Phase Retrieval in Superconducting Josephson Junctions : From Algorithms to Magnetic Sensing Applications

Over the past few decades, scanning probe techniques have undergone remarkable development, emerging as essential tools for exploring local physical, electrical, magnetic, and optical properties at the nanoscale. Methods such as magnetic force microscopy, electrostatic force microscopy, and current-sensitive probe techniques have enabled high-resolution investigations in various fields. However, these techniques often face a fundamental trade-off between spatial resolution and sensitivity. For example, in magnetic probe approaches like scanning SQUID microscopy and magnetic force microscopy, improving spatial resolution by reducing probe size typically leads to a decrease in magnetic sensitivity. This thesis introduces a novel magnetic sensing concept based on single Josephson junctions (JJs). In this approach, diffraction-like Ic(H) patterns are interpreted as holographic encodings of the local magnetic environment. To extract this information, phase retrieval algorithms are developed to reconstruct spatial magnetic field profiles from the junction’s critical current response. By solving the inverse problem—i.e., the extraction of distortions within the junction—magnetic field distributions can be recovered with high fidelity. This capability is validated through both numerical modeling and cryogenic experiments on planar JJs subjected to localized magnetic perturbations, including Abrikosov vortices and scanning magnetic probes. Furthermore, the design and testing of a novel scanning probe are presented: a JJ integrated directly onto the cantilever of a conventional atomic force microscope, enabling its use as a magnetic holography sensor. This approach provides a scalable alternative to conventional magnetometry methods, simultaneously achieving high spatial resolution and magnetic field sensitivity—addressing a key limitation of existing techniques.