Part I Prerequisites 1 A Short Introduction to Laser Physics 1.1 The Einstein Coefficients 1.2 Fundamentals of the Laser 1.2.1 Elementary Laser Theory 1.2.2 Realization of the Laser Principle 1.3 Pulsed Lasers 1.3.1 Frequency Comb 1.3.2 Carrier Envelope Phase 1.3.3 Husimi Representation of Laser Pulses 1.A Some Gaussian Integrals References 2 Time-Dependent Quantum Theory 2.1 The Time-Dependent SchrSdinger Equation 2.1.1 Introduction 2.1.2 Time-Evolution Operator 2.1.3 Spectral Information 2.1.4 Analytical Solutions for Wavepackets 2.2 Analytical Approaches 2.2.1 Feynman's Path Integral 2.2.2 Semiclassical Approximation 2.2.3 Time-Dependent Perturbation Theory 2.2.4 Magnus Expansion . 2.2.5 Time-Dependent Hartree Method 2.2.6 Quantum-Classical Methods 2.2.7 Floquet Theory 2.3 Numerical Methods 2.3.1 Orthogonal Basis Expansion 2.3.2 Split-Operator FFT Method 2.3.3 Alternative Methods of Time-Evolution 2.3.4 Semiclassical Initial Value Representations 2.A The Royal Road to the Path Integral 2.B Variational Calculus 2.C Stability Matrix 2.D From the HK- to the VVG-Propagator References Part II Applications 3 Field Matter Coupling and Two-Level Systems 3.1 Light Matter Interaction 3.1.1 Minimal Coupling 3.1.2 Length Gauge 3.1.3 Kramers-Henneberger Transformation 3.1.4 Volkov Wavepacket 3.2 Analytically Solvable Two-Level Problems 3.2.1 Dipole Matrix Element 3.2.2 Rabi Oscillations Induced by a Constant Perturbation 3.2.3 Time-Dependent Perturbations 3.2.4 Exactly Solvable Time-Dependent Cases 3.A Generalized Parity Transformation 3.B Two-Level System in an Incoherent Field References 4 Single Electron Atoms in Strong Laser Fields 4.1 The Hydrogen Atom 4.1.1 Hydrogen in Three Dimensions 4.1.2 The One-Dimensional Coulomb Problem 4.2 Field Induced Ionization 4.2.1 Tunnel Ionization 4.2.2 Multiphoton Ionization 4.2.3 ATI in the Coulomb Potential 4.2.4 Stabilization in Very Strong Fields 4.2.5 Atoms Driven by HCP 4.3 High Harmonic Generation 4.3.1 Three-Step Model 4.3.2 Odd Harmonics Rule 4.3.3 Semiclassical Explanation of the Plateau 4.3.4 Cutoff and Odd Harmonics Revisited 4.A More on Atomic Units References 5 Molecules in Strong Laser Fields 5.1 The Molecular Ion H+ 5.1.1 Electronic Potential Energy Surfaces 5.1.2 The Morse Potential 5.2 H+ in a Laser Field 5.2.1 Frozen Nuclei 5.2.2 Nuclei in Motion 5.3 Adiabatic and Nonadiabatic Nuclear Dynamics 5.3.1 Born-Oppenheimer Approximation 5.3.2 Dissociation in a Morse Potential 5.3.3 Coupled Potential Surfaces 5.3.4 Femtosecond Spectroscopy 5.4 Control of Molecular Dynamics 5.4.1 Control of Thnneling 5.4.2 Control of Population Transfer 5.4.3 Optimal Control Theory 5.4.4 Genetic Algorithms 5.4.5 Toward Quantum Computing with Molecules 5.A Relative and Center of Mass Coordinates for H+ 5.B Perturbation Theory for Two Coupled Surfaces 5.C Reflection Principle of Photodissociation 5.D The Undriven Double Well Problem 5.E The Quantum Mechanical Adiabatic Theorem References Index
