Quantum Statistics of Linear and Nonlinear Optical Phenomena

The quantum statistical properties of radiation represent an important branch of modern physics with rapidly increasing applications in spectroscopy, quantum generators of radiation, optical communication, etc. They have also an increasing role in fields other than pure physics, such as biophysics, psychophysics, biology, etc. The present monograph represents an extension and continuation of the previous monograph of this author entitled Coherence of Light (Van Nostrand Reinhold Company, London 1972, translated into Russian in the Publishing House Mir, Moscow 1974) and of a review chapter in Progress in Optics, Vol. 18 (E. Wolf (Ed.), North-Holland Publishing Company, Amsterdam 1980), published just recently. It applies the fundamental tools of the coherent-state technique, as described in Coherence of Light, to particular studies of the quantum statistical properties of radiation in its interaction with matter. In particular, nonlinear optical processes are considered, and purely quantum phenomena such as antibunching of photons are discussed. This book will be useful to research workers in the fields of quantum optics and electronics, quantum generators, optical communication and solid-state physics, as well as to students of physics, optical engineering and opto-electronics.

Table of Contents:
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.