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Journal of the European Optical Society Rapid Publications

Quantum theory of coherence and nonlinear optics

Jan Peřina

Published Sep 23, 2009• 1 citation
Publisher

Abstract

We review the beginning stage of quantum theory of coherence and research performed at the Palacký University in quantum and nonlinear optics related to quantum state reconstruction, generalized superposition of signal and quantum noise, quantum Zeno effect, nonlinear optical couplers and parametric down-conversion.
DOI
10.1051/jeos.2010.10048s

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Nonlinear phenomena in quantum optics are reviewed, with particular emphasis on scientific activities in quantum optics at the Natural Science Faculty of Palacký University ln Olomouc (Czech Republic). The first section is devoted to quantum and classical methods to obtain photon statistics in higher-harmonics generation, including a method of classical trajectories. It is followed by a discussion of photon bunching and antibunching of nonstationary fields. The chapter continues with a discussion of methods for reconstruction of quantum states. Other topics covered include the process of frequency downconversion with pulses, Zeno and anti-Zeno effects based on optical parametric processes, Raman nonlinear couplers as switching elements and sources of nonclassical light for optoelectronics and photonics, and quantum cryptography. Finally, quantum spatial propagation of a two-mode squeezed light in a cubically behaved quadratic medium is treated as another feature of a two-field squeezed steady-state light, and this approach is compared with the conventional one.
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Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.
Statistical properties of light generated in nonlinear optical couplers are discussed. Methods suitable for the description of non-classical properties of light are mentioned; special attention is paid to generalized superposition of coherent fields and noise. Regimes suitable for non-classical light generation in various types of nonlinear couplers based on second-harmonic and second- subharmonic generation, optical parametric processes, Kerr effect as well as Raman and Brillouin processes are analyzed. Special attention is devoted to the generation of light with sub-Poissonian statistics, squeezed light, and light in purely quantum states. Role of real effects like damping of optical fields and phase mismatches is also discussed.