Gain, directionality and noise in microwave SQUID amplifiers: Input-output approach

摘要

We present a new theoretical framework to analyze microwave amplifiers basedon the dc SQUID. Our analysis applies input-output theory generalized forJosephson junction devices biased in the running state. Using this approach weexpress the high frequency dynamics of the SQUID as a scattering between theparticipating modes. This enables us to elucidate the inherently nonreciprocalnature of gain as a function of bias current and input frequency. This methodcan, in principle, accommodate an arbitrary number of Josephson harmonicsgenerated in the running state of the junction. We report detailed calculationstaking into account the first few harmonics that provide simplesemi-quantitative results showing a degradation of gain, directionality andnoise of the device as a function of increasing signal frequency. We alsodiscuss the fundamental limits on device performance and applications of thisformalism to real devices.