Numerical analysis of Josephson junction arrays for multi-order quantum voltage steps

Abstract

The dynamics of overdamped Josephson junctions under varying microwave-driving conditions have been studied through numerical simulations using the resistively-shunted junction (RSJ) model, with a focus on primary voltage metrology applications, where a significantly high number of series-connected junctions and stringent uniformity of their electrical parameters are required. The aim is to determine the optimal junction characteristics and external microwave (rf) parameters that maximize the width of quantum voltage levels (Shapiro steps) from order $n=0$ to $n > 1$. Both the rf and dc power requirements, along with the junction parameter spread and power attenuation, are analyzed as key factors that need to be optimized for improved performance of the quantum device. This work aims to advance the development of next-generation Programmable Josephson Voltage Standards (PJVS) with logic architectures that surpass the conventional binary and ternary codifications used in present quantum voltage arrays, while significantly reducing the overall number of junctions as well as the number of sub-arrays and bias lines. Existing technologies exploiting $n = 0$ and $n = \pm 1$ voltage steps are first discussed and analyzed to verify the validity of the simulation model. They are then further investigated to extend their usability with multi-order quantum steps for $n$ up to 3. From the simulation results, it follows that present junction technologies may be employed with no modifications for the simultaneous operation of quantum steps up to $n=2$, although optimal power efficiency would require a retrimming of the junction's electrical parameters. On the contrary, extending the highest step order to $n=3$ strictly requires the junction's characteristic parameters to be properly adjusted to maintain sustainable power levels as well as acceptable quantum-locking ranges.