Dynamics During Spectroscopic Transitions

Among the key questions that lead to the development of quantum theory was the problem of understanding the interaction of light with matter. Modern time-resolved spectroscopy has contributed tremendously to current theoretical models. This book addresses final year undergraduates and graduate students in Chemistry and Physics.

I. Well-known Principles.- 1 Introduction.- 1.1 Electric Fields in Atoms and Waves.- 1.2 Photoionization and Nonresonant Scattering.- 1.3 Resonant Interactions and Spectroscopy.- 1.4 The Bouguer-Lambert-Beer Law.- 1.5 The Importance of Spectroscopic Transitions.- 1.6 The Question of Dynamics.- 1.7 Early History of the Quantum Theory.- 1.8 Dynamics During Spectroscopic Transitions.- 1.9 References.- 1.10 Problems.- 2 Elementary Quantum Theory.- 2.1 States and Their Properties: Operators and Kets.- 2.2 Stationary States: Eigenkets and Eigenfunctions.- 2.3 Schrödinger’s Equation: Time Dependence of ?.- 2.4 Kets and Bras: Orthogonality and Normalization.- 2.5 Quantum Systems “in-between” Eigenstates.- 2.6 Eigenvalues and Expectation Values.- 2.7 Superposed Eigenfunctions and Perturbed Eigenfunctions.- 2.8 References.- 2.9 Problems.- 3 Elementary Electromagnetic Theory.- 3.1 Relationship Between Classical and Quantum-Mechanical Theories.- 3.2 Applicability of Classical and Quantum Theories.- 3.3 When the Classical Theory May Be Used.- 3.4 Waves and Particles and Their “Sizes”.- 3.5 Electromagnetic Waves and Quantum Systems: Size Ratios.- 3.6 Series Expansions for Electromagnetic Fields.- 3.7 Interactions Between Multipoles and Field Asymmetries.- 3.8 Electromagnetic Waves and Quantum Systems: Interactions.- 3.9 Complex Susceptibilities, Electric and Magnetic.- 3.10 Effect of Susceptibilities on Wave Propagation.- 3.11 Absorption Coefficient and Refractive Index.- 3.12 Phase Relationships: Absorption, Emission, and Dispersion.- 3.13 References.- 3.14 Problems.- 4 Interaction of Radiation and Matter.- 4.1 Dipoles and Waves: the Semiclassical Theory.- 4.2 The Transition Dipole Moment of a Hydrogen Atom.- 4.3 Conceptual Problems with the Theory.- 4.4 Quantum Jumps and the Uncertainty Principle.- 4.5 The Spin?½ System.- 4.6 A Geometrical Model of the Transition Process.- 4.7 Quantum Jumps on the Sphere of Certainty.- 4.8 Magnetic Resonance in Bulk and in Beams.- 4.9 The Stern-Gerlach Experiment.- 4.10 State Selection in Beam Experiments.- 4.11 The Rabi Magnetic Resonance Experiment.- 4.12 The Ramsey Separated Oscillating Fields Experiment.- 4.13 A Thought Experiment.- 4.14 Difficulties with the Proposed Experiment.- 4.15 The Bloom Transverse Stern-Gerlach Effect.- 4.16 Quantum Jumps and Superposition States: Conclusion.- 4.17 References.- 4.18 Problems.- II. Quantum Statistics.- 5 Ensembles of Radiating Systems.- 5.1 Reasons for the Use of Statistical Methods.- 5.2 Coherent and Incoherent Perturbations.- 5.3 Strongly Coupled and Weakly Coupled Systems.- 5.4 Computing Expectation Values from Superposition Coefficients.- 5.5 Equations of Motion for the Operator D.- 5.6 The Density Operator.- 5.7 Properties of the Density Matrix.- 5.8 Effect of Relaxation on the Density Matrix.- 5.9 Equations of Motion for the Density Matrix.- 5.10 Coherence in Ensembles of Quantum Radiators.- 5.11 Creating, Observing, and Destroying Coherence.- 5.12 References.- 5.13 Problems.- 6 Relaxation Processes and Coherent Dissipative Structures.- 6.1 Dissipative Systems.- 6.2 Entanglement and Interference Effects.- 6.3 The Ensemble for an Ideal System.- 6.4 The Density Matrix.- 6.5 Variational Principles and the Negentropy.- 6.6 The Extreme Case.- 6.7 Resonance Picture of Unstable States.- 6.8 Resonances and Dissipative Dynamics.- 6.9 The Coherent-Dissipative Ensemble.- 6.10 References.- 6.11 Problems.- 7 Applications of CSM Theory.- 7.1 Occurrence of Coherent-Dissipative Structures.- 7.2 Proton Transfer Processes in Water and Aqueous Solutions.- 7.3 The Development of ODLRO and the Phases of High-Temperature Superconductors.- 7.4 Fractional Statistics in the Quantum Hall Effect.- 7.4.1 The Fractional QHE.- 7.4.2 Quantum States.- 7.4.3 The Many-Body System.- 7.4.4 High Correlation.- 7.4.5 Wigner Solids.- 7.5 Spontaneous and Stimulated Emission of Radiation in Masers.- 7.5.1 Einstein Relation.- 7.5.2 Cyclotron Maser Concept.- 7.5.3 Liouville Formulation of CMC.- 7.5.4 Self-Organization.- 7.5.5 Connection with the Gainfunction.- 7.5.6 Conclusion.- 7.6 Final Conclusions.- 7.7 References.- 7.8 Problems.- III. Gyrating Dipole Moments.- 8 Basic Principles of Magnetic Resonance.- 8.1 Operators Representing Orbital Angular Momentum.- 8.2 Operators Representing Spin Angular Momentum.- 8.3 Eigenkets of Spin; Raising and Lowering Operators.- 8.4 Number of States, Normalization, and Eigenvalues.- 8.5 Spinning Particles in Nature.- 8.6 The Effect of a Static Magnetic Field.- 8.7 The Effect of an Oscillating Magnetic Field.- 8.8 The Density Matrix for Magnetic Resonance.- 8.9 The Ensemble-Averaged Magnetization.- 8.10 Solutions to the Bloch Equations.- 8.11 Absorption and Stimulated Emission: Free-Induction Decay.- 8.12 The Crossed-Coil Nuclear Magnetic Resonance Spectrometer.- 8.13 Steady-State Magnetization: Curie’s Law.- 8.14 Conventional Nuclear Magnetic Resonance Spectroscopy: Slow Passage.- 8.15 Equivalence of Transient and Steady-State Methods.- 8.16 Spin Echoes.- 8.17 References.- 8.18 Problems.- 9 Spin Dynamics and Radical Reactions.- Key to Symbols.- 9.1 Molecules in Doublet States.- 9.2 Singlet and Triplet States.- 9.3 Intersystem Crossing by Magnetic Interactions.- 9.4 Spin Dynamics of Radical Pairs in High Fields.- 9.5 Combining Spin Dynamics and Radical Pair Dynamics.- 9.6 Chemically Induced Nuclear Spin Polarizations.- 9.7 Chemically Induced Electron Spin Polarizations.- 9.8 Quantum Beats.- 9.9 References.- 9.10 Problems.- 10 Generalization of the Gyroscopic Model.- 10.1 The Gyroscopic Model of the Interaction Process.- 10.2 Electric-Dipole-Allowed Transitions.- 10.3 Relaxation and Its Effect on Line Widths.- 10.4 Phase Interruption and Pressure Broadening.- 10.5 Other Relaxation Processes in Gases and Solids.- 10.6 Optical Analogs to Magnetic Resonance Phenomena.- 10.7 Photon Echoes: Qualitative Discussion.- 10.8 Angle of Echo Propagation Using the Gyroscopic Model.- 10.9 Mathematical Analysis of ?/2, ? Echoes.- 10.10 Self-Induced Transparency: Qualitative Discussion.- 10.11 Other Coherent Transient Phenomena.- 10.12 References.- 10.13 Problems.- IV. Applications of LASER and SR Techniques.- 11 Stimulated Scattering: Third Order Processes.- 11.1 Coherent Material Excitation.- 11.2 Theoretical Background of Four Wave Mixing (FWM).- 11.2.1 Extension of the Applicability of the Raman FWM-Equations and the Method of Their Solution.- 11.2.2 FWM Under Steady State Conditions.- 11.2.3 FWM Under Stationary Conditions.- 11.2.4 The Notation of Nonlinear Susceptibility.- 11.3 Coherent Antistokes Raman Spectroscopy.- 11.3.1 Determination of Nonlinear Susceptibilities by CARS Line Shape Analysis.- 11.3.2 Application of Special Polarization Arrangements to Discriminate Between Different Contributions to the CARS Signal.- 11.3.3 Background Suppression by Suitably Chosen Field Polarizations.- 11.4 Nonlinear Polarization Spectroscopy.- 11.4.1 Pressure-Induced FWM Signals.- 11.5 Time-Resolved Techniques of FWM.- 11.5.1 Characteristic Experimental Results.- 11.5.2 Increased Spectral Resolution Applying Specially Designed Pulsed FWM Techniques.- 11.5.3 Photon Echoes of Polyatomic Molecules in Condensed Phases.- 11.6 Time-Resolved Measurements with Incoherent Laser Beams Bearing ps- and Sub-ps-Fluctuations.- 11.6.1 CSRS with Incoherent Laser Light.- 11.6.2 White-Detector Limit.- 11.6.3 Spectrally Resolved Detection.- 11.6.4 Some Experimental Results.- 11.7 Material Excitation by SRS for a Frequency Modulated Statistically Fluctuating Laser.- 11.8 The Description of Molecular Susceptibilities by Feynman Diagrams.- 11.8.1 Rules for Deriving the ?(n)-Expressions from the Diagrams.- 11.8.2 The General Form of the ?(3)-Susceptibility Expression.- 11.8.3 Term Selection Under Resonance Excitation.- 11.8.4 Determination of Molecular Polarizations by the Feynman Diagram Technique in the Case of Time Dependent Fields.- 11.9 References.- 11.10 Problems.- 12 Transient Grating Spectroscopy.- Key to Symbols.- 12.1 Transient Grating and Four-Wave Interaction.- 12.2 Grating Excitation Mechanisms.- 12.3 Diffraction at a Grating.- 12.4 Characteristics of the Transient Grating Technique.- 12.5 Depopulation and Orientation Processes.- 12.6 Electronic Energy Transfer and Charge Carrier Dynamics.- 12.7 Mass and Heat Diffusion.- 12.8 Propagation of Ultrasonic Waves and Structural Relaxation.- 12.9 References.- 12.10 Problems.- 13 Synchrotron Radiation and Free Electron Lasers.- 13.1 Introduction.- 13.2 Synchrotron Radiation.- 13.3 Undulator Radiation.- 13.4 Free Electron Lasers.- 13.5 Accelerators for Light Sources and Undulators.- 13.6 VUV Optical Components.- 13.7 VUV Monochromators.- 13.8 Techniques for VUV Measurements.- 13.9 Far Infrared Instrumentation.- 13.10 Two-Color Experiments.- 13.11 References.- 13.12 Problems.