The Effect of Thermal Noise on the I-V Curves of High Inductance DC Squids in the Presence of Microwave Radiation

Abstract

The effect of thermal noise on the I-V curves of DC SQUIDs in the presence or absence of microwave radiation is analyzed in detail in the frame of a unitary analytical approach based on the 2D Fokker–Planck equation. The results are particularly relevant for SQUIDs with inductances comparable or higher than the fluctuation threshold inductance LF = (Φ0/2π)2/kBT (here kBis the Boltzmann constant, T is the absolute temperature, and Φ0is the flux quantum). This is the case of interest at 77 K in particular. A general analytical expression for the I-V's has been obtained that incorporates the system's operation in both cases: when it is microwave irradiated (the new device is called the Shapiro-Step SQUID) or not (the DC SQUID). That makes the analogy between the nonlinearities in the two cases straightforward. In the presence of microwave radiation the analytical expression describes the behavior of the Shapiro steps and related aspects for pumping microwave frequencies substantially larger than the characteristic frequency of the Josephson junctions, ωc = 2πIcR/Φ0(Icand R are, respectively, the critical current and the shunt resistance of the Josephson junctions). In the absence of microwave radiation the analytical expression forms the basis for a significant development of the previously obtained results for the characteristics of DC SQUIDs having β<1/π (β = 2LIc/Φ0is the reduced inductance) and large values for the noise parameter Γ = 2πkBT/IcΦ0.