Axial-Parallel Circuit Model for Macroscopic Josephson Junctions in Slug Devices: Applications in Ultra-Low-Noise Quantum Sensing

Superconducting low-inductance undulatory galvanometers (SLUGs) have emerged as promising non-lithographic alternatives to conventional super-conducting quantum interference devices (SQUIDs), offering simplified fabri- cation processes and enhanced noise performance at cryogenic temperatures. To advance the theoretical understanding of SLUGs, we propose an axial- parallel equivalence circuit model that treats SLUGs as coherent arrays of axially aligned Josephson junctions. The model effectively captures the in- terference behavior by accounting for distributed phase superposition, with the predicted I-Φ response matching experimental data within 3% error at 4.2K. High-resolution SEM imaging confirms the homogeneous distribution of weak links, validating key model assumptions. Parametric sensitivity anal- yses demonstrate strong thermal and geometric robustness, with SLUG de- vices exhibiting noise levels as low as 0.15μA at 2K and responsivity reaching 1810μA/Φ0 . The Model’s limitations under high-flux and high-temperature conditions are addressed by incorporating vortex dynamics and employing full 3D electromagnetic simulations. These findings provide a scalable frame- work for the optimisation of SLUG-based quantum sensing devices, offering a path toward the development of next-generation ultra-low-noise supercon- ducting quantum technologies.