Holographic reconstruction of magnetic field distribution in a Josephson junction from diffraction-like Ic(H) patterns

Abstract

A general problem of magnetic sensors is a trade-off between spatial resolution and magnetic-field sensitivity. With decreasing sensor size its resolution is improved but the sensitivity is deteriorated. Obviation of such a trade-off requires development of super-resolution imaging technique not limited by sensor size. Here we present a proof of concept for a super-resolution method of magnetic imaging by a Josephson junction (JJ). It is based on a solution of an inverse problem - reconstruction of a local magnetic-field distribution within a junction from the dependence of the critical current on an external magnetic field, Ic(H). The method resembles the Fourier-transform holography, with the diffractionlike Ic(H) pattern serving as a hologram. A simple inverse problem solution, valid for an arbitrary symmetric case, is derived. We verify the method numerically and show that the accuracy of reconstruction does not depend on the junction size and is only limited by the field range of the Ic(H) pattern. Finally, the method is tested experimentally using planar Nb JJs. Super-resolution reconstruction of stray magnetic fields from an Abrikosov vortex, trapped in the junction electrodes, is demonstrated. Thus our method facilitates both high field sensitivity and high spatial resolution, obviating the trade-off problem of magnetic sensors. We conclude that the holographic magnetic imaging by a planar JJ can be used in scanning probe microscopy.