Spatial control of supercurrent distribution in Josephson junctions*

Spatially separated Majorana zero modes (MZM) have generated interest as a promising basis for encoding topologically protected quantum information, but their hallmark non-Abelian exchange statistics have yet to be observed. One way to probe the non-Abelian phase is to perform a braiding sequence in real space, in which localized MZMs from different fermionic modes are moved around one another prior to fusion, and to sense the resulting charge excitation (or lack thereof). A prerequisite for such an experiment is the stable transport of MZMs on a timescale that is adiabatic compared to the inverse energy gap yet limited by the quasiparticle poisoning time. This may be achieved by controlling the charge distribution in a planar Josephson junction using an array of discrete electrostatic gates. We report preliminary device design and characterization of the junction critical current as a function of magnetic field applied perpendicular to the plane. We study this Fraunhofer pattern in the topologically trivial regime to reconstruct the supercurrent distribution in the channel and determine its spatial dependence on the applied gate voltages.