Laser Cooling and Trapping

I Introduction.- 1 Review of Quantum Mechanics.- 1.1 Time-Dependent Perturbation Theory.- 1.2 The Rabi Two-Level Problem.- 1.2.1 Light Shifts.- 1.2.2 The Dressed Atom Picture.- 1.2.3 The Bloch Vector.- 1.2.4 Adiabatic Rapid Passage.- 1.3 Excited-State Decay and its Effects.- 2 The Density Matrix.- 2.1 Basic Concepts.- 2.2 Spontaneous Emission.- 2.3 The Optical Bloch Equations.- 2.4 Power Broadening and Saturation.- 3 Force on Two-Level Atoms.- 3.1 Laser Light Pressure.- 3.2 A Two-Level Atom at Rest.- 3.3 Atoms in Motion.- 3.3.1 Traveling Wave.- 3.3.2 Standing Wave.- 4 Multilevel Atoms.- 4.1 Alkali-Metal Atoms.- 4.2 Metastable Noble Gas Atoms.- 4.3 Polarization and Interference.- 4.4 Angular Momentum and Selection Rules.- 4.5 Optical Transitions in Multilevel Atoms.- 4.5.1 Introduction.- 4.5.2 Radial Part.- 4.5.3 Angular Part of the Dipole Matrix Element.- 4.5.4 Fine and Hyperfine Interactions.- 5 General Properties Concerning Laser Cooling.- 5.1 Temperature and Thermodynamics in Laser Cooling.- 5.2 Kinetic Theory and the Maxwell-Boltzmann Distribution.- 5.3 Random Walks.- 5.4 The Fokker-Planck Equation and Cooling Limits.- 5.5 Phase Space and Liouville’s Theorem.- II Cooling & Trapping.- 6 Deceleration of an Atomic Beam.- 6.1 Introduction.- 6.2 Techniques of Beam Deceleration.- 6.2.1 Laser Frequency Sweep.- 6.2.2 Varying the Atomic Frequency: Magnetic Field Case.- 6.2.3 Varying the Atomic Frequency: Electric Field Case.- 6.2.4 Varying the Doppler Shift: Diffuse Light.- 6.2.5 Broadband Light.- 6.2.6 Rydberg Atoms.- 6.3 Measurements and Results.- 6.4 Further Considerations.- 6.4.1 Cooling During Deceleration.- 6.4.2 Non-Uniformity of Deceleration.- 6.4.3 Transverse Motion During Deceleration.- 6.4.4 Optical Pumping During Deceleration.- 7 Optical Molasses.- 7.1 Introduction.- 7.2 Low-Intensity Theory for a Two-Level Atom in One Dimension..- 7.3 Atomic Beam Collimation.- 7.3.1 Low-Intensity Case.- 7.3.2 Experiments in One and Two Dimensions.- 7.4 Experiments in Three-Dimensional Optical Molasses.- 8 Cooling Below the Doppler Limit.- 8.1 Introduction.- 8.2 Linear ? Linear Polarization Gradient Cooling.- 8.2.1 Light Shifts.- 8.2.2 Origin of the Damping Force.- 8.3 Magnetically Induced Laser Cooling.- 8.4 ?+-?- Polarization Gradient Cooling.- 8.5 Theory of Sub-Doppler Laser Cooling.- 8.6 Optical Molasses in Three Dimensions.- 8.7 The Limits of Laser Cooling.- 8.7.1 The Recoil Limit.- 8.7.2 Cooling Below the Recoil Limit.- 8.8 Sisyphus Cooling.- 8.9 Cooling in a Strong Magnetic Field.- 8.10 VSR and Polarization Gradients.- 9 The Dipole Force.- 9.1 Introduction.- 9.2 Evanescent Waves.- 9.3 Dipole Force in a Standing Wave: Optical Molasses at High Intensity.- 9.4 Atomic Motion Controlled by Two Frequencies.- 9.4.1 Introduction.- 9.4.2 Rectification of the Dipole Force.- 9.4.3 The Bichromatic Force.- 9.4.4 Beam Collimation and Slowing.- 10 Magnetic Trapping of Neutral Atoms.- 10.1 Introduction.- 10.2 Magnetic Traps.- 10.3 Classical Motion of Atoms in a Magnetic Quadrupole Trap.- 10.3.1 Simple Picture of Classical Motion in a Trap.- 10.3.2 Numerical Calculations of the Orbits.- 10.3.3 Early Experiments with Classical Motion.- 10.4 Quantum Motion in a Trap.- 10.4.1 Heuristic Calculations of the Quantum Motion of Magnetically Trapped Atoms.- 10.4.2 Three-Dimensional Quantum Calculations.- 10.4.3 Experiments in the Quantum Domain.- 11 Optical Traps for Neutral Atoms.- 11.1 Introduction.- 11.2 Dipole Force Optical Traps.- 11.2.1 Single-Beam Optical Traps for Two-Level Atoms.- 11.2.2 Hybrid Dipole Radiative Trap.- 11.2.3 Blue Detuned Optical Traps.- 11.2.4 Microscopic Optical Traps.- 11.3 Radiation Pressure Traps.- 11.4 Magneto-Optical Traps.- 11.4.1 Introduction.- 11.4.2 Cooling and Compressing Atoms in a MOT.- 11.4.3 Capturing Atoms in a MOT.- 11.4.4 Variations on the MOT Technique.- 12 Evaporative Cooling.- 12.1 Introduction.- 12.2 Basic Assumptions.- 12.3 The Simple Model.- 12.4 Speed and Limits of Evaporative Cooling.- 12.4.1 Boltzmann Equation.- 12.4.2 Speed of Evaporation.- 12.4.3 Limiting Temperature.- 12.5 Experimental Results.- III Applications.- 13 Newtonian Atom Optics and its Applications.- 13.1 Introduction.- 13.2 Atom Mirrors.- 13.3 Atom Lenses.- 13.3.1 Magnetic Lenses.- 13.3.2 Optical Atom Lenses.- 13.4 Atomic Fountain.- 13.5 Application to Atomic Beam Brightening.- 13.5.1 Introduction.- 13.5.2 Beam-Brightening Experiments.- 13.5.3 High-Brightness Metastable Beams.- 13.6 Application to Nanofabrication.- 13.7 Applications to Atomic Clocks.- 13.7.1 Introduction.- 13.7.2 Atomic Fountain Clocks.- 13.8 Application to Ion Traps.- 13.9 Application to Non-Linear Optics.- 14 Ultra-cold Collisions.- 14.1 Introduction.- 14.2 Potential Scattering.- 14.3 Ground-state Collisions.- 14.4 Excited-state Collisions.- 14.4.1 Trap Loss Collisions.- 14.4.2 Optical Collisions.- 14.4.3 Photo-Associative Spectroscopy.- 14.5 Collisions Involving Rydberg States.- 15 deBroglie Wave Optics.- 15.1 Introduction.- 15.2 Gratings.- 15.3 Beam Splitters.- 15.4 Sources.- 15.5 Mirrors.- 15.6 Atom Polarizers.- 15.7 Application to Atom Interferometry.- 16 Optical Lattices.- 16.1 Introduction.- 16.2 Laser Arrangements for Optical Lattices.- 16.3 Quantum States of Motion.- 16.4 Band Structure in Optical Lattices.- 16.5 Quantum View of Laser Cooling.- 17 Bose-Einstein Condensation.- 17.1 Introduction.- 17.2 The Pathway to BEC.- 17.3 Experiments.- 17.3.1 Observation of BEC.- 17.3.2 First-Order Coherence Experiments in BEC.- 17.3.3 Higher-Order Coherence Effects in BEC.- 17.3.4 Other Experiments.- 18 Dark States.- 18.1 Introduction.- 18.2 VSCPT in Two-Level Atoms.- 18.3 VSCPT in Real Atoms.- 18.3.1 Circularly Polarized Light.- 18.3.2 Linearly Polarized Light.- 18.4 VSCPT at Momenta Higher Than ±hk.- 18.5 VSCPT and Bragg Reflection.- 18.6 Entangled States.- IV Appendices.- A Notation and Definitions.- B Review Articles and Books on Laser Cooling.- C Characteristic Data.- D Transition Strengths.- References.