Probing the non-Abelian fusion of a pair of Majorana zero modes

TL;DR

This paper uses real-time simulations to explore the non-Abelian fusion of Majorana zero modes, proposing detection schemes via charge measurements in quantum dots and analyzing measurement signals for fusion outcome identification.

Contribution

It introduces practical detection methods for non-Abelian fusion outcomes of Majorana zero modes using charge measurements and continuous weak measurement analysis.

Findings

Gradual coupling provides a simpler detection scheme.

Charge occupation variations reveal fusion outcomes.

Power spectrum analysis identifies fusion signatures.

Abstract

In this work, we perform real time simulations for probing the non-Abelian fusion of a pair of Majorana zero modes (MZMs). The nontrivial fusion outcomes can be either a vacuum, or an unpaired fermion, which reflect the underlying non-Abelian statistics. The two possible outcomes can cause different charge variations in the nearby probing quantum dot (QD), while the charge occupation in the dot is detected by a quantum point contact. In particular, we find that gradual fusion and gradual coupling of the MZMs to the QD (in nearly adiabatic switching-on limit) provide a simpler detection scheme than sudden coupling after fusion to infer the coexistence of two fusion outcomes, by measuring the occupation probability of the QD. For the scheme of sudden coupling (after fusion), we propose and analyze continuous weak measurement for the quantum oscillations of the QD occupancy. From the power spectrum of the measurement currents, one can identify the characteristic frequencies and infer thus the coexistence of the fusion outcomes.