A Stochastic Theory of dc Superconducting Quantum InterferenceDevice Responsitivity in the Presence of Thermal Fluctuations

A symmetric superconducting quantum interference device (SQUID) with two Josephson junctions in the presence of thermal fluctuations is theoretically studied through two-dimensional Fokker-Planck equations. An analytical formula of SQUID transfer function (or responsitivity) is derived by using the potential condition in the case of the steady state. It is found that the relationship between the optimum bias current I_opt and the thermal fluctuation parameter Γ is I_opt/Γ > 1. The optimal reduced dc SQUID inductance β_opt is in the range of 0.80 < β_opt <1.25, which is remarkably in agreement with the result of numerical simulation β_opt ≈ 1.