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Part Ⅰ Prerequisites 3

1 A Short Introduction to Laser Physics 3

1.1 The Einstein Coefficients 3

1.2 Fundamentals of the Laser 6

1.2.1 Elementary Laser Theory 6

1.2.2 Realization of the Laser Principle 8

1.3 Pulsed Lasers 10

1.3.1 Frequency Comb 10

1.3.2 Carrier Envelope Phase 12

1.3.3 Husimi Representation of Laser Pulses 14

1.A Some Gaussian Integrals 15

References 16

2 Time-Dependent Quantum Theory 17

2.1 The Time-Dependent Schr？dinger Equation 17

2.1.1 Introduction 18

2.1.2 Time-Evolution Operator 20

2.1.3 Spectral Information 23

2.1.4 Analytical Solutions for Wavepackets 25

2.2 Analytical Approaches 30

2.2.1 Feynman's Path Integral 30

2.2.2 Semiclassical Approximation 35

2.2.3 Time-Dependent Perturbation Theory 38

2.2.4 Magnus Expansion 40

2.2.5 Time-Dependent Hartree Method 42

2.2.6 Quantum-Classical Methods 43

2.2.7 Floquet Theory 45

2.3 Numerical Methods 48

2.3.1 Orthogonal Basis Expansion 48

2.3.2 Split-Operator FFT Method 52

2.3.3 Alternative Methods of Time-Evolution 56

2.3.4 Semiclassical Initial Value Representations 58

2.A The Royal Road to the Path Integral 65

2.B Variational Calculus 67

2.C Stability Matrix 69

2.D From the HK- to the VVG-Propagator 71

References 72

Part Ⅱ Applications 77

3 Field Matter. Coupling and Two-Level Systems 77

3.1 Light Matter Interaction 77

3.1.1 Minimal Coupling 77

3.1.2 Length Gauge 79

3.1.3 Kramers-Henneberger Transformation 81

3.1.4 Volkov Wavepacket 82

3.2 Analytically Solvable Two-Level Problems 83

3.2.1 Dipole Matrix Element 83

3.2.2 Rabi Oscillations Induced by a Constant Perturbation 84

3.2.3 Time-Dependent Perturbations 86

3.2.4 Exactly Solvable Time-Dependent Cases 89

3.A Generalized Parity Transformation 91

3.B Two-Level System in an Incoherent Field 93

References 95

4 Single Electron Atoms in Strong Laser Fields 97

4.1 The Hydrogen Atom 97

4.1.1 Hydrogen in Three Dimensions 98

4.1.2 The One-Dimensional Coulomb Problem 99

4.2 Field Induced Ionization 101

4.2.1 Tunnel Ionization 101

4.2.2 Multiphoton Ionization 104

4.2.3 ATI in the Coulomb Potential 109

4.2.4 Stabilization in Very Strong Fields 111

4.2.5 Atoms Driven by HCP 113

4.3 High Harmonic Generation 119

4.3.1 Three-Step Model 119

4.3.2 Odd Harmonics Rule 123

4.3.3 Semiclassical Explanation of the Plateau 124

4.3.4 Cutoff and Odd Harmonics Revisited 126

4.A More on Atomic Units 131

References 133

5 Molecules in Strong Laser Fields 135

5.1 The Molecular Ion H2+ 135

5.1.1 Electronic Potential Energy Surfaces 135

5.1.2 The Morse Potential 140

5.2 H2+ in a Laser Field 142

5.2.1 Frozen Nuclei 142

5.2.2 Nuclei in Motion 147

5.3 Adiabatic and Nonadiabatic Nuclear Dynamics 151

5.3.1 Born-Oppenheimer Approximation 152

5.3.2 Dissociation in a Morse Potential 156

5.3.3 Coupled Potential Surfaces 159

5.3.4 Femtosecond Spectroscopy 168

5.4 Control of Molecular Dynamics 177

5.4.1 Control of Tunneling 178

5.4.2 Control of Population Transfer 185

5.4.3 Optimal Control Theory 189

5.4.4 Genetic Algorithms 195

5.4.5 Toward Quantum Computing with Molecules 197

5.A Relative and Center of Mass Coordinates for H2+ 200

5.B Perturbation Theory for Two Coupled Surfaces 201

5.C Reflection Principle of Photodissociation 202

5.D The Undriven Double Well Problem 203

5.E The Quantum Mechanical Adiabatic Theorem 205

References 206

Index 209