An Introduction to Cold and Ultracold Chemistry : Atoms, Molecules, Ions and Rydbergs

"This book provides advanced undergraduate and graduate students with an overview of the fundamentals of cold and ultracold chemistry. Beginning with definitions of what cold and ultracold temperatures mean in chemistry, the book then takes the student through the essentials of scattering theory (classical and quantum mechanical), light-matter interaction, reaction dynamics and Rydberg physics. The author aims to show the reader the richness of the topic while motivating students to understand the fundamentals of these intriguing reactions and underlying connecting relationships. Including material which was previously only found in specialized review articles, this book provides students working in the fields of ultracold gases, chemical physics and physical chemistry with the tools they need to immerse themselves in the realm of cold and ultracold chemistry. This book opens up the exciting chemical laws which govern chemistry at low temperatures to the next generation of researchers"--Publisher's website Preface 6 Contents 8 List of Figures 13 List of Tables 17 1 The Realm of Cold and Ultracold 18 1.1 Why Ultracold Temperatures? 18 1.2 Cold and Ultracold Chemistry 20 1.2.1 The Standard Approach 20 1.2.2 A More Physical Approach 20 1.3 Ultracold Physics and Fundamental Physics 22 References 23 2 Quantum Scattering Theory 25 2.1 Collisions 25 2.1.1 When Does a Collision Occur? 25 2.1.2 Experimental Approach: The Mean Free Path 26 2.1.3 Quantum Mechanical Cross Section 27 2.1.4 Classical Cross Section 28 2.1.4.1 Hard-Sphere Collisions 29 2.2 Elastic Cross Section 30 2.2.1 Definition 30 2.2.2 Wigner Threshold Law for the Elastic Cross Section 33 2.2.3 Collision Between Two Identical Particles 35 2.3 The Scattering Length 37 2.4 Inelastic Cross Section 40 2.4.1 Unitarity of the S-Matrix 42 2.4.2 Wigner Threshold Law for Inelastic Scattering 42 2.5 Scattering Resonances 43 2.5.1 Shape Resonances or Orbiting 44 2.5.2 Fano–Feshbach Resonances 45 2.5.3 The Glory Effect 47 References 49 3 Ultracold Gases 52 3.1 Bose–Einstein Condensation 52 3.1.1 The Ideal Bose Gas 52 3.2 Interacting Bose Gas 56 3.2.1 Gross–Pitaevskii Equation 57 3.2.2 Thomas–Fermi Approximation 59 3.2.3 Healing Length 60 3.3 Ultracold Dipolar Gases 61 3.3.1 Dipole–Dipole Interactions 62 3.3.2 Theory of the Dipolar Bose–Einstein Condensation 63 3.4 Spinor Bose–Einstein Condensates 65 References 66 4 Cooling and Trapping of Molecules 69 4.1 Stark Deceleration 70 4.2 Optical Stark Deceleration 72 4.3 Zeeman Decelerator 75 4.4 Laser Cooling 77 4.5 Buffer Gas Cooling 79 4.5.1 Loading of the Target Molecules 81 4.5.2 Thermalization 82 4.5.3 Diffusion of the Cold Target Molecules 83 4.6 Optical Trapping: Dipole Traps 84 4.7 Magnetic Trapping 86 4.8 Evaporative Cooling 87 4.9 Assembly of Molecules at Ultracold Temperatures 89 4.9.1 Photoassociation 89 4.9.2 Magnetoassociation 90 References 91 5 Ultracold Molecular Collisions 97 5.1 Introduction 97 5.2 Scattering Molecular Theory: Rigid Rotor–Rigid RotorScattering 97 5.2.1 Distinguishable Molecule–Molecule Scattering 97 5.2.2 Identical Molecule–Molecule Scattering 104 5.2.3 The Role of Indistinguishability in Molecule–Molecule Collisions 107 5.3 Molecular Collisions in an External Field 107 5.3.1 Distinguishable Molecules 108 5.3.2 Indistinguishable Molecules 110 5.4 Ultracold Collisions of Oxygen Molecules in the Presence of an External Magnetic Field 112 5.4.1 Zeeman Hamiltonian for 3 Molecules 112 5.4.2 Spin Relaxation and Zeeman Suppression 115 5.4.3 Molecular Scattering Theory in Action 118 5.4.3.1 Labeling of the States and Intermolecular Potentials 121 5.4.4 Fano–Feshbach Resonances in Ultracold Molecule–Molecule Collisions 123 5.4.5 Cross Section as a Function of the Collision Energy: The Wigner Threshold Laws 124 5.4.6 Do Short-Range Interactions Play a Role in Ultracold Collisions? 126 5.5 Computational Techniques 126 5.5.1 Single-Channel Scattering 127 5.5.2 Multi-channel Scattering: Elastic and InelasticChannels 130 References 131 6 Three-Body Collisions at Ultracold Temperatures: An Effective Field Theory Approach 133 6.1 The Renormalization Group 133 6.2 Effective Field Theory Approach for Low-Energy Two-Body Collisions 136 6.3 Effective Field Theory for Three-Body Bosonic Collisions Involving Short-Ranged Interactions 140 6.4 Universality on the Three Boson Problem: Efimov States from a Renormalization Group Approach 145 6.5 Concluding Remarks 147 References 148 7 Ultracold Rydberg Atoms and Ultralong-Range Rydberg Molecules 150 7.1 Rydberg Atoms 150 7.1.1 Sommerfeld Orbits 152 7.1.2 Properties of Rydberg Atoms 155 7.2 Rydberg Blockade 156 7.3 Ultralong-Range Rydberg Molecules 157 7.4 Potential Energy Curves for Ultralong-Range Rydberg Molecules 159 7.4.1 Low-l Ultralong-Range Rydberg Molecules 161 7.4.2 Trilobite Molecules 162 7.4.3 Butterfly Molecules 164 References 165 8 Rydberg-Neutral Ultracold Chemical Reactions 167 8.1 Rydberg-Neutral Elastic Collisions 167 8.2 Rydberg-Neutral Inelastic and Reactive Collisions 169 8.2.1 L-Mixing Collisions 171 8.2.2 Chemi-Ionization 175 8.2.3 Collision Time for Chemi-Ionization and L-Mixing Collisions: a molecular dynamics approach 178 8.2.4 Some Open Questions 181 References 181 9 Hybrid Atom–Ion Systems 183 9.1 What Is a Hybrid System? 183 9.2 Ion Traps 185 9.2.1 Penning Trap 185 9.2.2 Paul Trap 185 9.3 Dynamics of Ions in a Paul Trap 187 9.3.1 Is It Possible to Define Temperature for Ions in a Trap? 190 9.3.2 Coulomb Crystals 191 9.4 Atom–Ion Collisions 192 9.4.1 Atom–Ion Interactions 192 9.4.2 Langevin Rate 193 9.4.3 Elastic Atom–Ion Collisions 195 9.4.4 Radiative Charge Transfer and Radiative Association 198 References 202 10 Few-Body Processes Involving Ions and Neutrals at Cold Temperatures 205 10.1 Do We Really Need a Full Quantum Mechanical Treatment at Cold Temperatures? 205 10.2 Hyperspherical Coordinates 207 10.3 Classical Scattering Theory for Few-Body Problems 208 10.4 Classical Trajectory Calculations in Hyperspherical Coordinates for Three-Body Collisions 209 10.5 Classical Three-Body Recombination for Ion–Neutral–Neutral Systems at Cold Temperatures 214 10.6 Universality in Ion–Atom–Atom Three-Body Recombination Reactions 217 10.6.1 Threshold Law for Cold Ion–Atom–Atom Collisions 219 10.6.2 Threshold for Cold Ion–Atom–Atom Collisions: From the Cold to the Thermal Regime 220 10.7 Shadow Scattering: A Universal Feature of Few-BodyCollisions 222 References 225 11 Cold Chemical Reactions Between Molecular Ions and Neutral Atoms 227 11.1 Introduction 227 11.2 Quasi-Classical Trajectory Method 227 11.2.1 Initial Conditions 230 11.2.2 Reaction Products 231 11.2.3 Binning Methods 232 11.2.4 Cross Section 233 11.3 Vibrational Quenching of Molecular Ions by Ultracold Atoms 234 11.4 A Cold Highly Vibrational Excited Molecular Ion Immersed in an Ultracold Gas: QCT Method in Action 237 References 243 12 Ultracold Physics and the Quest of New Physics 246 12.1 The Fundamental Laws of Physics 246 12.2 Time Variation of Fundamental Constants 248 12.3 Ultracold Molecules and Their Role in the Existence of Extra Dimensions 250 12.3.1 The Arkani-Hamed, Dimopoulos, and Dvali Model 251 12.3.2 High-Precision Spectroscopy in Cold Molecules 252 12.4 Ultracold Molecules and the Quest of Physics Beyond the Standard Model 255 12.4.1 The Fifth Force 255 References 257 A Quasistatic Theory for Line Broadening 258 References 259 B Fluid Dynamics of Supersonic Expansions 260 B.1 Brief Introduction to Fluid Dynamics 260 B.1.1 Continuity Equation 261 B.1.2 Conservation of Linear Momentum or Newton's Second Law for Fluids 262 B.1.3 Energy Conservation 263 B.2 Gas Dynamics 263 B.2.1 The Ideal Gas 263 B.2.2 Isentropic Processes 264 B.2.3 Speed of Sound and Mach Number 265 B.2.4 Single-Dimensional Flow Equations for Compressible Fluids 265 References 267 C Computational Techniques for Quantum Mechanical Scattering 268 C.1 Coupled-Channel Equations: Propagators and Asymptotic Conditions 268 C.1.1 Log-Derivative Propagator of Manolopoulos 270 C.1.2 Airy Propagator 273 C.1.3 Hybrid Log-Derivative–Airy Propagator 274 References 275 Index 276 Front Matter ....Pages i-xix The Realm of Cold and Ultracold (Jesús Pérez Ríos)....Pages 1-7 Quantum Scattering Theory (Jesús Pérez Ríos)....Pages 9-35 Ultracold Gases (Jesús Pérez Ríos)....Pages 37-53 Cooling and Trapping of Molecules (Jesús Pérez Ríos)....Pages 55-82 Ultracold Molecular Collisions (Jesús Pérez Ríos)....Pages 83-118 Three-Body Collisions at Ultracold Temperatures: An Effective Field Theory Approach (Jesús Pérez Ríos)....Pages 119-135 Ultracold Rydberg Atoms and Ultralong-Range Rydberg Molecules (Jesús Pérez Ríos)....Pages 137-153 Rydberg-Neutral Ultracold Chemical Reactions (Jesús Pérez Ríos)....Pages 155-170 Hybrid Atom–Ion Systems (Jesús Pérez Ríos)....Pages 171-192 Few-Body Processes Involving Ions and Neutrals at Cold Temperatures (Jesús Pérez Ríos)....Pages 193-214 Cold Chemical Reactions Between Molecular Ions and Neutral Atoms (Jesús Pérez Ríos)....Pages 215-233 Ultracold Physics and the Quest of New Physics (Jesús Pérez Ríos)....Pages 235-246 Back Matter ....Pages 247-267 "This book provides advanced undergraduate and graduate students with an overview of the fundamentals of cold and ultracold chemistry. Beginning with definitions of what cold and ultracold temperatures mean in chemistry, the book then takes the student through the essentials of scattering theory (classical and quantum mechanical), light-matter interaction, reaction dynamics and Rydberg physics. The author aims to show the reader the richness of the topic while motivating students to understand the fundamentals of these intriguing reactions and underlying connecting relationships. Including material which was previously only found in specialized review articles, this book provides students working in the fields of ultracold gases, chemical physics and physical chemistry with the tools they need to immerse themselves in the realm of cold and ultracold chemistry. This book opens up the exciting chemical laws which govern chemistry at low temperatures to the next generation of researchers."-- Prové de l'editor