Tracking the motion of Josephson vortices and the Majorana fermion states bound to them in S-TI-S junctions networks designed for braiding*

Networks of S-TI-S (Superconductor-Topological Insulator-Superconductor) lateral Josephson junctions provide a potential platform for nucleating, manipulating, and braiding Majorana fermion states (MFs) for quantum information processing. In this system, the MFs are bound to the cores of Josephson vortices where the phase difference across the junction is an odd multiple of π and can be manipulated by moving the vortices. To assist in the design of braiding circuits, we are exploring ways to monitor the position of Josephson vortices in junction networks. A direct approach is to image the location of the vortices via Scanning SQUID Microscopy (SSM), for which we are developing an ultralow temperature SSM with sub-micron resolution based on a pickup coil fabricated by electron-beam lithography and focused ion-beam etching and an optical interferometer approach mechanism. We can also indirectly determine the vortices configuration by measuring the modulation of the supercurrent vs. magnetic field modulation patterns. We report on progress toward implementing these techniques.