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 Boltzman...

Laser cooling is a relatively new technique that has led to insights into the behavior of atoms as well as confirming with striking detail some of the fundamental notions of quantum mechanics, such as the condensation predicted by S.N. Bose. This elegant technique, whereby atoms, molecules, and even microscopic beads of glass, are trapped in small regions of free space by beams of light and subsequently moved at will using other beams, provides a useful research tool for the study of individual atoms and clusters of atoms, for investigating the details of chemical reactions, and even for determining the physical properties of individual macromolecules such as synthetic polymers and DNA. Intended for advanced undergraduates and beginning graduate students who have some basic knowledge of optics and quantum mechanics, this text begins with a review of the relevant results of quantum mechanics, it then turns to the electromagnetic interactions involved in slowing and trapping atoms and ions, in both magnetic and optical traps. The concluding chapters discuss a broad range of applications, from atomic clocks and studies of collision processes to diffraction and interference of atomic beams at optical lattices and Bose-Einstein condensation.