equations 137
7.6 The optical absorption cross-section 138
7.6.1 Cross-section for pure radiative broadening 141
7.6.2 The saturation intensity 142
7.6.3 Power broadening 143
7.7 The a.c. Stark effect or light shift 144
7.8 Comment on semiclassical theory 145
7.9 Conclusions 146
Further reading 147
Exercises 148
8 Doppler-free laser spectroscopy 151
8.1 Doppler broadening of spectral lines 151
8.2 The crossed-beam method 153
8.3 Saturated absorption spectroscopy 155
8.3.1 Principle of saturated absorption spectroscopy 156
8.3.2 Cross-over resonances in saturation spectroscopy 159
8.4 Two-photon spectroscopy 163
8.5 Calibration in laser spectroscopy 168
8.5.1 Calibration of the relative frequency 168
8.5.2 Absolute calibration 169
8.5.3 0ptical frequency combs 171
Further reading 175
Exercises 175
9 Laser cooling and trapping 178
9.1 The scattering force 179
9.2 Slowing an atomic beam 182
9.2.1 Chirp cooling 184
9.3 The optical molasses technique 185
9.3.1 The Doppler cooling limit 188
9.4 The magneto-optical trap 190
9.5 Introduction to the dipole force 194
9.6 Theory of the dipole force 197
9.6.1 0pticallattice 201
9.7 The Sisyphus cooling technique 203
9.7.1 General remarks 203
9.7.2 Detailed description of Sisyphus cooling 204
9.7.3 Limit of the Sisyphus cooling mechanism 207
9.8 Raman transitions 208
9.8.1 Velocity selection by Raman transitions 208
9.8.2 Raman cooling 210
9.9 An atomic fountain 211
9.10 Conclusions 213
Exercises 214
10 Magnetic trapping evaporative cooling and Bose-Einstein condensation 218
10.1 Principle of magnetic trapping 218
10.2 Magnetic trapping 220
10.2.1 Confinement in the radial direction 220
10.2.2 Confinement in the axial direction 221
10.3 Evaporative cooling 224
10.4 Bose-Einstein condensation 226
10.5 Bose-Einstein condensation in trapped atomic vapours 228
10.5.1 The scattering length 229
10.6 A Bose-Einstein condensate 234
10.7 Properties of Bose-condensed gases 239
10.7.1 Speed of sound 239
10.7.2 Healinglength 240
10.7.3 The coherence of a Bose-Einstein condensate 240
10.7.4 The atom laser 242
10.8 Conclusions 242
Exercises 243
11 Atom interferometry 246
11.1 Young's double-slit experiment 247
11.2 A diffraction grating for atoms 249
11.3 The three-grating interferometer 251
11.4 Measurement of rotation 251
11.5 The diffraction of atoms by light 253
11.5.1 Interferometry with Raman transitions 255
11.6 Conclusions 257
Further reading 258
Exercises 258
12 Ion traps 259
12.1 The force on ions in an electric field 259
12.2 Earnshaw's theorem 260
12.3 The Paul trap 261
12.3.1 Equilibrium of a ball on a rotating saddle 262
12.3.2 The effective potential in an a.c. field 262
12.3.3 The linear Paul trap 262
12.4 Buffer gas cooling 266
12.5 Laser cooling of trapped ions 267
12.6 Quantum jumps 269
12.7 The Penning trap and the Paul trap 271
12.7.1 The Penning trap 272
12.7.2 Mass spectroscopy of ions 274
12.7.3 The anomalous magnetic moment of the electron 274
12.8 Electron beam ion trap 275
12.9 Resolved sideband cooling 277
12.10 Summary of ion traps 279
Further reading 279
Exercises 280
13 Quantum computing 282
13.1 Qubits and their properties 283
13.1.1 Entanglement 284
13.2 A quantum logic gate 287
13.2.1 Making a CNOT gate 287
13.3 Parallelism in quantum computing 289
13.4 Summary of quantum computers 291
13.5 Decoherence and quantum error correction 291
13.6 Conclusion 293
Further reading 294
Exercises 294
A Appendix A：Perturbation theory 298
A.1 Mathematics of perturbation theory 298
A.2 Interaction of classical oscillators of similar frequencies 299
B Appendix B：The calculation of electrostatic energies 302
C Appendix C：Magnetic dipole transitions 305
D Appendix D：The line shape in saturated absorption spectroscopy 307
E Appendix E：Raman and two-photon transitions 310
E.1 Raman transitions 310
E.2 Two-photon transitions 313
F Appendix F：The statistical mechanics of Bose-Einstein condensation 315
F.1 The statistical mechanics of photons 315
F.2 Bose-Einstein condensation 316
F.2.1 Bose-Einstein condensation in a harmonic trap 318
References 319
Index 326