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Journal of Modern Optics

Influence of a Dispersive and Dissipative Medium on Spectral Squeezing

Ulf Leonhardt

Published Jun 1, 1993• 17 citations
Publisher

Abstract

The influence of dispersion and losses in a dielectric layer working as a frequency filter on the squeezing properties of light was considered with the help of the formalism of quantum optics in oscillator media. Squeezing is reduced due to two effects: absorption according Beer's law and lowering of the spectral resolution of the filter. Spectral squeezing in resonance fluorescence was studied as an example.

DOI
10.1080/09500349314551181

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The influence of dispersion and losses in a dielectric layer working as a frequency filter on the squeezing properties of light was considered with the help of the formalism of quantum optics in oscillator media. Squeezing is reduced due to two effects: absorption according Beer's law and lowering of the spectral resolution of the filter. Spectral squeezing in resonance fluorescence was studied as an example.
Abstract Absorption is usually expected to be detrimental to quantum coherence effects. However, there have been few studies into the situation for complex absorption spectra. We consider the resonance fluorescence of excitons in a semiconductor quantum well. The creation of excitons requires absorption of the incoming pump-laser light. Thus, the absorption spectrum of the medium acts as a spectral filter for the emitted light. Surprisingly, absorption can even improve quantum effects, as is demonstrated for the squeezing of the resonance fluorescence of the quantum-well system. This effect can be explained by an improved phase matching due to absorption.
The problem of spectral filtering of quantized light fields is studied, based on the recently developed quantum-optical theory of the action of passive, lossless optical systems [L. Kn\"oll, W. Vogel, and D.-G. Welsch, Phys. Rev. A 36, 3803 (1987)]. Expressions for the operator of the electric field strength of the light and the normally and time-ordered field-correlation functions are derived for the case of a Fabry-P\'erot interferometer being present. Various kinds of field decomposition that are usually considered in classical optics are studied. The results are compared with the Fourier approach to spectral properties of light. It is shown that, dependent on the experimental scheme used, new quantum effects appear, which may prevent the observation of the Fourier structure of the light as predicted from classical optics. Quantitatively this is demonstrated for the example of spectral squeezing in resonance fluorescence, where significant discrepancies between the measured and the full Fourier spectrum are found.
The behavior of short quantum light pulses propagating in dispersive and absorbing linear ground-state dielectrics is studied, with special emphasis on squeezed pulses. The analysis is based on normally ordered correlation functions of the electric-field strength, which are related to quantities at the entrance plane, on using quantum Langevin equations. Using nonmonochromatic-mode expansion and restricting attention to a single-mode pulse in a squeezed state, the influence on squeezing of the pulse propagation in the medium is discussed in both the time and frequency domains, and it is shown that the noise reduction observable in homodyne detection sensitively depends on the phase control used. Effects, such as squeezing enhancement associated with pulse compression and the destructive influence of the spectral shift caused by absorption, are demonstrated. The numerical results are supplemented by analytical estimations derived for narrow-bandwidth Gaussian pulses. \textcopyright{} 1996 The American Physical Society.
A quantum theory of the optical field in presence of a linear dispersive medium with losses representing a passive optical device is given. The medium is modelled by quantum oscillators coupled to thermal reservoirs. Time-ordered correlation functions of the optical field can be expressed by integrals of time-ordered source operators multiplied by classical field propagators which are influenced by dispersion and loss effects. Additionally correlation functions of thermal source quantities are needed. For a dielectric layer the propagator is derived, and some simple applications are discussed.