Time-dependent driving and topological protection in the fractional Josephson effect

The control of any type of quantum hardware invariably necessitates time-dependent driving. If the basis depends on the control parameter, the presence of a time-dependent control field yields an extra term in the Schr\"odinger equation that is often neglected. Here, we examine the effect of this term in a flux-controlled Majorana junction. We show that a time-varying flux gives rise to an electromotive force which is amplified when truncating to the junction's low-energy degrees of freedom. As a result, it compromises the robustness of the ground-state degeneracy present in the absence of the drive. The resulting flattening of the energy spectrum can be measured by a strong suppression of the dc supercurrent.