Laser Cooling and Trapping

Laser cooling is a new technique that has led to new insights into the behavior of atoms. This text covers the foundations, the techniques, and applications: from atomic clocks and studies of collision processes to diffraction and interference of atomic beams at optical lattices. It is aimed at advanced undergraduates and beginning graduates.

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 Boltzman...