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arXiv:quant-ph/9811062 · Europhysics Letters (EPL)

Quantum noise in ideal operational amplifiers

Jean-Michel Courty, Francesca Grassia, Serge Reynaud

Published Apr 1, 1999• 14 citations
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Abstract

We consider a model of quantum measurement built on an ideal operational amplifier operating in the limit of infinite gain, infinite input impedance and null output impedance and with a feedback loop. We evaluate the intensity and voltage noises which have to be added to the classical amplification equations in order to fulfill the requirements of quantum mechanics. We give a description of this measurement device as a quantum network scattering quantum fluctuations from input to output ports.

DOI
10.1209/epl/i1999-00558-3

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We consider a model of quantum measurement built on an ideal operational amplifier operating in the limit of infinite gain, infinite input impedance and null output impedance and with a feedback loop. We evaluate the intensity and voltage noises which have to be added to the classical amplification equations in order to fulfill the requirements of quantum mechanics. We give a description of this measurement device as a quantum network scattering quantum fluctuations from input to output ports.
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.
We have measured the quantum noise added to a signal by a Raman amplifier. This was done using a modified Mach-Zender interferometer with an amplifier placed in each leg. Quantum noise added by the amplifiers manifests itself by degrading the visibility of the ensemble-average output fringe patterns. The amount of noise added by the amplifiers is deduced from the degradation of the visibility. The experimental results are compared with both ideal, single-mode amplifier theory and Raman theory. We find that the Raman amplifier operates near the quantum limit with only a few input photons per mode required to dominate the noise added by the amplifiers.
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.
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.