# Quantum Statistics Of Linear And Nonlinear Optical Phenomena

## byJan Perina

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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.
Title:Quantum Statistics Of Linear And Nonlinear Optical PhenomenaFormat:PaperbackPublished:October 12, 2011Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9400962509

ISBN - 13:9789400962507

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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.- 3.2.1 Analytic properties.- 3.2.2 Spectral properties.- 3.2.3 Wave equations in vacuo.- 3.2.4 Symmetries and inequalities.- 3.2.5 Examples of the second-order degrees of coherence.- 3.3 Quantum coherence.- 3.3.1 Second-order phenomena.- 3.3.2 Higher-order phenomena.- 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.- 4.1.1 Definitions.- 4.1.2 Expansions in terms of coherent states.- 4.1.3 Minimum-uncertainty wave packets.- 4.1.4 Properties of the displacement operator $$\hat{D}(\alpha)$$.- 4.1.5 Expectation values of operators in coherent states.- 4.1.6 Generalized coherent states.- 4.1.7 Multimode description.- 4.1.8 Time development of the coherent states.- 4.1.9 Even and odd coherent states.- 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.- 4.6.1 Quantum and classical correlation functions.- 4.6.2 Photon-number and photocount distributions.- 4.7 Stationary conditions for the field.- 4.7.1 Time invariance properties of the correlation functions.- 4.7.2 Stationary conditions in phase space.- 4.8 Ordering of field operators.- 4.8.1 ?- and s-ordering and general decompositions.- 4.8.2 Connecting relations.- 4.8.3 Multimode description.- 4.9 Interference of independent light beams.- 4.10 Two-photon coherent states, atomic coherent states and coherent states for general potentials.- 4.10.1 Two-photon coherent states.- 4.10.2 Atomic coherent states.- 5. Special States of the Electromagnetic Field.- 5.1 Chaotic (Gaussian) light.- 5.1.1 Distributions and characteristic functions.- 5.1.2 The second-order correlation function for blackbody radiation.- 5.1.3 Photocount statistics.- 5.2 Laser radiation.- 5.2.1 Ideal laser model.- 5.2.2 Real laser model.- 5.3 Superposition of coherent and chaotic fields.- 5.3.1 One-mode field.- 5.3.2 Multimode field-characteristic generating function.- 5.3.3 Integrated intensity probability distribution.- 5.3.4 The photocount distribution.- 5.3.5 Factorial moments.- 5.3.6 Factorial cumulants.- 5.3.7 Accuracy of approximate M-mode formulae.- 6. Review of Nonlinear Optical Phenomena.- 6.1 General classical description.- 6.2 The second-order phenomena.- 6.3 The third- and higher-order phenomena.- 6.4 Transient coherent optical effects.- 6.4.1 Self-induced transparency.- 6.4.2 Photon echo.- 6.4.3 Superradiance.- 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.- 9.1.1 Degenerate case.- 9.1.2 Non-degenerate case.- 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.- 9.4.1 Reservoir phonon system.- 9.4.2 Dynamics of photon and phonon modes.- 9.4.3 Completely quantum description.- 9.4.4 Hyper-Raman scattering.- 9.5 Multiphoton absorption.- 9.6 Multiphoton emission.- 9.7 Resonance fluorescence.- 9.8 Other interesting nonlinear phenomena.- 9.8.1 Coherent ?-emission by stimulated annihilation of electron - positron pairs.- 9.8.2 A solvable model for light scattering.- 9.9 Phase-transition analogies.- 10. Conclusions.- References.

Editorial Reviews

...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)