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arXiv:1301.4787

Quantum Noise in Conventional Optical Heterodyne Devices

Dechao He, Boya Xie, Xiao, Yu, Sheng Feng

Published Jan 21, 2013• 0 citations
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Abstract

By invoking the quantum theory of optical coherence, we theoretically show that the quantum noise in conventional optical heterodyne devices, which were previously identified as usual phase-insensitive amplifiers with additional quantum noise, is similar to that in optical homodyne devices, as verified by experimental data. Albeit more study is demanded to understand this result, it is certain that neither the uncertainty principle nor Caves's theorem for quantum noise of linear amplifiers sets a limit to the quantum noise of heterodyne devices.

DOI
10.48550/arxiv.1301.4787

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By invoking the quantum theory of optical coherence, we theoretically show that the quantum noise in conventional optical heterodyne devices, which were previously identified as usual phase-insensitive amplifiers with additional quantum noise, is similar to that in optical homodyne devices, as verified by experimental data. Albeit more study is demanded to understand this result, it is certain that neither the uncertainty principle nor Caves's theorem for quantum noise of linear amplifiers sets a limit to the quantum noise of heterodyne devices.
It is nontrivial to describe in theory the quantum behavior of a phase-sensitive heterodyne detector with a bichromatic local oscillator. On the one hand, a 3 dB noise penalty is expected for the detector due to the existence of an image band vacuum, which was assumed in a previous theoretical study. On the other hand, as a phase-sensitive device, the detector should be free of the 3 dB extra quantum noise, as verified by a recent experiment. However, the mechanism for the absence of the 3 dB noise penalty in the experimental observation remains unknown. To understand the relevant physics, we develop a comprehensive quantum theory, in agreement with experiment, for phase-sensitive heterodyne detection. This work should be important for us to understand the origin of the quantum noise in heterodyne detection.
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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.
Using Caves's theory on the quantum-noise limit in an amplifier, we consider the quantum limit on noise in a Raman amplifier. We show explicitly that the full quantum equations for the Raman interaction can be transformed into the general form for a quantum amplifier. In addition, we show that in the steady-state limit the Raman amplifier becomes a phase-insensitive amplifier. At this limit we find that the output signal-to-noise ratio is unity when one photon per mode is input. Thus we conclude that the Raman amplifier, in the phase-insensitive limit, will operate at the quantum-noise limit.
A traditional heterodyne detector, as a phase-insensitive device, suffers the well-known 3 dB noise penalty caused by image sideband vacuum. In contrast, a heterodyne detector with a bichromatic local oscillator, as a phase-sensitive device, should be exempted from the 3 dB noise penalty, in spite of the existence of the image sideband vacuum. Assuming coherent light at the input, we develop in this work a theory to describe the quantum nature of the phase-sensitive heterodyne detector, in a good agreement with experiment. The absence of the quantum noise of the image vacuum modes in the heterodyne detector may be explained by that the studied detector senses only a single field of light, i.e., the signal field, according to the theory developed.