Optimization of dc SQUID linear amplifiers and the quantum noise limit

A model for inductively coupled linear amplifier and magnetometer circuits employing superconducting quantum interference devices (dc SQUID's), which is accurate to all values in the coupling strength, is described. The model explicitly includes the interaction between the input circuit and the dc SQUID. The optimization of the untuned linear amplifier is discussed in detail. The uncertainty principle constraint on the noise temperature of a linear amplifier is shown to place a constraint on the minimum achievable values of the noise figures of an isolated dc SQUID in the quantum noise limit.