Quantum limits on noise in linear amplifiers

Carlton M. Caves
Phys. Rev. D 26, 1817 – Published 15 October 1982
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Abstract

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 ("cosωt" and "sinωt"), 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.

  • Received 18 August 1981

DOI:https://doi.org/10.1103/PhysRevD.26.1817

©1982 American Physical Society

Authors & Affiliations

Carlton M. Caves

  • Theoretical Astrophysics 130-33, California Institute of Technology, Pasadena, California 91125

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Vol. 26, Iss. 8 — 15 October 1982

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