Fusion Channel Dependent Magnetic Moments in Topological Josephson Junctions

A key characteristic of non-Abelian anyons is that they may fuse to form multiple particle types. In topological superconductors, two Majorana zero modes may fuse to form a fully paired state or a state with a single unpaired quasiparticle. In order to read out the state of a topological qubit one needs a method to distinguish between these two scenarios. In this talk, I will explore how these two fusion channels should have opposite magnetic moments in a Rashba 2DEG Josephson Junction, and we propose methods to detect this in an experiment with two Josephson vortices. Furthermore, we will discuss how one may use 4 Josephson vortices to probe non-Abelian fusion rules.