Contents -- Foreword -- Acknowledgments -- 1. General introduction -- Purpose of this book -- Organization of the book -- Part 1 - Advances in spectroscopy -- Part 2 - Perturbations of atomic levels by light -- Part 3 - Multiphoton processes -- Part 4 - Control of atomic motion. Cooling and trapping -- Part 5 - Ultracold interactions and their control -- Part 6 - Atomic interferometry. Entangled states -- Part 7 - Quantum gases -- Part 8 - A few frontiers of atomic physics -- 2. General background -- 2.1 Introduction -- 2.2 The two interacting systems: atom and field -- 2.2.1 External and internal atomic variables -- 2.2.2 Classical versus quantum treatments of atomic variables -- 2.2.3 Classical description of field variables -- 2.2.4 Quantum description of field variables -- 2.2.5 Atom-field interaction Hamiltonian in the long wavelength approximation -- 2.2.6 Elementary interaction processes -- 2.3 Basic conservation laws -- 2.3.1 Conservation of the total linear momentum -- (i) Case of free atoms -- (ii) Case of atoms trapped in an external potential -- 2.3.2 Conservation of the total angular momentum -- (i) Selection rules for the internal angular momentum -- (ii) Selection rules for the external angular momentum -- 2.4 Two-level atom interacting with a coherent monochromatic field. The Rabi oscillation -- 2.4.1 A simple case: magnetic resonance of a spin 1/2 -- 2.4.2 Extension to any two-level atomic system -- 2.4.3 Perturbative limit -- 2.4.4 Two physical pictures for Ramsey fringes -- (i) Interference between two different paths -- (ii) Interpretation in terms of linear superpositions of states -- 2.5 Two-level atom interacting with a broadband field. Absorption and emission rates -- 2.5.1 Absorption rate deduced from a semiclassical treatment of the field -- 2.5.2 Physical discussion. Relaxation time and correlation time.

2.5.3 Sketch of a quantum treatment of the absorption process -- 2.5.4 Extension to spontaneous emission -- 2.6 Two-level atom interacting with a coherent monochromatic field in the presence of damping -- Light: a source of information on atoms -- Introduction -- 3. Optical methods -- 3.1 Introduction -- 3.2 Double resonance -- 3.2.1 Principle of the method -- 3.2.2 Predicted shape for the double resonance curve -- 3.2.3 Experimental results -- 3.2.4 Interpretation of the Majorana reversal -- 3.3 Optical pumping [Kastler (1950)] -- 3.3.1 Principle of the method for a Jg = 1/2 Je = 1/2 transition -- 3.3.2 Angular momentum balance -- 3.3.3 Double role of light -- 3.4 First experiments on optical pumping -- 3.5 How can optical pumping polarize atomic nuclei? -- 3.5.1 Using hyperfine coupling with polarized electronic spins -- 3.5.2 First example: optical pumping experiments with mercury-199 atoms -- 3.5.3 Second example: combining optical pumping with metastability exchange collisions for helium-3 -- 3.5.4 A new application: magnetic resonance imaging of the lung cavities -- 3.6 Brief survey of the main applications of optical methods -- 3.7 Concluding remarks -- 4. Linear superpositions of internal atomic states -- 4.1 Introduction -- 4.2 First experimental evidence of the importance of atomic coherences -- 4.3 Zeeman coherences in excited states -- 4.3.1 How to prepare Zeeman coherences in excited states e? -- 4.3.2 Physical interpretation -- 4.3.3 How to detect Zeeman coherences in e? -- 4.3.4 Equation of motion of Zeeman coherences in e -- 4.3.5 Level crossing resonances in the excited state e -- 4.3.6 Pulsed excitation. Quantum beats -- 4.3.7 Excitation with modulated light -- 4.3.8 Modulation of the fluorescence light in a double resonance experiment. Light beats -- 4.4 Zeeman coherences in atomic ground states.

4.4.1 Hanle effect in atomic ground states -- 4.4.2 Detection of the magnetic resonance in the ground state by the modulation of the absorbed light -- 4.5 Transfer of coherences -- (i) Transfers between two atoms mediated by a spontaneous photon -- (ii) Transfer between two atoms mediated by collision -- 4.6 Dark resonances. Coherent population trapping -- 4.6.1 Discovery of dark resonances -- 4.6.2 First theoretical treatment of dark resonances -- 4.6.3 Interpretation of the Raman resonance condition -- 4.6.4 A few applications of dark resonances -- (i) Electromagnetically induced transparency (EIT) -- (ii) Slow light -- (iii) Stimulated Raman adiabatic passage (STIRAP) -- (iv) Velocity selective coherent population trapping -- 4.7 Conclusion -- 5. Resonance fluorescence -- 5.1 Introduction -- 5.2 Low intensity limit. Perturbative approach -- 5.2.1 Lowest order process -- 5.2.2 Resonant scattering amplitude -- 5.2.3 Scattering of a light wave packet -- 5.2.4 First higher order processes -- 5.3 Optical Bloch equations -- 5.4 The dressed atom approach -- 5.4.1 The interacting systems -- 5.4.2 Uncoupled states of the atom-laser system -- 5.4.3 Effect of the coupling. Dressed states -- 5.4.4 Two different situations -- (i) Atom in a real cavity. Cavity Quantum Electrodynamics -- (ii) Atom in free space -- 5.4.5 Radiative cascade in the basis of uncoupled states -- 5.4.6 A new description of quantum dissipative processes -- 5.5 Photon correlations. The quantum jump approach -- 5.5.1 The waiting time distribution -- 5.5.2 From the waiting time distribution to the second order correlation function -- 5.5.3 Photon antibunching -- 5.6 Fluorescence triplet at high laser intensities -- 5.6.1 Limit of large Rabi frequency -- 5.6.2 Mollow fluorescence triplet -- 5.6.3 Widths and weights of the components of the Mollow triplet.

5.6.4 Time correlations between the photons emitted in the two sidebands of the fluorescence triplet -- 5.7 Conclusion -- 6. Advances in high resolution spectroscopy -- 6.1 Introduction -- Doppler effect and recoil shift for free atoms. Orders of magnitude -- Atom trapped in an external potential -- 6.2 Saturated absorption -- 6.2.1 Principle of the method -- 6.2.2 Crossover resonances -- 6.2.3 Recoil doublet -- 6.3 Two-photon Doppler-free spectroscopy -- 6.3.1 Principle of the method -- 6.3.2 Examples of results -- 6.3.3 Comparison between saturated absorption and two-photon spectroscopy -- 6.4 Recoil suppressed by confinement: the Lamb-Dicke effect -- 6.4.1 Intensities of the vibrational lines -- 6.4.2 Influence of the localization of the ion -- 6.4.3 Case of a harmonic potential -- 6.4.4 Historical perspective -- 6.5 The shelving method -- 6.5.1 Single ion spectroscopy -- 6.5.2 Intermittent fluorescence -- 6.5.3 Properties of the detected signal -- 6.5.4 Observation of quantum jumps -- 6.6 Quantum logic spectroscopy -- 6.7 Frequency measurement with frequency combs -- 6.8 Conclusion -- Atom-photon interactions: a source of perturbations for atoms which can be useful -- Introduction -- 7. Perturbations due to a quasi resonant optical excitation -- 7.1 Introduction -- 7.2 Light shift, light broadening and Rabi oscillation -- 7.2.1 Effective Hamiltonian -- 7.2.2 Weak coupling limit. Light shift and light broadening -- 7.2.3 High coupling limit. Rabi oscillation -- 7.2.4 Absorption rate versus Rabi oscillation -- 7.2.5 Semiclassical interpretation in the weak coupling limit -- 7.2.6 Generalization to a non-resonant excitation -- 7.2.7 Case of a degenerate ground state -- 7.3 Perturbation of the field. Dispersion and absorption -- 7.3.1 Atom in a cavity -- 7.3.2 Frequency shift of the field due to the atom -- 7.3.3 Damping of the field.

7.4 Experimental observation of light shifts -- 7.4.1 Principle of the experiment -- 7.4.2 Examples of results -- 7.5 Using light shifts for manipulating atoms -- 7.5.1 Laser traps -- 7.5.2 Atomic mirrors -- 7.5.3 Blue detuned traps: a few examples -- 7.5.4 Optical lattices -- 7.5.5 Internal state dependent optical lattices -- 7.5.6 Coherent transport -- 7.6 Using light shifts for manipulating fields -- 7.6.1 Linear superposition of two field states with different phases -- 7.6.2 Non-destructive detection of photons -- 7.7 Conclusion -- 8. Perturbations due to a high frequency excitation -- 8.1 Introduction -- 8.2 Spin 1/2 coupled to a high frequency RF field -- 8.2.1 Hamiltonian -- 8.2.2 Perturbative treatment of the coupling -- 8.2.3 Stimulated corrections -- 8.2.4 Radiative corrections -- 8.3 Weakly bound electron coupled to a high frequency field -- 8.3.1 Effective Hamiltonian describing the modifications of the dynamical properties of the electron -- 8.3.2 Stimulated effects -- 8.3.3 Spontaneous effects. Vacuum fluctuations and radiation reaction -- 8.4 New insights into radiative corrections -- 8.4.1 Examples of spontaneous corrections -- 8.4.2 Interpretation of the Lamb shift -- 8.4.3 Interpretation of the spin anomaly g - 2 -- 8.5 Conclusion -- Atom-photon interactions: a simple system for studying higher order effects -- Introduction -- 9. Multiphoton processes between discrete states -- 9.1 Introduction -- 9.2 Radiofrequency multiphoton processes -- 9.2.1 Multiphoton RF transitions between two Zeeman sublevels mF and mF + 2 -- 9.2.2 Experimental observation on sodium atoms -- 9.2.3 Multiphoton resonances between two Zeeman sublevels mF and mF + 1 -- 9.3 Radiative shift and radiative broadening of multiphoton resonances -- 9.3.1 Energy levels of the atom+RF photons system. Transition amplitude.

9.3.2 Pure single photon resonance. Simple anticrossing.