Abstract

We present the general theory of the linear response of a single boson mode embedded in an arbitrary background treated as a reservoir. This gives the master equation for linear amplifiers and attenuators. A conservation law similar to the Manley–Rowe relation aids the derivations. For a rigged reservoir the master equation is found to contain anomalous terms. We divide the reservoir correlation functions into linear-response and fluctuation contributions. The former give gain or loss; the latter determine the noise. The equation is written for the Wigner function, because this is suitable to describe squeezed states. The anomalous terms make the noise properties anisotropic, and the output may be squeezed, in contrast to that emerging from a device interacting with a thermal bath. For both components the output satisfies the added-noise inequality of Caves. We derive expressions for the excess noise in terms of reservoir correlation functions. In a thermal bath a fluctuation-dissipation theorem guarantees that the amplifier output cannot be squeezed when the gain exceeds the cloning value 2.

© 1987 Optical Society of America

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