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.

'...J. Perina gives an excellent coverage of the topic of quantum statistics of linear and non linear optical phenomena.' The Australian Physicist (August 1985) '...While the level is advanced and the presentation is mathematically sophisticated, the style is straightforward, systematic, clear, and readable. I recommend this monograph highly as a reference for students of quantum optics and related areas.' Bahaa E.A. Saleh, University of Wisconsin '... an excellent source of up-to-date information on the subject, including matters like photon antibunching and two-photon coherent states or squeezed states. I am convinced that this monograph will be very higly appreciated by research workers in the field of quantum mechanics.' Journal de Physique, 46:9 (1985)