Quantum limits on noise in linear amplifiers

TLDR

The study seeks to quantify the minimum quantum‑mechanical noise that a linear amplifier must add to a signal, with particular emphasis on multimode descriptions of unequal quadrature noise. The authors extend single‑mode analysis to a multimode framework for finite‑bandwidth amplifiers, developing a theory that accounts for unequal noise in the two quadrature phases. They show that phase‑insensitive amplifiers must add at least half a quantum of noise at high gain, while phase‑sensitive amplifiers obey a noise‑product uncertainty principle with bandwidth‑dependent corrections, establishing lower limits on noise for each quadrature.

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 ("$cos\ensuremath{\omega}t$" 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.