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arXiv:1104.3825

Causal signal transmission by quantum fields. Phase-space approach to quantum electrodynamics

Lev I. Plimak, Stig Stenholm

Published Apr 19, 2011• 0 citations
arXivHTMLPDF

Abstract

Phase-space techniques are generalized to nonlinear quantum electrodynamics beyond the rotating wave approximation, resulting in an essentially classical picture of radiation dynamics.
DOI
10.48550/arxiv.1104.3825

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Generalised phase-space techniques for electromagnetic interactions beyond the rotating wave approximation [L.P. and S.S., arXiv:1104.3825 (2011)] is applied to interactions of distinguishable devices. The paper is built around the concept of "doing quantum electrodynamics while thinking classically," which is a generalisation of Sudarshan's renowned optical equivalence theorem [E.C.G. Sudarshan, Phys. Rev. Lett. 10, 277 (1963)] to the interacting electromagnetic field. This concept allows one to reduce inherently quantum problems to semiclassical considerations.
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.
Conventional definition of the time-normal operator ordering (Kelley P. L. and Kleiner W. H., Phys. Rev. , 136 (1964) A316 ) is prone to causality violations (de Haan M., Physica A , 132 (1985) 375 ; 397 ). We show that such violations disappear if this definition is amended outside the rotating wave approximation. Nonrelativistic causality of an arbitrary time-normal product turns out to be a property of quantum kinematics, while relativistic causality is demonstrated for a time-normal product of two operators under the most general assumptions about quantum dynamics (commutativity of operators at space-like intervals). This eliminates the key obstacle preventing phase-space techniques of quantum optics from being extended to arbitrary quantum fields including fermions.
A perturbative description of photodetection without the rotating wave approximation is presented. With the help of Green function techniques on an extended time contour renormalized expressions for the single- and multitime counting probabilities are derived, which explicitly reflect the causal propagation of signals. In the case of classical light fields the moments of the counting statistics can be expressed in terms of field correlation functions in agreement with the result of Bykov and Tatarskii. For non-classical radiation fields such as squeezed states the Bykov-Tatarskii formula is shown to be incorrect.