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Journal of Nonlinear Optical Physics & Materials

QUANTUM CHANNELS IN NONLINEAR OPTICAL PROCESSES

David S. Bradshaw, Davıd L. Andrews

Published Jun 1, 2009• 48 citations
Publisher

Abstract

Quantum electrodynamics furnishes a new type of representation for the characterisation of nonlinear optical processes. The treatment elicits the detailed role and interplay of specific quantum channels, information that is not afforded by other methods. Following an illustrative application to the case of Rayleigh scattering, the method is applied to second and third harmonic generation. Derivations are given of parameters that quantify the various quantum channels and their interferences; the results are illustrated graphically. With given examples, it is shown in some systems that optical nonlinearity owes its origin to an isolated channel, or a small group of channels.

DOI
10.1142/s0218863509004609

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Quantum electrodynamics furnishes a new type of representation for the characterisation of nonlinear optical processes. The treatment elicits the detailed role and interplay of specific quantum channels, information that is not afforded by other methods. Following an illustrative application to the case of Rayleigh scattering, the method is applied to second and third harmonic generation. Derivations are given of parameters that quantify the various quantum channels and their interferences; the results are illustrated graphically. With given examples, it is shown in some systems that optical nonlinearity owes its origin to an isolated channel, or a small group of channels.
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.
The interaction of light with matter can generate different types of scattering that can be applied to quantum optics, photonics and integrated optics appropriately. The generation of certain pulses in certain waveguides can produce certain nonlinear optical pulses with important properties such as low energy and information loss applied, for example, to communication systems and quantum information. The method we describe is based on the generation and propagation of nonlinear optical pulses in multidimensional material structures: waveguides in 1 dimension, planar systems in 2 dimensions and crystalline systems in 3 dimensions. These structures can be appropriately designed to generate nonlinear and quantum optical pulses depending on the crystal structure and electrical susceptibility of the material. These optical pulses can be appropriately characterized whose respective scattering signals can be identified and processed providing an application basis for emerging technologies for transmission and processing systems based on quantum optics and quantum computing.
In this chapter the author discusses two nonlinear optical phenomena — second-harmonic generation and parametric downconversion — drawing particular attention to the signatures of quantum fluctuations of the optical fields that can be found in the phenomena. The ubiquitous vacuum fluctuations can manifest themselves in various ways when an optical field undergoes nonlinear transformation. The two processes considered here are only examples of a rich variety of nonlinear phenomena, but they are of great practical importance and thus have been studied for years. It is not the author's intention to collect all the facts known about the two processes, but rather to select some specific effects illustrating the role of quantum character of the field in the process. He presents several theoretical methods that are used to describe quantum properties of the field and that are now available to everybody owing to common access to computers and software.
Abstract The stochastic Schrödinger equation, a novel method for describing the dissipative dynamics of open quantum systems interacting with their environment, is applied to some nonlinear optical processes, namely nonlinear absorption and second‐harmonic generation, the latter also in the range of instabilities and classical chaotic behaviour. Where possible the results are compared with numerical simulations of the positive P representation, which in some cases are found to give unreliable results.
In this thesis, we present our experimental and theoretical work on modern and old topics of Nonlinear Quantum Optics. The thesis is structured as follows. \nIn the first chapter, we provide a general introduction about the basis of this field, in particular about the main concepts and results that will be needed in the following.\nIn the second and third chapters, we explain our research on the role of silicon photomultipliers in Quantum Optics experiments. After a specific characterization of the sensors, we used them to detect nonclassical states of light. Different strategies for the estimation of experimental quantities are suggested.\nIn the fourth chapter, we propose our quantum description for the second-harmonic-generation process, based on well-known perturbative methods. After a general introduction on the state of the art, we immediately dive into the problem by explaining the employed methods and showing our analytical results.\nFinally, we resume the essence of our achievements and draw our conclusions.