A Numerical Treatment of the rf SQUID: II. Noise Temperature

Abstract

We investigate rf SQUIDs (Superconducting QUantum Interference Devices), coupled to a resonant input circuit, a readout tank circuit and a preamplifier, by numerically solving the corresponding Langevin equations. The quantity of interest is the noise temperature T _N . We use an analytical expression T _N0,opt, which is already optimized for the parameters of the input circuit, and vary the model parameters of the remaining circuit to minimize T _N0,opt. We also compare T _N0,opt to numerical simulations of the full circuit and find good agreement. The best device performance is obtained when β′ _L ≡2π LI ₀/Φ ₀ is in the range 0.5–0.9; L is the SQUID inductance, I ₀ the junction critical current and Φ ₀ the flux quantum. For a tuned input circuit we find an optimal noise temperature T _N0,opt≈3Tf/f _c , where T, f and f _c denote temperature, signal frequency and junction characteristic frequency, respectively. This value is close to the optimal noise temperatures obtained by approximate analytical theories carried out previously in the limit β′ _L ≲1. We study the dependence of T _N0,opt on various model parameters away from their optimum values, and often find much lower values of T _N0,opt than predicted by the analytical theory. We finally discuss implications for devices that can be implemented experimentally.