PHYSICAL REVIEW B 109, 085403(2024)
Probing the non-Abelian Fusion of a Pair of Majorana Zero Modes
Jing Bai1, Qiongyao Wang1, Luting Xu1, Wei Feng1,* and Xin-Qi Li2,1,†
1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300072, China
2 Center for Quantum Physics and Technologies, School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China
* fwphy@tju.edu.cn, xinqi.li@tju.edu.cn
Abstract
In this paper we perform real-time simulations for probing the non-Abelian fusion of a pair of Majorana zeromodes (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.
