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Supervisor's Foreword; Abstract; Publications; Contents; 1 Introduction; 1.1 Motivation; 1.2 Nonlinear Optical Spectroscopy; 1.2.1 Nonlinear Spectroscopy of Potassium; 1.2.2 Molecular Aggregates; 1.3 Entangled Photons; 1.3.1 Parametric Downconversion; 1.3.2 Entangled-Photon Interferometry; 1.3.3 Entangled-Photon Spectroscopy; 1.4 Trapped Ions; 1.5 Time and Energy Scales in This Dissertation; References; 2 Nonlinear Optical Signals; 2.1 Motivation and Overview; 2.2 Light-Matter Hamiltonian and Liouville Space Notation; 2.2.1 Light-Matter Interaction; 2.2.2 Liouville Space Notation.
2.3 Quantum Optical Field Measurements2.3.1 Field Measurements; 2.3.2 Fluorescence Signals; 2.3.3 Classical Versus Quantum Response Functions; 2.4 Effective Interactions in Ion Chains; 2.4.1 Phonon Excitation by Stimulated Raman Scattering; 2.4.2 Electronic Transitions; 2.5 Diagram Construction; 2.5.1 Loop Diagrams; 2.5.2 Unrestricted Loop Diagrams; 2.5.3 Ladder Diagrams; 2.5.4 Time Versus Frequency Domain Expressions; 2.5.5 Impulsive Limit; 2.6 Susceptibilities Versus Transition Amplitudes in the Quantum Domain; 2.6.1 Linear Absorption; 2.6.2 Third-Order Absorption.
2.7 Synopsis: Diagrammatics in a Nutshell2.7.1 Loop Diagrams; 2.7.2 Ladder Diagrams; 2.7.3 Benefits of the Diagrammatic Representation; References; 3 Excited State Distributions and Fluorescence Signals; 3.1 Excursion: Matter Correlations Induced by Coupling to Quantum Light; 3.1.1 Classical Coherent Light; 3.1.2 Superpositions of Two-Photon Fock States; 3.2 Excited State Distributions and Fluorescence; 3.3 Two-Photon Induced Fluorescence (TPIF); 3.3.1 Entangled Two-Photon Induced Fluorescence; 3.3.2 Intensity Crossover; 3.4 The Bacterial Reaction Center; 3.4.1 The System.
3.4.2 Entangled Photons3.4.3 Classical Light; 3.4.4 Correlated Separable State; 3.5 Open Systems; 3.5.1 Ladder Diagrams; 3.5.2 Entangled Photons; 3.5.3 Correlated Separable State; 3.5.4 Time-Energy Uncertainty; 3.6 Fluorescence Signals of the Bacterial Reaction Center; 3.7 Summary; References; 4 Pump-Probe Measurements with Entangled Photons; 4.1 Absorption Signals; 4.2 Pump-Probe-Like Signals of Model Systems; 4.2.1 Linear Response; 4.2.2 The Signal; 4.2.3 Off-Resonant Intermediate States; 4.2.4 Resonant Intermediate States; 4.2.5 Comparison: Classical Laser Pulses; 4.2.6 Intensity Crossover.
4.3 Pump-Probe Signals of the Bacterial Reaction Center4.4 Summary; References; 5 Interferometric Setups; 5.1 Frequency-Resolved Measurements; 5.1.1 Classical Measurements; 5.2 Two-State Jump Model; 5.2.1 Frequency Domain Expressions; 5.2.2 Results; 5.3 Interferometric Signals of the Bacterial Reaction Center; 5.3.1 Frequency Domain Signals; 5.3.2 Classical Pump-Probe Signal; 5.3.3 Two-Photon Counting Setup; 5.4 Summary; References; 6 Frequency Conversion; 6.1 Frequency Conversion Hamiltonian; 6.2 Field Correlation Functions; 6.2.1 Two-Point Correlation Function.
2.3 Quantum Optical Field Measurements2.3.1 Field Measurements; 2.3.2 Fluorescence Signals; 2.3.3 Classical Versus Quantum Response Functions; 2.4 Effective Interactions in Ion Chains; 2.4.1 Phonon Excitation by Stimulated Raman Scattering; 2.4.2 Electronic Transitions; 2.5 Diagram Construction; 2.5.1 Loop Diagrams; 2.5.2 Unrestricted Loop Diagrams; 2.5.3 Ladder Diagrams; 2.5.4 Time Versus Frequency Domain Expressions; 2.5.5 Impulsive Limit; 2.6 Susceptibilities Versus Transition Amplitudes in the Quantum Domain; 2.6.1 Linear Absorption; 2.6.2 Third-Order Absorption.
2.7 Synopsis: Diagrammatics in a Nutshell2.7.1 Loop Diagrams; 2.7.2 Ladder Diagrams; 2.7.3 Benefits of the Diagrammatic Representation; References; 3 Excited State Distributions and Fluorescence Signals; 3.1 Excursion: Matter Correlations Induced by Coupling to Quantum Light; 3.1.1 Classical Coherent Light; 3.1.2 Superpositions of Two-Photon Fock States; 3.2 Excited State Distributions and Fluorescence; 3.3 Two-Photon Induced Fluorescence (TPIF); 3.3.1 Entangled Two-Photon Induced Fluorescence; 3.3.2 Intensity Crossover; 3.4 The Bacterial Reaction Center; 3.4.1 The System.
3.4.2 Entangled Photons3.4.3 Classical Light; 3.4.4 Correlated Separable State; 3.5 Open Systems; 3.5.1 Ladder Diagrams; 3.5.2 Entangled Photons; 3.5.3 Correlated Separable State; 3.5.4 Time-Energy Uncertainty; 3.6 Fluorescence Signals of the Bacterial Reaction Center; 3.7 Summary; References; 4 Pump-Probe Measurements with Entangled Photons; 4.1 Absorption Signals; 4.2 Pump-Probe-Like Signals of Model Systems; 4.2.1 Linear Response; 4.2.2 The Signal; 4.2.3 Off-Resonant Intermediate States; 4.2.4 Resonant Intermediate States; 4.2.5 Comparison: Classical Laser Pulses; 4.2.6 Intensity Crossover.
4.3 Pump-Probe Signals of the Bacterial Reaction Center4.4 Summary; References; 5 Interferometric Setups; 5.1 Frequency-Resolved Measurements; 5.1.1 Classical Measurements; 5.2 Two-State Jump Model; 5.2.1 Frequency Domain Expressions; 5.2.2 Results; 5.3 Interferometric Signals of the Bacterial Reaction Center; 5.3.1 Frequency Domain Signals; 5.3.2 Classical Pump-Probe Signal; 5.3.3 Two-Photon Counting Setup; 5.4 Summary; References; 6 Frequency Conversion; 6.1 Frequency Conversion Hamiltonian; 6.2 Field Correlation Functions; 6.2.1 Two-Point Correlation Function.