Emulating Majorana fermions and their braiding by Ising spin chains

by Alexander Shnirman

at Condensed Matter Theory Seminar

Wed, 28 Jun 2017, 13:30
Physics building (#54) room 207


We analyse the control of Majorana zero energy states by mapping the fermionic system onto a chain of Ising spins Although the topological protection is lost for the Ising chain the properties of this system provide added insight into the nature of the quantum states By controlling the local magnetic field the Ising chain can be separated into topological and non topological parts In this paper we propose topologically non protected schemes which allow performing the braiding operation and in fact also more general rotations We consider a T junction geometry but we also propose a protocol for a strictly one dimensional setup Both setups rely on an extra spin 1 2 coupler included either in the T junction or as part of the chain such that it controls one of the Ising links Depending on the quantum state of the coupler this link can be either ferromagnetic or antiferromagnetic The coupler can be manipulated once the topological parts of the chain hosting the Majorana fermions are moved far away Our scheme overcomes limitations which are a consequence of the 1D character of the Jordan Wigner transformation We also propose an experimental implementation of our scheme based on a chain of flux qubits with a design providing the needed control fields

Created on 25-06-2017 by Bar Lev, Yevgeny (ybarlev)
Updaded on 25-06-2017 by Bar Lev, Yevgeny (ybarlev)