Molecules in Electromagnetic Fields

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 fields

Molecules 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 text

Written 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.

Auteur

ROMAN V. KREMS is a professor of theoretical chemistry at the University of British Columbia in Vancouver, Canada. His current research focuses on understanding the effects of electromagnetic fields on dynamics of few- and many-body molecular systems, the interaction properties of molecules at extremely low temperatures, and applications of machine learning to molecular physics.

Contenu
List of Figures xiii

List of Tables xxv

Preface xxvii

Acknowledgments xxxi

1 Introduction to Rotational, Fine, and Hyperfine Structure of Molecular Radicals 1

1.1 Why Molecules are Complex 1

1.2 Separation of Scales 3

1.2.1 Electronic Energy 5

1.2.2 Vibrational Energy 10

1.2.3 Rotational and Fine Structure 14

1.3 Rotation of a Molecule 17

1.4 Hund's Cases 21

1.4.1 Hund's Coupling Case (a) 21

1.4.2 Hund's Coupling Case (b) 22

1.4.3 Hund's Coupling Case (c) 23

1.5 Parity of Molecular States 23

1.6 General Notation for Molecular States 27

1.7 Hyperfine Structure of Molecules 28

1.7.1 Magnetic Interactions with Nuclei 28

1.7.2 Fermi Contact Interaction 29

1.7.3 Long-Range Magnetic Dipole Interaction 30

1.7.4 Electric Quadrupole Hyperfine Interaction 31

Exercises 31

2 DCStarkEffect 35

2.1 Electric Field Perturbations 35

2.2 Electric Dipole Moment 37

2.3 Linear and Quadratic Stark Shifts 40

2.4 Stark Shifts of Rotational Levels 42

2.4.1 Molecules in a 1 Electronic State 42

2.4.2 Molecules in a 2 Electronic State 46

2.4.3 Molecules in a 3 Electronic State 48

2.4.4 Molecules in a 1Π Electronic State -Doubling 51

2.4.5 Molecules in a 2Π Electronic State 54

Exercises 56

3 Zeeman Effect 59

3.1 The Electron Spin 59

3.1.1 The Dirac Equation 60

3.2 Zeeman Energy of a Moving Electron 63

3.3 Magnetic Dipole Moment 64

3.4 Zeeman Operator in the Molecule-Fixed Frame 66

3.5 Zeeman Shifts of Rotational Levels 67

3.5.1 Molecules in a 2 State 67

3.5.2 Molecules in a 2Π Electronic State 71

3.5.3 Isolated States 74

3.6 Nuclear Zeeman Effect 75

3.6.1 Zeeman Effect in a 1 Molecule 76

Exercises 78

4 ACStarkEffect 81

4.1 Periodic Hamiltonians 82

4.2 The Floquet Theory 84

4.2.1 Floquet Matrix 88

4.2.2 Time Evolution Operator 89

4.2.3 Brief Summary of Floquet Theory Results 90

4.3 Two-Mode Floquet Theory 92

4.4 RotatingWave Approximation 94

4.5 Dynamic Dipole Polarizability 96

4.5.1 Polarizability Tensor 97

4.5.2 Dipole Polarizability of a DiatomicMolecule 99

4.5.3 Rotational vs Vibrational vs Electronic Polarizability 101

4.6 Molecules in an Off-Resonant Laser Field 104

4.7 Molecules in a Microwave Field 107

4.8 Molecules in a Quantized Field 109

4.8.1 Field Quantization 109

4.8.2 Interaction of Molecules with Quantized Field 116

4.8.3 Quantized Field vs Floquet Theory 117

Exercises 118

5 Molecular Rotations Under Control 121

5.1 Orientation and Alignment 122

5.1.1 OrientingMolecular Axis in Laboratory Frame 123

5.1.2 Quantum Pendulum 126

5.1.3 Pendular States of Molecules 129

5.1.4 Alignment of Molecules by Intense Laser Fields 131

5.2 Molecular Centrifuge 136

5.3 OrientingMolecules Matters Which Side Chemistry 140

5.4 Conclusion 142

Exercises 142

6 External Field Traps 145

6.1 Deflection and Focusing of Molecular Beams 146

6.2 Electric (and Magnetic) Slowing of Molecular Beams 151

6.3 Earnshaw'sTheorem 155

6.4 Electric Traps 158

6.5 Magnetic Traps 162

6.6 Optical Dipole Trap 165

6.7 Microwave Trap 167

6.8 Optical Lattices 168

6.9 Some Applications of External Field Traps 171

Exercises 173

7 Molecules in Superimposed Fields 175

7.1 Effects of Combined DC Electric andMagnetic Fields 175 7.1.1 Linear Star...