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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Propogation of non-classical light

R. Loudon

Published Dec 15, 1997• 6 citations
Publisher

Abstract

The theoretical descriptions of the main varieties of non–classical light and the principal measures of their specifically quantum properties are outlined. The theories of quantum–optical propagation of the light through slabs of amplifying or attenuating materials are presented and the main features of the quantum noise effects produced by transmission are summarized. It is found that, while quantum light may have lower noise than classical coherent light, transmission through the slab generally increases the noise. Thus initial enthusiasm for practical low–noise advantages of non–classical light has been tempered by the realization that most kinds of optical propagation or processing enhance the noise to near–classical levels.

DOI
10.1098/rsta.1997.0129

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The theoretical descriptions of the main varieties of non–classical light and the principal measures of their specifically quantum properties are outlined. The theories of quantum–optical propagation of the light through slabs of amplifying or attenuating materials are presented and the main features of the quantum noise effects produced by transmission are summarized. It is found that, while quantum light may have lower noise than classical coherent light, transmission through the slab generally increases the noise. Thus initial enthusiasm for practical low–noise advantages of non–classical light has been tempered by the realization that most kinds of optical propagation or processing enhance the noise to near–classical levels.
We calculate the effects of normal transmission through an amplifying dielectric slab on the properties of an incident pulse of light. The transmitted pulse shows shifts in peak position and additional lengthening or shortening with respect to the unamplified incident pulse. The magnitudes of these effects are generally larger than those of the corresponding changes that occur in transparent or attenuating slabs. They are interpreted in terms of the interference of multiply reflected contributions to the transmitted pulse. The theory is valid for pulses of nonclassical light, but the same reshaping occurs for appropriate pulses of classical light.
Two types of noise are discussed that may become important when light frequencies are used for communication purposes. At such high frequencies a quantum of energy is not negligible compared to the total transmitted energies (low number of quanta!). The fluctuations caused by the nonzero size of a quantum of energy will predominate over thermal noise, and the usual amplifier noise encountered at microwave (and lower) frequencies. The two types of processes producing quantum noise that we intend to discuss are shown in Pig. 1. They are: The radiative attenuation noise introduced when a signal, phase-and amplitude-control1ed at the high-power transmitter end, is highly attenuated through the inverse square law radiative attenuation. Such a process would take place in the use of optical frequencies for energy transmission over large distances. The noise introduced in linear amplification. objective of this paper is to show how these forms of noise can be analyzed using simple statistics and classical electromagnetic theory with the aid of only a few quantum-theoretical results that have a simple physical meaning.
The quantum properties of optical devices are important • In conventional optical communication systems, quantum effects are responsible for noise inherent in the si (by amplifiers and attenuators) and noise in the detectors. gnals, noise added during transmission • Noise obscures the signals and lowers the information capacities. • There are many schemes for quantum communication and computation that rely on the quantum properties of light. • • Examples include quantum key distribution (QKD) and linear optical quantum computation (LOQC). • Common requirements for quantum information experiments include photon generators (singlet or pair) and (distortionless) photon frequency-convertors.
Abstract The study of the classical theory of optical fluctuations and coherence is an important preliminary to the development of the corresponding quantum-mechanical theory. The classical theory is useful for a physical understanding of the various effects and many of the classical concepts carry over into the quantum theory. In addition, a knowledge of the classical theory is useful for identification of the nature of the specifically quantum properties that some light beams may exhibit. Thus it is shown in Chapter 5 that the classical and quantum theories yield the ame predictions for chaotic light, but that there exist other kinds of light that elude any satisfactory classical description. The nature of such ‘nonclassical’ light i5, of course, more sharply appreciated by contrast with the limitations on the possible kinds of light inherent in the classical theory.
This chapter presents a synopsis on nonclassical light, emphasizes the roles of different quantum amplifiers, and discusses the problem of overcoming the detrimental effect of loss. The generation of two-photon coherent state (TCS) and near-number state (NNS) via nonlinear optical processes are, in some sense, surprisingly similar. This similarity is in addition to that between TCS and number-phase minimum uncertainty states when the nonclassical effects are small. It seems to arise from an underlying intrinsic quantum correlation. Nonclassical light do not propagate well. This is because significant loss, be it radiative, absorption, or otherwise, is often incurred during propagation. Nonclassical light with matching detection leads to significant improvement in signal-to-noise (SNR) ratio. Even in situations where SNR is not the most appropriate performance measure, it is clear that the low noise characteristics of TCS and NNS, or simply their difference from classical states, could be useful.
Classical optics describes quite successfully the propagation of laser light, both in free-space and inside a transparent medium. On the other hand, neither classical optics nor the conventional formulation of quantum optics can address adequately the propagation of nonclassical light. Nonclassical states of light are usually described by second-quantization operators acting onto the vacuum state of the radiation field, and the corresponding expectation values of the electric and magnetic fields are often zero. Clearly, the description of propagation of nonclassical light requires a direct quantum mechanical treatment of the spatial progression of the field operators. This chapter outlines the main features of propagative quantum optics, and examines more particularly the treatment of propagation through a linear (refractive) medium, and across a refractive interface. In order to facilitate the discussion of the physical ideas, a plane-wave propagation geometry, which greatly simplifies the mathematical treatment, is used.