Designing arrays of Josephson junctions for specific static responses

TL;DR

This paper presents a method to design arrays of Josephson junctions with specific static current responses by solving an inverse Fourier problem, enabling tailored superconducting devices for applications like magnetometry and Terahertz oscillators.

Contribution

It introduces a novel inverse design approach for Josephson junction arrays using Fourier analysis, simplifying the creation of devices with desired static current patterns.

Findings

The maximum current pattern is modeled as a cosine Fourier series.

Inverse Fourier transform is used to determine junction parameters.

Examples demonstrate tailored device designs for specific responses.

Abstract

We consider the inverse problem of designing an array of superconducting Josephson junctions that has a given maximum static current pattern as function of the applied magnetic field. Such devices are used for magnetometry and as Terahertz oscillators. The model is a 2D semilinear elliptic operator with Neuman boundary conditions so the direct problem is difficult to solve because of the multiplicity of solutions. For an array of small junctions in a passive region, the model can be reduced to a 1D linear partial differential equation with Dirac distribution sine nonlinearities. For small junctions and a symmetric device, the maximum current is the absolute value of a cosine Fourier series whose coefficients (resp. frequencies) are proportional to the areas (resp. the positions) of the junctions. The inverse problem is solved by inverse cosine Fourier transform after choosing the area of the central junction. We show several examples using combinations of simple three junction circuits. These new devices could then be tailored to meet specific applications.