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Journal of Optics B Quantum and Semiclassical Optics

A noiseless amplifier paradox

Scott Roger Shepard

Published May 24, 2002• 1 citation
Publisher

Abstract

Semiclassically, the signal-spontaneous beat noise in an optical amplifier can be reduced by 3 dB via a filtering technique. This creates a paradox since the noise figure's quantum limit of 3 dB could then be reduced to 0 dB, implying noiseless amplification even though noise is still being introduced by the amplifier. We discuss ways in which this paradox might be resolved and present experimental evidence that dispenses (up to the noise floor of our detectors) with one of these. A semiclassical treatment of the effects of a real (rather than ideal) filter is also presented and suggestions are made for improved (multi-mode) quantum models of this noise.

DOI
10.1088/1464-4266/4/3/382

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Semiclassically, the signal-spontaneous beat noise in an optical amplifier can be reduced by 3 dB via a filtering technique. This creates a paradox since the noise figure's quantum limit of 3 dB could then be reduced to 0 dB, implying noiseless amplification even though noise is still being introduced by the amplifier. We discuss ways in which this paradox might be resolved and present experimental evidence that dispenses (up to the noise floor of our detectors) with one of these. A semiclassical treatment of the effects of a real (rather than ideal) filter is also presented and suggestions are made for improved (multi-mode) quantum models of this noise.
The beat between an amplified optical signal and the amplified spontaneous emission (ASE) noise is typically the primary limitation to the performance of optical fiber amplifiers. A filtering technique which might reduce this beat noise by 3dB creates a paradox since the noise figure's quantum limit of 3dB could then be reduced to 0dB implying noiseless amplification, which is impossible. The conjecture that this paradox might be resolved by different attenuations of the quantum and semiclassical descriptions of signal-spontaneous noise has been experimentally rejected . Herein, we present a variation of that experiment and telecommunication' applications of this filtering technique are discussed.
We show that a saturable amplifier can beat the "3 dB" quantum noise figure of linear amplifiers, approaching the ideal "0 dB" Heisenberg limit. Noise suppression is due to nonlinear saturation effects which cut off the high-intensity tail of the photon distribution. A Monte Carlo simulation of an actual semiconductor laser amplifier leads to a minimum noise figure of 0.51 dB, with a still sizable gain of 10.8 dB. The best performance corresponds to an output signal photon number which equals 0.7 times the saturation number.
We used a spatially broadband optical parametric amplifier for image amplification. In the phase-sensitive configuration of the amplifier, we observed noiseless amplification of input images. For a gain of $\ensuremath{\simeq}2.5$, we measured noise-figure values of ( $0.2\ifmmode\pm\else\textpm\fi{}0.6$) and ( $0.4\ifmmode\pm\else\textpm\fi{}0.5$) dB, respectively, for two amplifiers of different lengths. These experimental values agree with theory (for an ideal noiseless amplifier the noise figure is 0 dB) and are almost 2 dB lower than the quantum limit of an ideal phase-insensitive amplifier.
After pointing out some questionable assumptions of the standard beating theory, we formulate a new semiclassical wave theory of the noise in optical amplifiers. The theory is simple yet rigorous and uses a few quantum statements in a classical signal framework. The amplifier is modeled as a 2/spl times/2 port device, and the amplified spontaneous emission and associated noise are shown to be just the amplified coherent state (or vacuum state) fluctuation of the field entering the idler input. The new theory can treat other closely related detection schemes as well, correctly supplying both mean signal and noise.
Quantum fluctuations in optical amplification are investigated with a nondegenerate optical parametric amplifier whose internal idler mode is coupled to a squeezed vacuum. Reductions of the inherent quantum noise of the amplifier are observed with a minimum noise level 0.7 dB below the usual noise level of the amplifier with its internal idler mode in a vacuum state. With a small coherent field as the signal input, the amplified output exhibits an improvement in signal-to-noise ratio of 0.5 dB for the case of a squeezed-vacuum as compared to a vacuum state for the amplifier's internal mode.
We demonstrate experimentally that a phase-sensitive optical parametric amplifier used to amplify the incoming optical signal on a lossy photodiode improves the noise figure of detection. At high parametric gains this noise figure tends to 0 dB corresponding to a detection quantum efficiency approaching 100%. This result contrasts with the performance of preamplification by a classical laserlike amplifier in which the noise figure tends to 3 dB giving a saturation of the detection quantum efficiency at 50%.