I. Introduction
Over the past two decades, there has been a significant shift toward the miniaturization of quantum experiments and technologies. Such miniaturization has many advantages and applications, including the improved scalability of ion-trap quantum computers [1]–[3], the development of atom chips for quantum sensing with condensates [4]–[6], and (more recently) toward the tests of quantum gravity using Stern–Gerlach interferometry with chip-based traps [7]. The primary motivation for the work discussed herein is toward the miniaturization of a planar magnetic field source for trapped electrons in a Penning trap [8]–[11]—the so-called Geonium Chip—which forms the functional hardware of a reliable and tunable single microwave photon detector [12], with potential applications in defense, microscopy, and communications [13], [14]. Conventional Penning trap experiments use large superconducting solenoids as their magnetic field source [15], [16], similar to those used in nuclear magnetic resonance (NMR) spectroscopy. To our knowledge, while remote magnetization schemes have been successfully implemented in shim coils for NMR [17], flux pumping as a method for magnetization or field shimming in an ion trap has never previously been employed. The magnetization technique discussed here could also be useful for other scalable atomic experiments and quantum hardware, particularly chip-based traps for cold atoms and condensates. In such experiments, high magnetic field stability and precise control of the magnetic field distribution are essential to their operation; yet, the overall required magnetic field strengths are considerably lower than those required for a Penning trap (on the order of millitesla, rather than tesla [18]).