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 6ne structure of h、rdrogen 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 Hyperflne strueture 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 6.3.2 Zeeman effect of a strong 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 monochtomatic radiation 7.3.1 The concepts of π-pulses andπ/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 Calmration in 1aser 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 foroe 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 Equilbrium 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 Mathera&tics 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