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

TL;DR

This paper investigates how time-dependent flux control affects the topological protection in Majorana junctions, revealing that dynamic driving can weaken ground-state degeneracy and suppress supercurrent, impacting quantum hardware robustness.

Contribution

It demonstrates that time-dependent control fields introduce an electromotive force that can compromise topological protection in Majorana-based systems.

Findings

Time-varying flux induces an electromotive force in Majorana junctions.

Dynamic driving can flatten the energy spectrum and reduce supercurrent.

Topological protection is sensitive to time-dependent control fields.

Abstract

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.