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arXiv 0901.3439quant-ph
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非线性光学量子理论导论

An Introduction to the Quantum Theory of Nonlinear Optics

Mark Hillery

备注：
80 pages,
发表信息：
Acta Physica Slovaca 59, No.1, 1-80 (2009)
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摘要：

本文介绍非线性介质光学的量子理论。首先，我们对非线性光学的经典理论作一个简短的总结，即用经典场来完成非线性光学。然后讨论场的正则形式及其量子化。这是适用于量子化的电磁场在自由空间。定义的电磁场的非经典状态，并检查了几个例子。这是其次是一个简短的介绍纠缠的背景下，场模式。下一个任务是非均匀线性电介质中电磁场的量子化。在讨论非线性介质中的场量子化之前，我们讨论了一些常用的量子非线性光学过程的唯象模型。然后，我们在非色散和色散的非线性介质中的字段。指出并讨论了完成这项任务的最常用方法中的缺陷。一旦量子化完成，它就被用来研究参数下转换和量子孤立子传播的多模理论。

英文摘要：

This article is provides an introduction to the quantum theory of optics in nonlinear dielectric media. We begin with a short summary of the classical theory of nonlinear optics, that is nonlinear optics done with classical fields. We then discuss the canonical formalism for fields and its quantization. This is applied to quantizing the electromagnetic field in free space. The definition of a nonclassical state of the electromagnetic field is presented, and several examples are examined. This is followed by a brief introduction to entanglement in the context of field modes. The next task is the quantization of the electromagnetic field in an inhomogeneous, linear dielectric medium. Before going on to field quantization in nonlinear media, we discuss a number of commonly employed phenomenological models for quantum nonlinear optical processes. We then quantize the field in both nondispersive and dispersive nonlinear media. Flaws in the most commonly used methods of accomplishing this task are pointed out and discussed. Once the quantization has been completed, it is used to study a multimode theory of parametric down conversion and the propagation of quantum solitons.

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