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

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.

7 pages, 5 figures

References in corpus (7)

• Non-Abelian Anyons and Topological Quantum Computation
• Spontaneous Relaxation of a Charge Qubit under Electrical Measurement
• Fusion of Majorana Bound States with Mini-Gate Control in Two-Dimensional Systems
• Readout of Majorana Qubits
• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Fusion protocol for Majorana modes in coupled quantum dots
• Fusion rules in a Majorana single-charge transistor

Cited by in corpus (2)

• Transport and fusion of Majorana zero modes in the presence of nonadiabatic transitions
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model