Superconducting ‘fragments’ Reveal How to Maintain Quantum Coherence at Scale

Scientists have long sought to understand how superconductivity maintains coherence over substantial distances, a crucial factor for developing advanced quantum technologies. Xi Wang, Asbjørn C. C. Drachmann (Niels Bohr Institute, University of Copenhagen), and Candice Thomas (Purdue University) et al. now present direct imaging of long-range phase coherence within a hybrid Josephson junction array, revealing how this delicate state responds to external magnetic fields. Their research, utilising scanning SQUID microscopy, demonstrates the emergence of periodic patterns and large-scale coherence fragmentation with minimal applied flux. This work represents the first direct measurement of long-range coherence in such an array, offering vital insights into the behaviour of complex superconducting states and paving the way for improved superconducting device design. This work details how the coherence of superconductivity is governed by the interplay between local pairing and macroscopic coherence, revealing insights into its suppression near a quantum phase transition. Researchers utilized a scanning SQUID microscope to image the local susceptibility within a hybrid Josephson junction array, simultaneously accessing both the amplitude and spatial structure of sensitive superconducting states. The study employed a square lattice of narrow superconducting islands, enabling simultaneous access to both the amplitude and spatial phase structure of these sensitive states. Periodic phase patterns were observed at commensurate magnetic fillings, demonstrating a high degree of order within the system. Notably, long-range coherence was found to be strongest at zero applied magnetic field, indicating optimal superconducting behavior under these conditions. As a small magnetic field, less than one percent of a flux quantum per unit cell, was applied, the system fragmented into large regions of constant superconducting phase, revealing a complex interplay between coherence and external influence. To demonstrate the sensitivity of their technique, researchers first measured a continuous niobium superconducting grid. Below the critical temperature, the static magnetic landscape displayed quantized flux trapped within the grid cells. A susceptibility map revealed a homogeneous diamagnetic response across the grid, indicating uniform superconducting phase stiffness. Introducing weak links into the grid near the critical temperature disrupted the superconducting continuity, resulting in a significantly reduced signal and demonstrating the impact of these disruptions on phase coherence. Further investigation of a hybrid Josephson junction array revealed organized checkerboard phase patterns at integer and fractional fillings of the unit cell, aligning with theoretical predictions. Applying a small but finite magnetic field caused the array to break into spatially phase-coherent regions, identifying specific junctions where the superconducting phase remained consistent. These measurements provide a high-resolution visualization of phase coherence and its systematic suppression, offering a detailed understanding of the underlying mechanisms governing superconductivity in these complex systems. This advancement paves the way for future scanning SQUID measurements on hybrid Josephson junction arrays and the development of novel superconducting devices. Susceptometry and ac susceptibility measurements of hybrid Josephson junction arrays reveal complex magnetic responses Scanning SQUID susceptometry forms the basis of this work, enabling high-resolution imaging of the local susceptibility within a hybrid Josephson junction array. A planar SQUID, comprising a 1.5μm diameter pick-up loop and an 8μm field coil for the grid sample, and a 1.5μm pick-up loop with a 6μm field coil for the Josephson junction array, was employed to scan the superconducting landscape of the samples. The SQUID measures static magnetic flux, as depicted in figures referenced within the study, and simultaneously records local ac susceptibility by applying an alternating current through the pick-up loop at frequencies around kilo-Hertz. This ac susceptibility measurement, equivalent to the susceptibility, reveals the ac diamagnetic response of the material. When positioned above grid wires, the SQUID detects strong peaks in susceptibility due to local currents screening the applied field. Conversely, above empty grid cells, a washed-out peak emerges as screening currents flow further from the SQUID, demonstrating a pattern directly reproducing the physical dimensions of the grid. The amplitude of the susceptibility measurement provides information regarding the penetration depth, with a value of 180 /A detected for a 50-nm-thick Nb film below its critical temperature, corresponding to a penetration depth of 47nm. Sample fabrication began with the deposition of a 50-nm-thick continuous Nb grid onto a silicon substrate using e-beam evaporation under ultra-high vacuum conditions. This grid was patterned using standard photolithography and lift-off techniques with a Heidelberg Instruments MLA 150 system. The hybrid Josephson junction array was fabricated using e-beam lithography on a shallow InAs quantum well heterostructure grown on InP, terminated with 8nm of epitaxial Al. A 300nm mesa was etched into the heterostructure, followed by selective stripping of Al, and the creation of Ti/Au ohmic contacts for bonding. A high-precision Transene-D Al etch defined the JJA on the mesa, followed by the deposition of 15nm hafnia via atomic layer deposition, and a 3/16nm Ti/Au junction gate grid aligned to the JJA. Electrical connection to the junction gate was achieved with a 10/390nm Ti/Au stack, and a second 15nm hafnia layer was deposited, capped with 5/40nm Ti/Au. Both gates were shorted and fixed at 0V during the experiment. Quantified phase coherence and flux quantization in a Josephson junction array demonstrate macroscopic quantum phenomena Scanning SQUID imaging reveals periodic phase patterns at commensurate magnetic fillings within a hybrid Josephson junction array. Long-range coherence is strongest at zero applied field, with the system exhibiting fragmentation into large regions of constant superconducting phase when subjected to fields smaller than one percent of a flux quantum per unit cell. This work presents the first direct measurement of long-range phase coherence in such an array. Measurements conducted on a continuous niobium superconducting grid below its critical temperature demonstrate quantized flux trapped within the grid cells. The filling factor, defined by the average flux quantum per cell, is controlled by the external magnetic field applied during cooling. At a filling factor of -0.2, twenty percent of the cells exhibit one flux quantum level lower than the remaining cells. These observations confirm the sensitivity of the scanning SQUID to superconducting phase coherence. Further investigation focused on a hybrid Josephson junction array, revealing maximized phase coherence at zero magnetic field. Application of a small but finite magnetic field induced fragmentation of the array into spatially phase-coherent regions where the coherence length exceeds the coherence length ξ. These regions identify specific junctions maintaining phase coherence across them. The study detected organized checkerboard phase patterns at integer and fractional fillings of the unit cell, aligning with theoretical predictions. High-resolution visualization of phase coherence and its suppression was achieved, providing detailed insight into the long-range phase behavior within the Josephson junction array. Local susceptibility measurements reconstructed spatial phase information even when phase stiffness was extremely small, enabling detailed mapping of the superconducting state. Visualising spatial coherence and vortex formation in a Josephson junction array reveals complex dynamics The interplay between local pairing and macroscopic coherence governs the superconducting state, and recent work directly measures long-range coherence within a Josephson junction array. Using a scanning Superconducting Quantum Interference Device, researchers imaged local susceptibility in a hybrid array, simultaneously determining both the amplitude and spatial structure of its superconducting states. Observations reveal periodic patterns at specific magnetic field strengths, with the strongest long-range coherence occurring at zero applied field. As a small magnetic field is applied, the system fragments into sizable regions exhibiting consistent superconductivity, demonstrating how Josephson junction arrays emulate the behaviour of a superconductor. The number of non-superconducting regions increases with the magnetic field, mirroring the behaviour of vortices.

This research establishes the ability to directly image local susceptibility, providing a detailed map of phase coherence even in weakly superconducting materials, with signals significantly weaker than those from fully superconducting films. The authors acknowledge limitations related to quantifying the precise area of non-superconducting regions and estimating the flux within each. Future research will focus on tuning hybrid Josephson junction arrays between superconducting and insulating states to investigate open questions in condensed matter physics, such as the mechanism behind the anomalous phase near the superconductor-insulator transition. Further investigations will also explore triggering phase slips within the array using the scanning SQUID’s field coil, and engineering complex lattice geometries to potentially host unconventional phases and topologically protected qubits. These findings establish hybrid Josephson junction arrays as a highly tunable model system, with scanning SQUID susceptometry serving as a powerful tool for probing their fragile phase coherence. 👉 More information 🗞 Long-range phase coherence and phase patterns in hybrid Josephson junction arrays 🧠 ArXiv: https://arxiv.org/abs/2602.02255 Tags: