Laser Cooling and Trapping

by Metcalf, Harold J.; Van Der Straten, Peter

• ISBN13: 9780387987286
• ISBN10: 0387987282
• Format: Paperback
• Copyright: 1999-09-01
• Publisher: Springer Verlag

Summary

Laser cooling allows one to slow atoms to roughly the speed of a mosquito and to control their motions with unprecedented precision. This elegant technique, whereby atoms, molecules, and even microscopic beads of glass, can be trapped in small regions of free space by beams of light and subsequently moved at will using other beams, has revolutionized many areas of physics. In particular, it provides a useful research tool for the study of individual atoms, for investigating the details of chemical reactions, and even for the study of atomic motion in the quantum domain.This text begins with a review of the relevant aspects of quantum mechanics; it then turns to the electromagnetic interactions involved in slowing and trapping atoms, in both magnetic and optical traps. The concluding chapters discuss a broad range of applications, including atomic clocks, studies of ultra-cold collision processes, diffraction and interference of atomic beams, optical lattices, and Bose-Einstein condensation. The book is intended for advanced undergraduates and beginning graduate students who have some basic knowledge of optics and quantum mechanics. An extensive bibliography provides access to the current research literature.

Table of Contents

Foreword	vii
Preface	ix
I Introduction	1	(70)
Review of Quantum Mechanics	3	(14)
Time-Dependent Perturbation Theory	3	(1)
The Rabi Two-Level Problem	4	(10)
Light Shifts	7	(2)
The Dressed Atom Picture	9	(2)
The Bloch Vector	11	(1)
Adiabatic Rapid Passage	12	(2)
Excited-State Decay and its Effects	14	(3)
The Density Matrix	17	(12)
Basic Concepts	17	(3)
Spontaneous Emission	20	(3)
The Optical Bloch Equations	23	(1)
Power Broadening and Saturation	24	(5)
Force on Two-Level Atoms	29	(10)
Laser Light Pressure	29	(2)
A Two-Level Atom at Rest	31	(3)
Atoms in Motion	34	(5)
Traveling Wave	34	(1)
Standing Wave	35	(4)
Multilevel Atoms	39	(18)
Alkali-Metal Atoms	39	(4)
Metastable Noble Gas Atoms	43	(2)
Polarization and Interference	45	(2)
Angular Momentum and Selection Rules	47	(3)
Optical Transitions in Multilevel Atoms	50	(7)
Introduction	50	(1)
Radial Part	51	(1)
Angular Part of the Dipole Matrix Element	52	(1)
Fine and Hyperfine Interactions	53	(4)
General Properties Concerning Laser Cooling	57	(14)
Temperature and Thermodynamics in Laser cooling	58	(3)
Kinetic Theory and the Maxwell-Boltzmann Distribution	61	(2)
Random Walks	63	(3)
The Fokker-Planck Equation and Cooling Limits	66	(2)
Phase Space and Liouville's Theorem	68	(3)
II Cooling & Trapping	71	(106)
Deceleration of an Atomic Beam	73	(14)
Introduction	73	(1)
Techniques of Beam Deceleration	74	(6)
Laser Frequency Sweep	76	(1)
Varying the Atomic Frequency: Magnetic Field Case	77	(1)
Varying the Atomic Frequency: Electric Field Case	77	(1)
Varying the Doppler Shift: Diffuse Light	78	(1)
Broadband Light	79	(1)
Rydberg Atoms	79	(1)
Measurements and Results	80	(3)
Further Considerations	83	(4)
Cooling During Deceleration	83	(1)
Non-Uniformity of Deceleration	84	(1)
Transverse Motion During Deceleration	85	(1)
Optical Pumping During Deceleration	86	(1)
Optical Molasses	87	(12)
Introduction	87	(1)
Low-Intensity Theory for a Two-Level Atom in One Dimension	88	(2)
Atomic Beam Collimation	90	(5)
Low-Intensity Case	90	(2)
Experiments in One and Two Dimensions	92	(3)
Experiments in Three-Dimensional Optical Molasses	95	(4)
Cooling Below the Doppler Limit	99	(24)
Introduction	99	(1)
Linear ⊥ Linear Polarization Gradient Cooling	100	(4)
Light Shifts	101	(1)
Origin of the Damping Force	102	(2)
Magnetically Induced Laser Cooling	104	(2)
σ + -σ- Polarization Gradient Cooling	106	(1)
Theory of Sub-Doppler Laser Cooling	107	(4)
Optical Molasses in Three Dimensions	111	(2)
The Limits of Laser Cooling	113	(3)
The Recoil Limit	113	(1)
Cooling Below the Recoil Limit	114	(2)
Sisyphus Cooling	116	(2)
Cooling in a Strong Magnetic Field	118	(2)
VSR and Polarization Gradients	120	(3)
The Dipole Force	123	(14)
Introduction	123	(1)
Evanescent Waves	124	(2)
Dipole Force in a Standing Wave: Optical Molasses at High Intensity	126	(2)
Atomic Motion Controlled by Two Frequencies	128	(9)
Introduction	128	(1)
Rectification of the Dipole Force	129	(2)
The Bichromatic Force	131	(4)
Beam Collimation and Slowing	135	(2)
Magnetic Trapping of Neutral Atoms	137	(12)
Introduction	137	(1)
Magnetic Traps	138	(2)
Classical Motion of Atoms in a Magnetic Quadrupole Trap	140	(5)
Simple Picture of Classical Motion in a Trap	140	(1)
Numerical Calculations of the Orbits	141	(2)
Early Experiments with Classical Motion	143	(2)
Quantum Motion in a Trap	145	(4)
Heuristic Calculations of the Quantum Motion of Magnetically Trapped Atoms	146	(1)
Three-Dimensional Quantum Calculations	146	(1)
Experiments in the Quantum Domain	147	(2)
Optical Traps for Neutral Atoms	149	(16)
Introduction	149	(1)
Dipole Force Optical Traps	150	(6)
Single-Beam Optical Traps for Two-Level Atoms	150	(2)
Hybrid Dipole Radiative Trap	152	(1)
Blue Detuned Optical Traps	153	(2)
Microscopic Optical Traps	155	(1)
Radiation Pressure Traps	156	(1)
Magneto-Optical Traps	156	(9)
Introduction	156	(2)
Cooling and Compressing Atoms in a MOT	158	(1)
Capturing Atoms in a MOT	159	(3)
Variations on the MOT Technique	162	(3)
Evaporative Cooling	165	(12)
Introduction	165	(1)
Basic Assumptions	166	(1)
The Simple Model	167	(4)
Speed and Limits of Evaporative Cooling	171	(4)
Boltzmann Equation	171	(1)
Speed of Evaporation	171	(3)
Limiting Temperature	174	(1)
Experimental Results	175	(2)
III Applications	177	(86)
Newtonian Atom Optics and its Applications	179	(20)
Introduction	179	(1)
Atom Mirrors	180	(1)
Atom Lenses	181	(4)
Magnetic Lenses	181	(3)
Optical Atom Lenses	184	(1)
Atomic Fountain	185	(1)
Application to Atomic Beam Brightening	186	(4)
Introduction	186	(2)
Beam-Brightening Experiments	188	(1)
High-Brightness Metastable Beams	189	(1)
Application to Nanofabrication	190	(2)
Applications to Atomic Clocks	192	(2)
Introduction	192	(1)
Atomic Fountain Clocks	193	(1)
Application to Ion Traps	194	(1)
Application to Non-Linear Optics	195	(4)
Ultra-cold Collisions	199	(20)
Introduction	199	(1)
Potential Scattering	200	(4)
Ground-state Collisions	204	(3)
Excited-state Collisions	207	(11)
Trap Loss Collisions	207	(2)
Optical Collisions	209	(4)
Photo-Associative Spectroscopy	213	(5)
Collisions Involving Rydberg States	218	(1)
deBroglie Wave Optics	219	(12)
Introduction	219	(1)
Gratings	220	(3)
Beam Splitters	223	(1)
Sources	224	(1)
Mirrors	225	(1)
Atom Polarizers	226	(1)
Application to Atom Interferometry	227	(4)
Optical Lattices	231	(10)
Introduction	231	(1)
Laser Arrangements for Optical Lattices	232	(3)
Quantum States of Motion	235	(3)
Band Structure in Optical Lattices	238	(1)
Quantum View of Laser Cooling	239	(2)
Bose-Einstein Condensation	241	(10)
Introduction	241	(2)
The Pathway to BEC	243	(1)
Experiments	244	(7)
Observation of BEC	244	(2)
First-Order Coherence Experiments in BEC	246	(2)
Higher-Order Coherence Effects in BEC	248	(1)
Other Experiments	249	(2)
Dark States	251	(12)
Introduction	251	(1)
VSCPT in Two-Level Atoms	252	(2)
VSCPT in Real Atoms	254	(4)
Circularly Polarized Light	255	(2)
Linearly Polarized Light	257	(1)
VSCPT at Momenta Higher Than ±hk	258	(1)
VSCPT and Bragg Reflection	259	(2)
Entangled States	261	(2)
IV Appendices	263	(28)
A Notation and Definitions	265	(4)
B Review Articles and Books on Laser Cooling	269	(4)
C Characteristic Data	273	(6)
D Transition Strengths	279	(12)
References	291	(26)
Index	317