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Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume with Commentaries

Optical Trapping and Manipulation of Neutral Particles Using Lasers: A Reprint Volume with Commentaries

by Arthur Ashkin
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This important volume contains selected papers and extensive commentaries on laser trapping and manipulation of neutral particles using radiation pressure forces. Such techniques apply to a variety of small particles, such as atoms, molecules, macroscopic dielectric particles, living cells, and organelles within cells. These optical methods have had a revolutionary impact on the fields of atomic and molecular physics, biophysics, and many aspects of nanotechnology.In atomic physics, the trapping and cooling of atoms down to nanokelvins and even picokelvin temperatures are possible. These are the lowest temperatures in the universe. This made possible the first demonstration of Bose-Einstein condensation of atomic and molecular vapors. Some of the applications are high precision atomic clocks, gyroscopes, the measurement of gravity, cryptology, atomic computers, cavity quantum electrodynamics and coherent atom lasers.A major application in biophysics is the study of the mechanical properties of the many types of motor molecules, mechanoenzymes, and other macromolecules responsible for the motion of organelles within cells and the locomotion of entire cells. Unique in vitro and in vivo assays study the driving forces, stepping motion, kinetics, and efficiency of these motors as they move along the cell's cytoskeleton. Positional and temporal resolutions have been achieved, making possible the study of RNA and DNA polymerases, as they undergo their various copying, backtracking, and error correcting functions on a single base pair basis.Many applications in nanotechnology involve particle and cell sorting, particle rotation, microfabrication of simple machines, microfluidics, and other micrometer devices. The number of applications continues to grow at a rapid rate.The author is the discoverer of optical trapping and optical tweezers. With his colleagues, he first demonstrated optical levitation, the trapping of atoms, and tweezer trapping and manipulation of living cells and biological particles.This is the only review volume covering the many fields of optical trapping and manipulation. The intention is to provide a selective guide to the literature and to teach how optical traps really work.

Product Details

ISBN-13: 9789810240585
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 04/28/2007
Pages: 940
Sales rank: 883,344
Product dimensions: 7.50(w) x 10.20(h) x 2.10(d)

Table of Contents

Preface     vii
Introduction     1
Beginnings     3
Radiation Pressure Using Microwave Magnetrons     3
Runners and Bouncers     3
Back of the Envelope Calculation of Laser Radiation Pressure     5
First Observation of Laser Radiation Pressure     7
Observation of the First Three-Dimensional All-Optical Trap     10
Scattering Force on Atoms     11
Saturation of the Scattering Force on Atoms     13
Gradient (Dipole) Force on Atoms     13
Dispersive Properties of the Dipole Force on Atoms     14
Applications of the Scattering Force     16
"It's not Even Wrong!"     16
Optical Traps and the Prepared Mind     19
1969-1979     21
Optical Levitation     23
Levitation in Air     23
Scientific American Article of 1973     27
Levitation with TEM[subscript 01]* Donut Mode Beams     28
Levitation of Liquid Drops     30
Radiometric or Thermal Forces     31
Levitation at Reduced Air Pressure     34
Feedback Damping of Levitated Particles and Automatic Force Measurement     36
Feedback Measurement of Axial Scattering Force     37
Feedback Force Measurement of High-Q Surface Wave Resonances     38
Measurement of Electric Forces by Feedback Control of Levitated Particles     44
Atom Trapping and Manipulation by Radiation Pressure Forces     47
Early Concepts and Experiments with Atoms     47
Deflection of atoms by the scattering force     47
Doppler cooling of atoms using the scattering force and fluctuational heating of atoms     47
Damping of macroscopic particles     50
Saturation of the gradient force on atoms     52
Optimum potential p for a given laser power     55
Conservative and nonconservative properties of the radiation pressure force components     56
Two-beam optical dipole traps for atoms     58
Single-beam optical dipole trap, or tweezer trap, for atoms     59
Separate trapping and cooling beams and the Stark shift problem     61
First demonstration of the dipole force on atoms using detuned light     65
Origin of atom optics     67
Theoretical Aspects of Optical Forces on Atoms     68
Quantum theory of "The motion of atoms in a radiation trap"     68
Optical Stark shifts and dipole force traps for atoms     69
Optical dipole forces     70
Conservation of momentum in light scattering by atoms and sub-micrometer particles     70
Summary of the First Decade's Work on Optical Trapping and Manipulation of Particles     75
1980-1990     77
Trapping of Atoms and Biological Particles in the 1980-1990 Decade     79
Optical Trapping and Cooling of Neutral Atoms in the Decade 1980-1990     80
Slowing of atomic beams by the scattering force     81
Scattering force traps and the optical Earnshaw theorem     81
Arrival of Steve Chu at the Holmdel Laboratory     82
Planning for the first atom trapping experiment     83
Stable alternating beam scattering force atom traps     84
First demonstration of optical molasses and early work on an optical trap     86
Cooling below the Doppler limit of molasses and below the recoil limit     87
Evaporative cooling from optical dipole traps     88
First atom trapping experiment using the single-beam dipole trap     91
Proposal for stable spontaneous force light traps     93
Nature's comments on the first atom trapping experiment     94
The first experimental demonstration of a MOT     94
Radiation trapping in MOTs     95
Atom cooling below the Doppler limit     96
Trapping of Biological Particles      99
Artificial nonlinear media     101
Trapping of submicrometer Rayleigh particles     102
Tweezer trapping of micrometer-sized dielectric spheres     103
Optical trapping and manipulation of viruses and bacteria     105
Optical alignment of tobacco mosaic viruses     106
Fixed particle arrays of tobacco mosaic viruses     106
Tweezer trapping of bacteria and "opticution"     107
Tweezer trapping of bacteria in a high-resolution microscope     109
Optical tweezers using infrared light from a Nd:YAG laser     111
Damage-free trapping of living cells     111
Internal cell trapping and manipulation     113
Separation of bacteria using tweezers     114
Elastic properties of the cytoplasm     115
1990-2006     117
Biological Applications     123
General Biological Applications     125
Application of Tweezers to the Study of Bacteria     125
Bacteria flagella and bacterial motors     125
Optical manipulation of extremophilia     126
Archaea     126
Sequencing of Thermotoga maritima, a eubacterium     127
Pilus retraction powers bacterial twitching motility     128
Direct observation of extension and retraction of type-IV pili     128
A force-dependent switch reverses type-IV pilus retraction     129
Characterization of photodamage to Escherichia coli in optical traps     129
Use of UV Cutting Plus Tweezers to Study Cell Fusion and Chromosomes     130
Tweezer Manipulation of Live Sperm and Application to In Vitro Fertilization     130
Tweezer Study of the Immune Response of T-Lymphocytes     130
Adhesion of Influenza Virus to Red Blood Cells Using OPTCOL Technique     131
Mechanical Properties of Membranes Studied by Tether Formation Using Tweezers     131
Deformation of Single Cells by Light Forces     132
Artificial Gravity in Plants     134
Guiding of Neuronal Growth with Light     135
Self-Rotation of Red Blood Cells in Optical Tweezers     135
Use of Optical Tweezers to Study Single Motor Molecules     137
In Vivo Force Measurement of Dynein in Giant Amoeba Reticulomyxa     138
Measurement of the Force Produced by Kinesin     140
Resolution of the Stepping Motion of Kinesin on Microtubules by Interferometry     140
Observation of Single Stepwise Motion of Muscle Myosin-II Molecules on Actin Using Feedback and Tweezers     143
Measurement of Diffusional Motion and Stepping in Actin-Myosin Interactions      145
Measurement of Myosin Step Size Using an Oriented Single-Headed Molecule     145
Forces on Smooth Muscle Myosin and Use of Fluorescently Labeled ATP with Total Internal Reflection Microscopy     145
Observation of Two-Step Behavior of Myosin I Using the Tweezer Dumbbell Technique     147
Study of Processive Class-V Myosins Using a Pair of Tweezer Traps     148
Force vs. Velocity Measurement on Kinesin Motor Molecules     148
Single Enzyme Kinetics of Kinesin     149
Kinesin Hydrolyses One ATP Molecule per 8 nm Step     149
Feedback Control of Tweezers: Force Clamps and Position Clamps     149
Study of Single Kinesin Molecules with a Force Clamp     150
Structural Measurements on Kinesin     152
Substeps within the 8 nm Step of the ATPase Cycle of Single Kinesin Molecules     153
Processivity of a Single-Headed Kinesin Construct C351 and the Brownian Ratchet     154
Myosin VI is a Processive Motor with a Large Step Size     156
Mapping the Actin Filament with Myosin     156
Development Regulation of Vesicle Transport in Drosophila Embryos: Forces and Kinetics     157
Dynein-Mediated Cargo Transport In Vivo: A Switch Controls Travel Distance     159
Kinesin Moves by an Asymmetric Hand-Over-Hand Mechanism      160
Applications to RNA and DNA     163
Observation of the Force of an RNA Polymerase Molecule as it Transcribes DNA     163
Force and Velocity Measured for Single Molecules of RNA Polymerase     163
Measurement of the Mechanical Properties of DNA Polymer Strands     164
Measurement of Flexural Rigidity of Microtubule Fibers and Torsional Rigidity of Microtubules and Actin Filaments     165
Measurement of the Stretching of Double- and Single-Stranded DNA     165
Polymerization of RecA Protein on Individual ds DNA Molecules     166
Study of Elasticity of RecA-DNA Filaments with Constant Tension Feedback     166
Possible Role of Tweezers in DNA Sequencing     167
Study of the Structure of DNA and Chromatin Fibers by Stretching with Light Forces     168
Condensation and Decondensation of the Same DNA Molecule by Protamine and Arginine Molecules     170
Non-Mendelian Inheritance of Chloroplast DNA in Living Algal Cells Using Tweezers     170
Measurement of the Force and Mechanical Properties of DNA Polymerase with Optical Tweezers     171
Reversible Unfolding of Single RNA Molecules by Mechanical Force     172
Grafting of Single DNA Molecules to AFM Cantilevers Using Optical Tweezers     173
Structural Transition and Elasticity from Torque Measurements on DNA      174
Backtracking by Single RNA Polymerase Molecules Observed at Near-Base-Pair Resolution     175
Ubiquitous Transcriptional Pausing is Independent of RNA Polymerase Backtracking     176
RNA Polymerase can Track a DNA Groove During Promoter Search     177
The Bacterial Condensin MukBEF Compacts DNA into a Repetitive, Stable Structure     178
Forward and Reverse Motion of RecBCD Molecules on DNA     179
Direct Observation of Base-Pair Stepping by RNA Polymersase     179
Study of the Mechanical Properties of Other Macromolecules with Optical Tweezers     181
Stretching and Relaxation of the Giant Molecule Titin     181
Cell Motility of Adherent Cells Over an Extra-Cellular Matrix     182
Study of Forces that Regulate the Movement of Plasma Membrane Proteins     184
Membrane Tube Formation from Giant Vesicles by Dynamic Association of Motor Proteins     187
Other Recent Applications in Physics and Chemistry     189
Origin of Tweezer Forces on Macroscopic Particles Using Highly Focused Beams     191
Origin of the Net Backward Radiation Pressure Force in Tweezer Traps     191
Light Propagation at the Focus of a High Numerical Aperture Beam     192
Calculation of the Tweezer Forces on Dielectric Spheres in the Ray-Optics Regime     193
Corrections to Paraxial Ray Approximation for Strongly Focused Gaussian Beams     194
Fifth-Order Corrected Electromagnetic Field Components for a Focused Fundamental Gaussian Beam     194
Computation of Net Force and Torque for a Spherical Particle Illuminated by a Focused Laser Beam     195
Measurements of the Forces on Microspheres Held by Optical Tweezers     196
Generalized Lorenz-Mie Theory for Convergent Gaussian Beams     196
Computation of Backward Radiation Pressure Using GLMT     197
Single-Beam Trapping of Rayleigh and Macroscopic Particles Using Exact Diffraction Theory     198
Optical Gradient Forces of Strongly Localized Fields     199
Exact Theory of Optical Tweezers for Macroscopic Dielectric Spheres     200
Use of Optical Tweezers as a Stylus Support for Scanning Force Microscopy     201
Localized Dynamic Light Scattering     202
Thermal Ratchet Motors     202
Experimental Test of Kramers' Theory of Thermally Driven Transition Rates     203
Study of Charge-Stabilized Colloidal Suspensions     205
Optically Induced Colloidal Crystals     205
Optical Matter: Crystallization and Binding of Particles in Intense Laser Fields     206
Microscopic Measurement of the Pair Interaction of Charge-Stabilized Colloids Using Tweezers      207
Theoretical Approaches to the Understanding of Pair Interactions of Charge-Stabilized Colloids     209
Confinement-Induced Colloidal Attractions in Equilibrium     210
Entropic Forces in Binary Colloids     211
Entropic Control of Particle Motion Using Passive Surface Microstructures     212
Entropic Attraction and Repulsion in Binary Colloids Probed with a Line Optical Tweezer     212
Rotation of Particles by Radiation Pressure     215
Optically Induced Rotation of an Anisotropic Micro-Particle Fabricated by Surface Micromachining     215
Optically Induced Rotation of a Trapped Micro-Object about an Axis Perpendicular to the Laser Beam Axis     217
Optical Microrotors     218
Orbital Angular Momentum     218
Observation of Transfer of Angular Momentum to Absorptive Particles from a Laser Beam with a Phase Singularity     221
Mechanical Equivalence of Spin and Orbital Angular Momentum of Light: An Optical Spanner     222
Controlled Rotation of Optically Trapped Microscopic Particles     223
Optical Torque Wrench: Angular Trapping, Rotation, and Torque Detection of Quartz Microparticles     224
Microchemistry     225
It Laser Trapping, Electrochemistry, and Photochemistry of a Single Microdroplet     227
Control of Dye Formation Inside a Single Laser-Positioned Droplet by Electrolysis     227
Laser-Controlled Phase Transitions in PNIPAM and Reversible Formation of Liquid Drops     228
Holographic Optical Tweezers and Fluidic Sorting     231
Nanofabrication with Holographic Tweezers     231
Dynamic Holographic Tweezers     231
Sorting by Periodic Potential Energy Landscapes: Optical Fractionation     233
Optical Peristalsis     234
Microfluidic Sorting in an Optical Lattice     234
Microfluidic Control Using Colloidal Devices     235
Applications of Atom Trapping and Cooling     237
Uses of Slow Atoms     239
Atomic Clocks Using Slow Atoms     239
Atom Optics     241
The first guiding arid focusing of atoms using dipole forces     241
Lenses based on the scattering force     241
Magneto-optic waveguide and atomic beam brightness     242
Evanescent wave mirors     245
Atomic beam splitters     245
Neutral atom lithography     245
Atom Interferometers     245
Atomic Waveguide Devices     246
Optical guiding of atoms     246
Magnetic guiding of atoms near wires     246
Magnetic guiding using atom chips      247
Magnetic guiding around curves     248
Magnetic guides as atomic beam splitters     248
Cold Atom Collisions     249
Photoassociation vs. associative ionization     250
Dark spot MOTs     252
Scanning photoassociative spectroscopy using far-off-resonance dipole traps     252
Optical shielding or suppression of trap loss     254
Bose-Einstein Condensation and Related Developments     257
Introduction to Bose-Einstein Condensation     259
First Demonstration of BEC, Using the TOP Magnetic Trap     260
Bose-Einstein Condensation Using an Optically Plugged Magnetic Trap     262
Bose-Einstein Condensation Using the "Cloverleaf" Magnetic Trap     263
Bose-Einstein Condensation in [superscript 7]Li     263
Expanding Bose-Einstein Condensates     263
Gross-Pitaevskii Mean Field Theory     264
Collective Excitation of a Bose-Einstein Condensate     265
Coherence of Bose-Einstein Condensates     265
Interference between two condensates     265
Measurement of [Delta]p and the uncertainty principle     267
Coherence and interference in the time domain     267
Coherence of atoms tunneling out of arrays      268
Spatial coherence of atoms ejected from a trap     268
Condensate Formation by Bose Stimulation     269
Atom Lasers     269
Pulsed sodium atom laser     270
cw atom laser     270
Quasi-continuous atom laser by Raman ejection     272
Coherent beams by Bragg scattering     272
Coherent beam generation by four-wave mixing     274
Commentary on Bose-Einstein condensates and nonlinear matter waves     276
Two-component Bose-Einstein condensates in [superscript 87]Rb and sympathetic cooling     277
Dynamics of two-component Bose-Einstein condensates in [superscript 87]Rb     277
Phase memory in [superscript 87]Rb two-component Bose-Einstein condensates     278
Role of All-Optical Traps and MOTs in Atomic Physics     279
Far-Off-Resonance Optical Traps for [superscript 85]Rb     280
Far-Off-Resonance Traps for Cesium Using CO[subscript 2] Lasers     280
Evaporative Cooling of Sodium Atoms from an Optical Dipole Trap     282
Raman Cooling of Trapped Atoms in a Dipole Trap     282
Laser Noise Heating in Far-Off-Resonance Optical Dipole Traps     282
Sisyphus Cooling of Cesium in Far-Off-Resonance Optical Dipole Traps     283
Raman Cooling of Cesium in Far-Off-Resonance Optical Dipole Traps     283
Two-Step Narrow-Line Cooling of Strontium in Optical Dipole Traps     283
Continuous Doppler Cooling of Strontium Atoms in an Optical Dipole Trap     285
Three-Dimensional (3D) Raman Sideband Cooling of Cesium in Optical Dipole Traps     286
Blue-Detuned Optical Dark Traps for Achieving High Atomic Density     287
Transfer of Bose-Einstein Condensates into Optical Dipole Traps     288
Spinor Condensates in Optical Dipole Traps     291
Dynamics of Formation     291
Metastable Excited Spin States     291
Optical Tunneling of Trapped Spinor States     292
Feshbach Resonances     295
Magnetic Tuning of the Scattering Length in a Dipole Trap     295
Magnetic Tuning in Photoassociative Spectroscopy     297
Feshbach Resonance of Ground State Cesium at Low Magnetic Field     297
Elastic and Inelastic Collisions Near Feshbach Resonances in Sodium     298
Suppression of Collision Loss in Cesium Near Feshbach Resonances     299
Discovery of New Low-Field Feshbach Resonances by High-Resolution Spectroscopy     299
Observation of Optically Induced Feshbach Resonances in Collisions of Cold Atoms     301
Recent Work on Bose-Einstein Condensation     303
Diffraction of a Released Bose-Einstein Condensate by a Pulsed Standing Lightwave     303
Collective Collapse in a Bose-Einstein Condensate with Attractive Interactions     305
[superscript 85]Rb Bose-Einstein Condensates with Magnetically Tunable Interactions     305
Bose-Einstein Condensation in Metastable Helium Atoms     306
Observation of Bose-Einstein Condensation Using Optical Dipole Traps     307
Bose-Einstein Condensation of Potassium Atoms by Sympathetic Cooling     309
Realization of Bose-Einstein Condensates in Lower Dimensions     310
Josephson Junction Arrays with Bose-Einstein Condensates     311
Josephson Effects in Dilute Bose-Einstein Condensates     313
Squeezed States in a Bose-Einstein Condensate     314
Quantum Phase Transition from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms     315
Bose-Einstein Condensation on a Microelectronic Chip     316
Bose-Einstein Condensates Near a Microfabricated Surface     317
Tonks-Girardeau 1D Gas of Ultracold Atoms     318
All-Optical Production of a Degenerate Fermi Gas     319
Bose-Einstein Condensation of Cesium by Evaporative Cooling from Optical Dipole Traps     319
Optimized Production of a Cesium Bose-Einstein Condensate     320
Cooling Bose-Einstein Condensates Below 500 pK     320
Design for an Optical cw Atom Laser     320
Trapping Single Atoms with Single Photons in Cavity Quantum Electrodynamics     333
The Simple One-Atom Maser     324
The Two-Photon Maser     324
Trapping Single Atoms in a MOT     324
Coupling Single Atoms to a High-Finesse Optical Cavity     325
Coupling of Single Slow Cesium Atoms to a High-Finesse Optical Cavity     325
Cooling an Atom Strongly Coupled to a High-Q Standing Wave Cavity     325
Real-Time CQED and Atom Channeling with Single Atoms     326
Formation of Giant Quasi-Bound Cold Diatoms by Strong Atom-Cavity Coupling     326
Single Atoms Trapped in Orbit by Single Photons     326
The Atom Cavity Microscope     327
Dynamics of Single Atom Motion in the Field of a Single Photon     328
Commentary on CQED in Nature's "News and Views"     329
Experimental Realization of a One-Atom Laser in the Regime of Strong Coupling     329
Cavity Cooling of a Single Atom     330
Deterministic Generation of Single Photons from One Atom Trapped in a Cavity     330
Trapping of Single Atoms in an Off-Resonance Optical Dipole Trap     333
Single Atoms in an Optical Dipole Trap: Towards a Deterministic Source of Cold Atoms      333
Sub-Poissonian Loading of Single Atoms in a Microscopic Dipole Trap     334
Vortices and Frictionless Flow in Bose-Einstein Condensates     337
Vortices in a Two-Component Bose-Einstein Condensate     337
Observation of Two-Component Vortices in a Bose-Einstein Condensate     338
Single-Component Vortices in Bose-Einstein Condensates     339
Single-Component Vortices Generated by an Optical Stirring Spoon     339
Scissors Mode Excitation of Superfluidity     340
Suppression and Enhancement of Impurity Scattering in a Bose-Einstein Condensate     342
Hydrodynamic Flow in a Bose-Einstein Condensate Stirred by a Macroscopic Object     344
Observation of Vortex Lattices in Bose-Einstein Condensates     345
Measurement of the Angular Momentum of a Rotating Bose-Einstein Condensate     346
Vortex Precession in Bose-Einstein Condensates: Observations with Filled and Empty Cores     347
Generating Solitons by Phase Engineering of a Bose-Einstein Condensate     348
Trapping and Manipulation of Small Molecules     351
Deflection of Neutral Molecules Using the Nonresonant Dipole Force     352
Observation of Optically Trapped Cold Cesium Molecules     353
Magnetic Trapping of Calcium Monohydride Molecules at mK Temperatures      353
Stimulated Raman Molecule Production in Bose-Einstein Condensates     354
Optical Centrifuge for Molecules     354
Cooling of Molecules by DC Electric Field Gradients     355
Cooling Molecules by Time-Varying Inhomogeneous Fields and Expansion from Nozzles     357
Electrostatic Trapping of Ammonia Molecules     358
Creation of Molecules from Atoms in a Bose-Einstein Condensate     359
Prospects for Trapping and Manipulating Ultracold Molecules     359
Dynamics of Coupled Atomic and Molecular Bose-Einstein Condensates     360
Trapped Fermi Gases     363
Superfluid State of Atomic [superscript 6]Li in a Magnetic Trap     363
Elastic and Inelastic Collisions in [superscript 6]Li     364
Sympathetic Cooling of an Atomic Bose-Fermi Gas Mixture     365
Cooper Pair Formation in Trapped Atomic Fermi Gases     366
Collisional Relaxation in a Fermionic Gas     366
Observation of Fermi Degeneracy in Trapped [superscript 40]K Atomic Gas     367
Stable, Strongly Attractive Two-State Mixtures of [superscript 6]Li Fermions in an Optical Trap     368
Observation of Fermi Pressure in a Doubly Degenerate Gas of Fermions and Bosons     370
Observation of a Strongly Interacting Degenerate Fermi Gas of Atoms      371
Emergence of a Molecular Bose-Einstein Condensate from a Fermi Gas     371
Observation of Resonance Condensation of Fermionic Atom Pairs     372
Evidence for Superfluidity in a Resonantly Interacting Fermi Gas     373
Collective Excitations of a Degenerate Gas at the BEC-BCS Crossover     373
Observation of the Pairing Gap in a Strongly Interacting Fermi Gas     375
Heat Capacity of a Strongly Interacting Fermi Gas     376
Commentary on the Search for Superfluidity in Fermi Gases     377
Vortices and Superfluidity in a Strongly Interacting Fermi Gas     380
Fermion Pairing in a Gas with Unequal Spin Populations     380
Afterword     383
Press Release: The 1997 Nobel Prize in Physics     391
Atoms Floating in Optical Molasses     391
Slowing Down Atoms with Photons     392
Doppler Cooling and Optical Molasses     393
Doppler Limit Broken     393
Recoil Limit also Broken     204
Applications Just Round the Corner     394
Additional background material on the Nobel Prize in Physics 1997     397
Historical Background     398
Optical Molasses     399
Sub-Doppler Cooling     411
Sub-Recoil Cooling      401
Applications     402
Uproar over Nobel Physics Prize     495
References     407
Acknowledgments     433
Biography of Arthur Ashkin     435
List of Reprints     439

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