Field Induced Oscillation of Two Majorana Modes for a finite Quantum Wire

TL;DR

This paper studies how applying a small vector potential causes intrinsic quantum oscillations of Majorana modes in a finite quantum wire, with potential applications in decoherence-free qubits.

Contribution

It reveals the oscillation behavior of Majorana modes under vector potential and proposes a method to control these oscillations using external electric fields.

Findings

Quantum walk evolution exhibits intrinsic oscillation of Majorana modes.

External electric field induces beat modulation in oscillations.

Potential application in decoherence-free qubit preparation.

Abstract

The evolution of quantum walk on a finite wire under a small increment of vector potential $\alpha$ can exhibit intrinsic quantum oscillation of the two topologically protected bound states corresponding to the Majorana modes. By tuning an external electric field corresponding to the addition of an $\alpha$ impulse at the end of each intrinsic period, the intrinsic oscillation is enveloped by a beat modulation with a longer period. This beat oscillation is useful in the preparation of decoherence-free qubit in trapped ion chain and may be observed in several experiments.