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arXiv:2010.13851 · Physical Review A

Quantum limits on noise for a class of nonlinear amplifiers

Jeffrey M. Epstein, K. Birgitta Whaley, Joshua Combes

Published May 14, 2021• 8 citations
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Abstract

Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogs are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detectors, these amplifiers implement ideal measurements of the normal operator.

DOI
10.1103/physreva.103.052415

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Nonlinear amplifiers such as the transistor are ubiquitous in classical technology, but their quantum analogs are not well understood. We introduce a class of nonlinear amplifiers that amplify any normal operator and add only a half quantum of vacuum noise at the output. In the large-gain limit, when used in conjunction with a noisy linear detectors, these amplifiers implement ideal measurements of the normal operator.
Nonlinear amplifiers, such as the transistor, are ubiquitous in classical technology. Little is understood about the noise properties and applications of quantum nonlinear amplifiers. We introduce a class of nonlinear amplifiers that allow one to measure any normal operator with a linear detector while adding a half-quantum of vacuum fluctuations as noise at the output. When these nonlinear amplifiers are used in conjunction with noisy linear detectors, the resulting measurement in the large gain limit becomes equivalent to ideal projective measurement of the normal operator.
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.
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.
In a linear amplifier, the output signal is linearly related to the input signal with an additive noise that is independent of the input. Here we show that entanglement between the input signal and the amplifying medium can produce exponentially-large decoherence in an ideal optical amplifier even when the gain is arbitrarily close to unity and the added noise is arbitrarily small. These nonlinear effects show that the usual input/output relationship of a 'linear' amplifier does not provide a complete description of its performance.