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Journal of Optics

Quantum noise properties of non-ideal optical amplifiers and attenuators

Zhimin Shi, Ksenia Dolgaleva, Robert W. Boyd

Published Nov 24, 2011• 11 citations
Publisher

Abstract

We generalize the standard quantum model (Caves 1982 Phys.Rev. D 26 1817) of the noise properties of ideal linear amplifiers to include the possibility of non-ideal behavior.We find that under many conditions the non-ideal behavior can be described simply by assuming that the internal noise source that describes the quantum noise of the amplifier is not in its ground state.We validate this model by showing that it reproduces the known predictions of two models of non-ideal amplifiers: a laser amplifier with incomplete inversion and a cascade of alternating ideal amplifiers and ideal attenuators.We also describe implications of this model for practical devices.

DOI
10.1088/2040-8978/13/12/125201

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We generalize the standard quantum model (Caves 1982 Phys.Rev. D 26 1817) of the noise properties of ideal linear amplifiers to include the possibility of non-ideal behavior.We find that under many conditions the non-ideal behavior can be described simply by assuming that the internal noise source that describes the quantum noise of the amplifier is not in its ground state.We validate this model by showing that it reproduces the known predictions of two models of non-ideal amplifiers: a laser amplifier with incomplete inversion and a cascade of alternating ideal amplifiers and ideal attenuators.We also describe implications of this model for practical devices.
The input-output relations for linear amplifiers and attenuators that have two input and two output channels are used to derive inequalities that relate their gain profiles and output noise spectra. The results generalize earlier derivations, which mainly focus their attention on single-channel devices, to the two-ended amplifiers and attenuators often used in practical communications systems. The present inequalities are satisfied by the results of previous calculations for specific model systems. It is shown that; in contrast to single-channel devices, a two-ended system can act as an amplifier for some input signals and an attenuator for others, even when all the signal frequencies are the same. The output from the two-channel amplifier has a minimum noise determined by the sum of the gains for both input channels, even when only one input channel is used and the other is in its vacuum state. The conditions on device construction needed to achieve equal gains for signals that arrive at the two ends of the device are determined. The present results reduce to those of single-channel theory in special cases where the two output channels are each separately fed by only one of the two input channels.
In an ideal linear amplifier, the output signal is linearly related to the input signal with an additive noise that is independent of the input. The decoherence of a quantum-mechanical state as a result of optical amplification is usually assumed to be due to the addition of quantum noise. Here we show that entanglement between the input signal and the amplifying medium can produce an exponentially-large amount of decoherence in an ideal optical amplifier even when the gain is arbitrarily close to unity and the added noise is negligible. These effects occur for macroscopic superposition states, where even a small amount of gain can leave a significant amount of which-path information in the environment. Our results show that the usual input/output relation of a linear amplifier does not provide a complete description of the output state when post-selection is used.
A field noise spectral density matrix for the noise from a linear optical device, modeled as an optical multiport, is derived semi-classically. The noise is formulated in the scattering parameters, population inversion factor, and internal efficiency of the device. From this noise expression, a new equation for the amplified spontaneous emission spectral density from an optical amplifier is derived. This equation is more general than those previously published. The derivations are accomplished with the aid of methods from ordinary (classical) electrical network theory and only one quantum mechanical result regarding the noise from a conductance. As a result, the first-mentioned noise expression also includes the so-called vacuum field fluctuations. Further, the current noise spectrum of a square-law detector is derived with classical methods. The optical input to the detector includes the vacuum field fluctuations, which are shown to be the cause of the detector shot noise. Here, a second quantum mechanical result has to be employed, viz., that the vacuum field fluctuations cannot be detected alone. The results in this paper agree with the special cases found in the literature. The noise expressions are well suited for examination of the optical noise performance of arbitrary linear optical networks including, e.g., amplifiers, attenuators, isolators, reflections, filters, and couplers.>
The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.