Quantum Statistics of Linear and Nonlinear Optical Phenomena

1. Introduction.- 2. Quantum Theory of the Electromagnetic Field.- 2.1 Quantum description of the field.- 2.2 Statistical states.- 2.3 Multimode description.- 2.4 Calculation of commutators of the field operators.- 2.5 Time development of quantum states.- 3. Optical Correlation Phenomena.- 3.1 Definition of quantum correlation functions.- 3.2 Properties of quantum correlation functions.- 3.3 Quantum coherence.- 3.4 Measurements corresponding to antinormally ordered products of field operators — quantum counters.- 3.5 Quantum characteristic functionals.- 3.6 Measurements of mixed-order correlation functions.- 3.7 Photocount distribution and photocount statistics.- 3.8 Determination of the integrated intensity probability distribution from the photocount distribution.- 3.9 Short-time measurements.- 3.10 Bunching and antibunching of photons.- 3.11 Hanbury Brown — Twiss effect — correlation interferometry and correlation spectroscopy.- 4. Coherent-State Description of the Electromagnetic Field.- 4.1 Coherent states of a harmonic oscillator and of the electromagnetic field.- 4.2 Glauber — Sudarshan representation of the density matrix.- 4.3 The existence of the Glauber — Sudarshan representation.- 4.4 The phase operators.- 4.5 Multimode description.- 4.6 Relation between the quantum and classical descriptions.- 4.7 Stationary conditions for the field.- 4.8 Ordering of field operators.- 4.9 Interference of independent light beams.- 4.10 Two-photon coherent states, atomic coherent states and coherent states for general potentials.- 5. Special States of the Electromagnetic Field.- 5.1 Chaotic (Gaussian) light.- 5.2 Laser radiation.- 5.3 Superposition of coherent and chaotic fields.- 6. Review of Nonlinear Optical Phenomena.- 6.1 General classical description.- 6.2 Thesecond-order phenomena.- 6.3 The third- and higher-order phenomena.- 6.4 Transient coherent optical effects.- 7. Heisenberg — Langevin and Master Equations Approaches to the Statistical Properties of Radiation Interacting With Matter.- 7.1 The Heisenberg — Langevin approach.- 7.2 The master equation and generalized Fokker — Planck equation approaches.- 7.3 The interaction of radiation with the atomic system of a nonlinear medium.- 8. Quantum Statistics of Radiation in Random Media.- 8.1 Phenomenological description of propagation of radiation through turbulent atmosphere and Gaussian media.- 8.2 The hamiltonian for radiation interacting with a random medium.- 8.3 Heisenberg—Langevin equations and the generalized Fokker — Planck equation.- 8.4 Solutions of the generalized Fokker — Planck equation and the Heisenberg — Langevin equations.- 8.5 Photocount statistics.- 8.6 Diament—Teich and Tatarskii descriptions.- 8.7 Comparison of the quantum and phenomenological descriptions.- 8.8 Speckle phenomenon.- 9. Quantum Statistics of Radiation in Nonlinear Media.- 9.1 Optical parametric processes with classical pumping.- 9.2 Interaction of three one-mode boson quantum fields.- 9.3 Second and higher harmonic and subharmonic generation.- 9.4 Raman, Brillouin and hyper-Raman scattering.- 9.5 Multiphoton absorption.- 9.6 Multiphoton emission.- 9.7 Resonance fluorescence.- 9.8 Other interesting nonlinear phenomena.- 9.9 Phase-transition analogies.- 10. Conclusions.- References.