Atomic Physics by C. J. FOOT, Department of Physics ,University of Oxford free download pdf

 Atomic Physics by C. J. FOOT, Department of Physics ,University of Oxford free download pdf 

Atomic physics book by C. J. Foot

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 Relativistic 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 observation of the Zeeman effect 17

1.9 Summary of atomic units 18

Exercises 19

2 The hydrogen atom 22

2.1 The Schr¨odinger 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 Schr¨odinger 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 LS-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 LS-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 Hydrogen maser 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 of π-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 Optical 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 Optical lattice 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 Healing length 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

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