Molecules in Electromagnetic Fields

From Ultracold Physics to Controlled Chemistry
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Roman V. Krems
775 g
237x159x25 mm

List of Figures xiiiList of Tables xxvPreface xxviiAcknowledgments xxxi1 Introduction to Rotational, Fine, and Hyperfine Structure of Molecular Radicals 11.1 Why Molecules are Complex 11.2 Separation of Scales 31.2.1 Electronic Energy 51.2.2 Vibrational Energy 101.2.3 Rotational and Fine Structure 141.3 Rotation of a Molecule 171.4 Hund's Cases 211.4.1 Hund's Coupling Case (a) 211.4.2 Hund's Coupling Case (b) 221.4.3 Hund's Coupling Case (c) 231.5 Parity of Molecular States 231.6 General Notation for Molecular States 271.7 Hyperfine Structure of Molecules 281.7.1 Magnetic Interactions with Nuclei 281.7.2 Fermi Contact Interaction 291.7.3 Long-Range Magnetic Dipole Interaction 301.7.4 Electric Quadrupole Hyperfine Interaction 31Exercises 312 DCStarkEffect 352.1 Electric Field Perturbations 352.2 Electric Dipole Moment 372.3 Linear and Quadratic Stark Shifts 402.4 Stark Shifts of Rotational Levels 422.4.1 Molecules in a 1Sigma Electronic State 422.4.2 Molecules in a 2Sigma Electronic State 462.4.3 Molecules in a 3Sigma Electronic State 482.4.4 Molecules in a 1Pi Electronic State - Lambda-Doubling 512.4.5 Molecules in a 2Pi Electronic State 54Exercises 563 Zeeman Effect 593.1 The Electron Spin 593.1.1 The Dirac Equation 603.2 Zeeman Energy of a Moving Electron 633.3 Magnetic Dipole Moment 643.4 Zeeman Operator in the Molecule-Fixed Frame 663.5 Zeeman Shifts of Rotational Levels 673.5.1 Molecules in a 2Sigma State 673.5.2 Molecules in a 2Pi Electronic State 713.5.3 Isolated Sigma States 743.6 Nuclear Zeeman Effect 753.6.1 Zeeman Effect in a 1Sigma Molecule 76Exercises 784 ACStarkEffect 814.1 Periodic Hamiltonians 824.2 The Floquet Theory 844.2.1 Floquet Matrix 884.2.2 Time Evolution Operator 894.2.3 Brief Summary of Floquet Theory Results 904.3 Two-Mode Floquet Theory 924.4 RotatingWave Approximation 944.5 Dynamic Dipole Polarizability 964.5.1 Polarizability Tensor 974.5.2 Dipole Polarizability of a DiatomicMolecule 994.5.3 Rotational vs Vibrational vs Electronic Polarizability 1014.6 Molecules in an Off-Resonant Laser Field 1044.7 Molecules in a Microwave Field 1074.8 Molecules in a Quantized Field 1094.8.1 Field Quantization 1094.8.2 Interaction of Molecules with Quantized Field 1164.8.3 Quantized Field vs Floquet Theory 117Exercises 1185 Molecular Rotations Under Control 1215.1 Orientation and Alignment 1225.1.1 OrientingMolecular Axis in Laboratory Frame 1235.1.2 Quantum Pendulum 1265.1.3 Pendular States of Molecules 1295.1.4 Alignment of Molecules by Intense Laser Fields 1315.2 Molecular Centrifuge 1365.3 OrientingMolecules Matters -Which Side Chemistry 1405.4 Conclusion 142Exercises 1426 External Field Traps 1456.1 Deflection and Focusing of Molecular Beams 1466.2 Electric (and Magnetic) Slowing of Molecular Beams 1516.3 Earnshaw'sTheorem 1556.4 Electric Traps 1586.5 Magnetic Traps 1626.6 Optical Dipole Trap 1656.7 Microwave Trap 1676.8 Optical Lattices 1686.9 Some Applications of External Field Traps 171Exercises 1737 Molecules in Superimposed Fields 1757.1 Effects of Combined DC Electric andMagnetic Fields 1757.1.1 Linear Stark Effect at Low Fields 1757.1.2 Imaging of Radio-Frequency Fields 1787.2 Effects of Combined DC and AC Electric Fields 1817.2.1 Enhancement of Orientation by Laser Fields 1817.2.2 Tug ofWar Between DC and Microwave Fields 1828 Molecular Collisions in External Fields 1878.1 Coupled-ChannelTheory of Molecular Collisions 1888.1.1 A Very General Formulation 1888.1.2 Boundary Conditions 1918.1.3 Scattering Amplitude 1948.1.4 Scattering Cross Section 1978.1.5 Scattering of Identical Molecules 2008.1.6 Numerical Integration of Coupled-Channel Equations 2048.2 Interactions with External Fields 2088.2.1 Coupled-Channel Equations in Arbitrary Basis 2088.2.2 External Field Couplings 2098.3 The Arthurs-Dalgarno Representation 2118.4 Scattering Rates 2149 Matrix Elements of Collision Hamiltonians 2179.1 Wigner-EckartTheorem 2189.2 Spherical Tensor Contraction 2209.3 Collisions in a Magnetic Field 2219.3.1 Collisions of 1S-Atoms with 2Sigma-Molecules 2219.3.2 Collisions of 1S-Atoms with 3Sigma-Molecules 2259.4 Collisions in an Electric Field 2299.4.1 Collisions of 2Pi Molecules with 1S Atoms 2299.5 Atom-Molecule Collisions in a Microwave Field 2329.6 Total Angular Momentum Representation for Collisions in Fields 23410 Field-Induced Scattering Resonances 23910.1 Feshbach vs Shape Resonances 23910.2 The Green's Operator in Scattering Theory 24210.3 Feshbach Projection Operators 24310.4 Resonant Scattering 24610.5 Calculation of Resonance Locations andWidths 24910.5.1 Single Open Channel 24910.5.2 Multiple Open Channels 24910.6 Locating Field-Induced Resonances 25211 Field Control of Molecular Collisions 25711.1 Why to Control Molecular Collisions 25711.2 Molecular Collisions are Difficult to Control 25911.3 General Mechanisms for External Field Control 26111.4 Resonant Scattering 26111.5 Zeeman and Stark Relaxation at Zero Collision Energy 26411.6 Effect of Parity Breaking in Combined Fields 26911.7 Differential Scattering in Electromagnetic Fields 27111.8 Collisions in Restricted Geometries 27211.8.1 Threshold Scattering of Molecules in Two Dimensions 27611.8.2 Collisions in a Quasi-Two-Dimensional Geometry 28012 Ultracold Controlled Chemistry 28312.1 Can Chemistry Happen at Zero Kelvin? 28412.2 Ultracold Stereodynamics 28712.3 Molecular Beams Under Control 28912.4 Reactions in Magnetic Traps 28912.5 Ultracold Chemistry - The Why and What's Next? 29112.5.1 Practical Importance of Ultracold Chemistry? 29112.5.2 Fundamental Importance of Ultracold Controlled Chemistry 29312.5.3 A Brief Outlook 294A Unit Conversion Factors 297B Addition of AngularMomenta 299B.1 The Clebsch-Gordan Coefficients 301B.2 TheWigner 3j-Symbols 303B.3 The Raising and Lowering Operators 304C Direction Cosine Matrix 307D Wigner D-Functions 309D.1 Matrix elements involving D-functions 311E Spherical tensors 315E.1 Scalar and Vector Products of Vectors in Spherical Basis 317E.2 Scalar and Tensor Products of Spherical Tensors 318References 321Index 347
A tutorial for calculating the response of molecules to electric and magnetic fields with examples from research in ultracold physics, controlled chemistry, and molecular collisions in fieldsMolecules in Electromagnetic Fields is intended to serve as a tutorial for students beginning research, theoretical or experimental, in an area related to molecular physics. The author--a noted expert in the field--offers a systematic discussion of the effects of static and dynamic electric and magnetic fields on the rotational, fine, and hyperfine structure of molecules. The book illustrates how the concepts developed in ultracold physics research have led to what may be the beginning of controlled chemistry in the fully quantum regime. Offering a glimpse of the current state of the art research, this book suggests future research avenues for ultracold chemistry.The text describes theories needed to understand recent exciting developments in the research on trapping molecules, guiding molecular beams, laser control of molecular rotations, and external field control of microscopic intermolecular interactions. In addition, the author presents the description of scattering theory for molecules in electromagnetic fields and offers practical advice for students working on various aspects of molecular interactions.This important text:* Offers information on theeffects of electromagnetic fields on the structure of molecular energy levels
* Includes thorough descriptions of the most useful theories for ultracold molecule researchers
* Presents a wealth of illustrative examples from recent experimental and theoretical work
* Contains helpful exercises that help to reinforce concepts presented throughout textWritten for senior undergraduate and graduate students, professors, researchers, physicists, physical chemists, and chemical physicists, Molecules in Electromagnetic Fields is an interdisciplinary text describing theories and examples from the core of contemporary molecular physics.