Dynamical formation and manipulation of Majorana fermions in driven quantum wires

TL;DR

This paper investigates how to dynamically generate and control Majorana fermions in driven quantum wires, emphasizing the importance of adiabatic protocols for maintaining their topological properties for quantum computing.

Contribution

It demonstrates that only slow, adiabatic protocols can reliably produce and manipulate Majorana fermions in superconducting nanowires, highlighting the limitations of sudden quenches.

Findings

Sudden quenches cannot produce fully developed Majorana fermions.

Adiabatic protocols enable the topological phase to be reached.

The degree of adiabaticity affects Majorana fermion manipulation.

Abstract

Controlling the dynamics of Majorana fermions (MF) subject to time-varying driving fields is of fundamental importance for the practical realization of topological quantum computing. In this work we study how it is possible to dynamically generate and maintain the topological phase in one-dimensional superconducting nanowires after the temporal variation of the Hamiltonian parameters. Remarkably we show that for a sudden quench the system can never relax towards a state exhibiting fully developed MF, independently of the initial and final Hamiltonians. Only for sufficiently slow protocols the system behaves adiabatically, and the topological phase can be reached. Finally we address the crucial question of how "adiabatic" a protocol must be in order to manipulate the MF inside the topological phase without deteriorating their Majorana character.