Contents XIII. Preface XVII. List of Contributors. PartOne ColdAtomsandMolecules 1

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1 V Contents Preface XIII List of Contributors XVII PartOne ColdAtomsandMolecules 1 1 Cooling and Trapping of Atoms 3 Peter van der Straten and Harold Metcalf 1.1 Introduction Phase-Space Density Doppler Cooling Two-Level Atom in a Light Field Optical Bloch Equations Steady State Force on a Two-Level Atom Atoms in Motion Laser Slowing Introduction Slowing of an Atomic Beam Zeeman-Compensated Slowing Measurements and Results Laser Cooling Optical Molasses Low-Intensity Theory for a Two-Level Atom in One Dimension Experiments in Three-Dimensional Optical Molasses Magneto-Optical Traps Introduction Cooling and Compressing Atoms in an MOT Measurements and Results Cooling Below the Doppler Limit Introduction Linear Linear Polarization Gradient Cooling 35 Cold Atoms and Molecules. Edited by Matthias Weidemüller and Claus Zimmermann Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

2 VI Contents Magnetically Induced Laser Cooling Optical Molasses in Three Dimensions Magnetic Trapping Evaporative Cooling Introduction Basic Assumptions The Simple Model Speed and Limits of Evaporative Cooling Experimental Results Beyond Optical Molasses Raman Sideband Cooling Trapping Atoms with a CO 2 Laser Conclusions 57 References 57 Appendix: Cooling Limits 61 2 Quantum Collisions 63 John Weiner 2.1 General Introduction Introduction to Cold Collision Theory Basic Concepts of Scattering Theory Quantum Properties as Energy Approaches Zero Relations Between Phase Shift, Scattering Length, and Bound States Scattering Length in a Square-Well Potential Collisions in a Light Field Inelastic Exoergic Collisions in MOTS Excited-State Trap-Loss Collisions Early Quasistatic Models The Gallagher Pritchard Model Excited-State Trap-Loss Measurements Photoassociation at Ambient and Cold Temperatures Associative and Photoassociative Ionization Photoassociative Ionization in a MOT Photoassociative Ionization in Atom Beams Ground-State Collisions Early Work Bose Einstein Condensation Designer Condensates Quantum-Information Collisions 124 References Frozen Rydberg Gases 147 Thomas Amthor, Markus Reetz-Lamour, and Matthias Weidemüller 3.1 Introduction Experimental Realizations 148

3 Contents VII 3.3 Rydberg Atoms and Their Interactions Quantitative Description of Alkali Rydberg Atoms Alkali Rydberg States Rydberg Wavefunctions Dipole Moments and Stark Shifts Dipolar Interactions Induced Dipoles van der Waals Interaction Resonant Dipoles Förster Resonances Permanent Dipoles Ultralong-Range Forces and Exotic Molecules Ionizing Collisions Avalanches and Ultracold Plasmas Molecules of Rydberg Atoms Molecules of Rydberg and Ground-State Atoms Resonant Energy Transfer Resonance Broadening by Excitation Diffusion Dynamics of Energy Transfer Quantum-Information Processing and Dipole Blockade Fast Quantum Gates with Rydberg Atoms Excitation Suppression Coherent Excitation Conclusion 174 References Cold Molecules 179 Eberhard Tiemann 4.1 Introduction and Motivation From Atoms to Molecules Atomic Basics Atom Pairs and Asymptotic Coupling Molecules Born Oppenheimer Approximation Hund s Coupling Cases Determination of Molecular Potentials Determination of the Asymptotic Potential The LeRoy Bernstein Approach The Accumulated Phase Method Determination of the Full Potential Transition Probabilities and Franck Condon Principle A Spectroscopic Example for Cold Collisions Schemes for Generating Cold Molecules Cooling in a Coolant Environment: Supersonic Expansion, Matrix Isolation, Buffer Gas Cold Molecules from Photoassociation Cold Molecules Through Feshbach Resonances 215

4 VIII Contents Deceleration of Polar Molecules by Inhomogeneous Electric Fields Cold Molecular Ions Current Status and Future Aspects of Cold Molecules 221 Acknowledgment 224 References 225 Part Two Cool Interactions Introduction to Bose Einstein Condensation 233 Kai Bongs and Klaus Sengstock 5.1 Introduction Theory What is BEC? Qualitative Answer Quantum Statistics (Ideal Gas Case) Statistics Finite Systems Statistics Interactions Condensate Wavefunction Interactions The Ideal Gas Interacting Gas The Gross Pitaevskii Equation Thomas Fermi Approximation Bogoliubov Approximation Limits of the Gross Pitaevskii Equation A Few Relevant Scales Length Scales Energy Scales Experimental Creation of BEC Selected Examples of the Physics of BEC Excitations BEC Interference Evidence of Interference Nonlinear Effects Four-Wave Mixing Solitons Superfluidity Phase Fluctuations and Coherence Properties Magnetism in Quantum Gases Quantum Gas Mixtures Creation of Ultracold Molecules from Ultracold Atoms 272 Acknowledgments 275 References 276

5 Contents IX 6 Ultracold Fermi Gases: Properties and Techniques 283 Selim Jochim 6.1 Introduction Ultracold Fermions in a Trap Ideal Fermi Gas Finite Temperature Chemical Potential Preparing an Ultracold Fermi Gas Several Spin States Different Isotopes Different Atoms Very Low Temperatures: Overcome Pauli Blocking Diagnostics: Temperature Measurements Interactions Collisions Weakly Attractive Fermions, Superfluidity Tunable Interactions: Feshbach Resonances Feshbach Resonances Weakly Bound Molecules Enhancing Elastic Collision Rates Strong Interactions Feshbach Molecules and Molecular Condensates Formation of Feshbach Molecules Magnetic Field Ramps Three-Body Recombination Three-Body Recombination of a Spin Mixture of Fermions Chemical Equilibrium Detection of Feshbach Molecules BEC of Molecules A Molecular BEC Out of a Fermi Sea A Molecular BEC by Direct Evaporation of Thermal Fermions BEC BCS Crossover From Fermions to Bosons, a Continuous Crossover! High-T C -Superfluidity in a Fermi Gas of Atoms Conclusion 309 References Bose Einstein Condensates in Optical Lattices 315 Immanuel Bloch, Markus Greiner, and Theodor W. Hänsch 7.1 Introduction Periodic Potentials with Optical Lattices Optical Lattices in Different Dimensions D Lattice Potential D Lattice Potential D Lattice Potential 317

6 X Contents Bloch Bands Wannier Functions Ground State Wavefunction of a BEC in an Optical Lattice Discretization Ground State Superfluid to Mott Insulator Transition Experimental Setup Bose Hubbard Hamiltonian Ground States of the Bose Hubbard Hamiltonian Double-Well Case Multiple-Well Case Superfluid to Mott Insulator Transition Collapse and Revival of the Matter-Wave Field of a Bose Einstein Condensate 330 References 333 Part Three Bonus Chapter Tutorial on Experimental Physics of Ultracold Gases 337 Allard Mosk 8.1 Introduction Peace of Mind and Safety Where to Find More Information Ultrahigh Vacuum Residual-Gas-Induced Decay Time Vacuum Science is Residual Gas Science Common Residual Gases Patience and Cleanliness Vacuum Seals Optical Access in Vacuum Systems Glass Cells Viewports Leaks Pumping Valves Further Reading Trapping of Neutral Particles Magnetostatic Trapping Scaling Cooling of Coils Switching of Magnetic Fields Cryogenic Techniques Superconducting Coils Principles of Cryogenic Cooling Dilution Refrigerators 354

7 Contents XI Further Reading Dealing with Noise Know your Noise The Spectrum Analyzer Lowest Frequencies: Drifts Low-Frequency Vibrations Mechanical Vibrations Electromagnetic Interference Good and Clean Contacts Line Hum EMI and Computers Photodetection Vacuum Photodiodes and Photomultiplier Tubes Semiconductor Photodiodes and Preamplifiers Imaging Detectors Electron Multiplying CCD Control Loops Applications of Feedback Loops Common Problems with Servo Loops Transfer Functions Nonlinearity and Unlocking Servo Nonlinearity and Limits PID Controllers Measurement of the Transfer Functions 374 Acknowledgments 375 Epilogue 375 References 375 Index 379

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