Effect of Josephson junction parameter spread on the performance of SQUID arrays

Abstract: Josephson junctions based on grain boundaries, such as those made of Yttrium Barium Copper Oxide (YBCO), exhibit inherent parameter spreads in their critical current and normal state resistance. This variation in junction properties leads to a decrease in array performance for magnetic sensing applications. Therefore, we must develop a quantitative understanding of how junction parameter spreads impact arrays with different designs. In this paper, we use numerical simulations to investigate how the ensemble averaged voltage modulation depth (eta) of one-dimensional SQUID arrays varies with the statistical spread in the junction parameters. In these calculations for arrays we vary the number of junctions, loop inductance and thermal noise strength. We show that eta decreases with increasing spread, and that this reduction is accelerated further by the number of junctions and SQUID cell inductance, but is robust to changes in the thermal noise strength.