Laser Cooling and Trapping

Intended for advanced undergraduates and beginning graduates with some basic knowledge of optics and quantum mechanics, this text begins with a review of the relevant results of quantum mechanics, before turning 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.

Contenu

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.