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Journal of Modern Optics

Squeezed Quantum Fluctuations and Noise Limits in Amplifiers and Attenuators

Claire R Gilson, Stephen Mark Barnett, Stig Stenholm

Published Jun 1, 1987• 25 citations
Publisher

Abstract

Conventional amplifiers add quantum noise to a signal. Both amplifiers and attenuators lead to a reduction of the signal-to-noise ratio. We find, however, that devices exhibiting squeezed fluctuations in the gain or loss medium lead to an improved signal-to-noise ratio, in one quadrature of the output, compared to the limits associated with conventional devices. We investigate amplifier and attenuator noise properties using a simple model in which the gain or loss medium is a broad-band reservoir in a specially prepared, or ‘rigged’, state.

DOI
10.1080/09500348714550861

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Conventional amplifiers add quantum noise to a signal. Both amplifiers and attenuators lead to a reduction of the signal-to-noise ratio. We find, however, that devices exhibiting squeezed fluctuations in the gain or loss medium lead to an improved signal-to-noise ratio, in one quadrature of the output, compared to the limits associated with conventional devices. We investigate amplifier and attenuator noise properties using a simple model in which the gain or loss medium is a broad-band reservoir in a specially prepared, or ‘rigged’, state.
How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.
In this paper we utilize the idea of multiatom squeezed states to build a rigged reservoir for linear amplification or attenuation. The reservoir state is constructed such that the processed boson mode is driven by a collective reservoir operator that offers squeezed stationary noise. Then the amplifier can retain squeezing for arbitrary gain, and the amplifier added noise can be made widely different in the two quadrature components. The attenuator drives the signal toward a squeezed noise state. In contrast to the case of a multimode squeezed reservoir, we can in this case make the noise exactly zero for one component, but only at the expense of a vanishing linear gain (or loss) coefficient. The noise-over-gain ratio can, however, become arbitrarily small. The results are discussed and related to earlier work.
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.
Recently optical parametric amplifiers (OPAs) with vacuum inputs have been extensively studied and shown to generate a significant amount of squeezing, but little is known about the quantum noise behavior of an OPA with an injected signal field. We have performed a linearized quantum analysis of a nondegenerate OPA operated in the saturated gain regime showing that the amplified output intensity of a coherent-state input signal becomes squeezed when the classical small-signal gain falls below unity. In uses such as master-oscillator power amplifiers, for which the signal of interest is the mean output intensity, the output signal-to-noise ratio (SNR) can be higher than the input SNR over a broad operating range. For an OPA pumped at 90% of threshold, the SNR improvement is about a factor of 3, and with a 10-Db amplitude squeezed pump, the improvement increases to about a factor of 7. Such a tunable gain-saturated OPA with large-signal gain and improved SNR can be potentially useful in digital communication.
It has long been known that amplification will degrade an optical signal and will rapidly destroy any intrinsically quantum features that may have been associated with the input. However, devices that exhibit squeezed fluctuations in the gain or loss medium can reduce the detrimental effects of the inevitable amplifier noise. This makes it possible to retain nonclassical features (in particular squeezing) at higher levels of gain than is possible in conventional devices. In this paper we study the effect of these amplifiers on the photon-number fluctuations. We find that, for suitable inputs, phase-sensitive amplifiers can reduce the tendency for the photon-number distribution to spread and allow us to retain sub-Poissonian statistics at a higher level of gain than is possible in conventional devices.
Linear quantum amplifiers are indispensable tools for quantum technologies, yet their performance is fundamentally limited by quantum noise, precluding any signal-to-noise ratio (SNR) enhancement unless supplemented by post-selection or non-classical resources. To surpass this limitation, we propose a nonlinear quantum amplification strategy that exploits the interplay between a gain-stabilized bright eigenmode of a coupled two-mode bosonic system and Kerr nonlinearity. We demonstrate that this interplay enables the signal gain to surpass the noise gain in a selected quadrature, leading to a net increase in the SNR beyond the quantum limits of conventional linear amplifiers. Our work thus establishes a novel nonlinear amplification paradigm capable of enhancing the SNR, with promising applications across quantum information processing, quantum communications, and quantum metrology.