Series page -- Title page -- Copyright page -- Preface -- Contents -- 1 Early Atomic Physics -- 1.1 Introduction -- 1.2 Spectrum of Atomic Hydrogen -- 1.3 Bohr's Theory -- 1.4 Relativistic Effects -- 1.5 Moseley and the Atomic Number -- 1.6 Radiative Decay -- 1.7 Einstein A and B Coefficients -- 1.8 The Zeeman Effect -- 1.8.1 Experimental Observation of the Zeeman Effect -- 1.9 Summary of Atomic Units -- Exercises -- 2 The Hydrogen Atom -- 2.1 The Schrödinger Equation -- 2.1.1 Solution of the Angular Equation -- 2.1.2 Solution of the Radial Equation -- 2.2 Transitions -- 2.2.1 Selection Rules -- 2.2.2 Integration with Respect to θ -- 2.2.3 Parity -- 2.3 Fine Structure -- 2.3.1 Spin of the Electron -- 2.3.2 The Spin-orbit Interaction -- 2.3.3 The Fine Structure of Hydrogen -- 2.3.4 The Lamb Shift -- 2.3.5 Transitions between Fine-Structure Levels -- Further Reading -- Exercises -- 3 Helium -- 3.1 The Ground State of Helium -- 3.2 Excited States of Helium -- 3.2.1 Spin Eigenstates -- 3.2.2 Transitions in Helium -- 3.3 Evaluation of the Integrals in Helium -- 3.3.1 Ground State -- 3.3.2 Excited States: The Direct Integral -- 3.3.3 Excited States: The Exchange Integral -- Further Reading -- Exercises -- 4 The Alkalis -- 4.1 Shell Structure and the Periodic Table -- 4.2 The Quantum Defect -- 4.3 The Central-Field Approximation -- 4.4 Numerical Solution of the Schrödinger Equation -- 4.4.1 Self-Consistent Solutions -- 4.5 The Spin-Orbit Interaction: A Quantum Mechanical Approach -- 4.6 Fine Structure in the Alkalis -- 4.6.1 Relative Intensities of Fine-Structure Transitions -- Further Reading -- Exercises -- 5 The LS-Coupling Scheme -- 5.1 Fine Structure in the LS-Coupling Scheme -- 5.2 The jj-Coupling Scheme -- 5.3 Intermediate Coupling: The Transition between Coupling Schemes -- 5.4 Selection Rules in the LS-Coupling Scheme -- 5.5 The Zeeman Effect.

5.6 Summary -- Further Reading -- Exercises -- 6 Hyperfine Structure and Isotope Shift -- 6.1 Hyperfine Structure -- 6.1.1 Hyperfine Structure for s-Electrons -- 6.1.2 Hydrogen Maser -- 6.1.3 Hyperfine Structure for l ≠ 0 -- 6.1.4 Comparison of Hyperfine and Fine Structures -- 6.2 Isotope Shift -- 6.2.1 Mass Effects -- 6.2.2 Volume Shift -- 6.2.3 Nuclear Information from Atoms -- 6.3 Zeeman Effect and Hyperfine Structure -- 6.3.1 Zeeman Effect of a Weak Field, μBB A -- 6.3.3 Intermediate Field Strength -- 6.4 Measurement of Hyperfine Structure -- 6.4.1 The Atomic-Beam Technique -- 6.4.2 Atomic Clocks -- Further Reading -- Exercises -- 7 The Interaction of Atoms with Radiation -- 7.1 Setting up the Equations -- 7.1.1 Perturbation by an Oscillating Electric Field -- 7.1.2 The Rotating-Wave Approximation -- 7.2 The Einstein B Coefficients -- 7.3 Interaction with Monochromatic Radiation -- 7.3.1 The Concepts of π-Pulses and π/2-Pulses -- 7.3.2 The Bloch Vector and Bloch Sphere -- 7.4 Ramsey Fringes -- 7.5 Radiative Damping -- 7.5.1 The Damping of a Classical Dipole -- 7.5.2 The Optical Bloch Equations -- 7.6 The Optical Absorption Cross-Section -- 7.6.1 Cross-Section for Pure Radiative Broadening -- 7.6.2 The saturation Intensity -- 7.6.3 Power Broadening -- 7.7 The a.c. Stark Effect or Light Shift -- 7.8 Comment on Semiclassical Theory -- 7.9 Conclusions -- Further Reading -- Exercises -- 8 Doppler-Free Laser Spectroscopy -- 8.1 Doppler Broadening of Spectral Lines -- 8.2 The Crossed-Beam Method -- 8.3 Saturated Absorption Spectroscopy -- 8.3.1 Principle of Saturated Absorption Spectroscopy -- 8.3.2 Cross-Over Resonances in Saturation Spectroscopy -- 8.4 Two-Photon Spectroscopy -- 8.5 Calibration in Laser Spectroscopy -- 8.5.1 Calibration of the Relative Frequency -- 8.5.2 Absolute Calibration.

8.5.3 Optical Frequency Combs -- Further Reading -- Exercises -- 9 Laser Cooling and Trapping -- 9.1 The Scattering Force -- 9.2 Slowing an Atomic Beam -- 9.2.1 Chirp Cooling -- 9.3 The Optical Molasses Technique -- 9.3.1 The Doppler Cooling Limit -- 9.4 The Magneto-Optical Trap -- 9.5 Introduction to the Dipole Force -- 9.6 Theory of the Dipole Force -- 9.6.1 Optical Lattice -- 9.7 The Sisyphus Cooling Technique -- 9.7.1 General Remarks -- 9.7.2 Detailed Description of Sisyphus Cooling -- 9.7.3 Limit of the Sisyphus Cooling Mechanism -- 9.8 Raman Transitions -- 9.8.1 Velocity Selection by Raman Transitions -- 9.8.2 Raman Cooling -- 9.9 An Atomic Fountain -- 9.10 Conclusions -- Exercises -- 10 Magnetic Trapping, Evaporative Cooling and Bose-Einstein Condensation -- 10.1 Principle of Magnetic Trapping -- 10.2 Magnetic Trapping -- 10.2.1 Confinement in the Radial Direction -- 10.2.2 Confinement in the Axial Direction -- 10.3 Evaporative Cooling -- 10.4 Bose-Einstein Condensation -- 10.5 Bose-Einstein Condensation in Trapped Atomic Vapours -- 10.5.1 The Scattering Length -- 10.6 A Bose-Einstein Condensate -- 10.7 Properties of Bose-Condensed Gases -- 10.7.1 Speed of Sound -- 10.7.2 Healing Length -- 10.7.3 The Coherence of a Bose-Einstein Condensate -- 10.7.4 The Atom Laser -- 10.8 Conclusions -- Exercises -- 11 Atom Interferometry -- 11.1 Young's Double-Slit Experiment -- 11.2 A Diffraction Grating for Atoms -- 11.3 The Three-Grating Interferometer -- 11.4 Measurement of Rotation -- 11.5 The Diffraction of Atoms by Light -- 11.5.1 Interferometry with Raman Transitions -- 11.6 Conclusions -- Further Reading -- Exercises -- 12 Ion Traps -- 12.1 The Force on Ions in an Electric Field -- 12.2 Earnshaw's Theorem -- 12.3 The Paul Trap -- 12.3.1 Equilibrium of a Ball on a Rotating Saddle -- 12.3.2 The Effective Potential in an a.c. Field.

12.3.3 The Linear Paul Trap -- 12.4 Buffer Gas Cooling -- 12.5 Laser Cooling of Trapped Ions -- 12.6 Quantum Jumps -- 12.7 The Penning Trap and The Paul Trap -- 12.7.1 The Penning Trap -- 12.7.2 Mass Spectroscopy of Ions -- 12.7.3 The Anomalous Magnetic Moment of the Electron -- 12.8 Electron Beam ion Trap -- 12.9 Resolved Sideband Cooling -- 12.10 Summary of Ion Traps -- Further Reading -- Exercises -- 13 Quantum Computing -- 13.1 Qubits and Their Properties -- 13.1.1 Entanglement -- 13.2 A Quantum Logic Gate -- 13.2.1 Making a CNOT Gate -- 13.3 Parallelism in Quantum Computing -- 13.4 Summary of Quantum Computers -- 13.5 Decoherence and Quantum Error Correction -- 13.6 Conclusion -- Further Reading -- Exercises -- A Appendix A: Perturbation Theory -- A.1 Mathematics of Perturbation Theory -- A.2 Interaction of Classical Oscillators of Similar Frequencies -- B Appendix B: The Calculation of Electrostatic Energies -- C Appendix C: Magnetic Dipole Transitions -- D Appendix D: The Line Shape in Saturated Absorption Spectroscopy -- E Appendix E: Raman and Two-Photon Transitions -- E.1 Raman transitions -- E.2 Two-Photon Transitions -- F Appendix F: The Statistical Mechanics of Bose-Einstein Condensation -- F.1 The Statistical Mechanics of Photons -- F.2 Bose-Einstein Condensation -- F.2.1 Bose-Einstein Condensation in a Harmonic Trap -- References -- Index.