Print Email Facebook Twitter Dynamical edge-vortex excitations: injection, braiding and detection Title Dynamical edge-vortex excitations: injection, braiding and detection Author Flór, Ian Matthias (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Applied Sciences) Contributor Beenakker, Carlo (mentor) Akhmerov, A.R. (mentor) Dubbeldam, J.L.A. (mentor) Degree granting institution Delft University of Technology Programme Applied Mathematics | Applied Physics Project Master Thesis Date 2023-02-13 Abstract The detection of non-Abelian exchange statistics is an open challenge which holds important promises for the advent of topological quantum computation. A recent work proposes to rely on the edges to reveal the braiding statistics of nonAbelian anyons in the bulk, in an entirely deterministic dynamical process. A time-dependent gap in a Josephson junction couples two co-propagating Majorana fermions, and as the gap closes, a pair of edge-vortices is injected into the edges. Because these defects have the same non-Abelian statistics, they are braided with vortices in the bulk. Conveniently, the fusion of the edge-vortices results in a quantized unit of charge at the exit. However, this process is so far only predicted in the adiabatic limit. In this work, this assumption is relaxed by means of a full manybody evolution of the superconducting ground state in the Bogoliubov-de-Gennes formalism. Beyond revealing the collective nature of the edge-vortex excitation, we demonstrate that the quantization of charge still holds if the system does not return to the ground state. Furthermore, the effect of path length difference between the edge-vortices confirms the theoretical predictions done in another work on the subject. At fast injections, we reveal weak oscillations in current contributed by the bound states in the junction which average to zero and are removed in the short junction limit. This work is concluded with a preliminary evaluation of the manybody parity operator, which indicates that the edge-vortex may encode the parity of the bulk vortices. This opens the possibility for sequential qubit manipulations on the edge-vortex. Subject Edge vortexMajorana zero modenon-Abelian anyons braiding To reference this document use: http://resolver.tudelft.nl/uuid:2a539675-df6d-4caf-b153-232d05655106 Embargo date 2023-02-27 Part of collection Student theses Document type master thesis Rights © 2023 Ian Matthias Flór Files PDF edgevortex.pdf 5.18 MB Close viewer /islandora/object/uuid:2a539675-df6d-4caf-b153-232d05655106/datastream/OBJ/view