C. W. J. Beenakker, A. Grabsch, Y. Herasymenko
SciPost Phys. 6, 022 (2019) ·
published 11 February 2019
Majorana zero-modes bound to vortices in a topological superconductor have a
non-Abelian exchange statistics expressed by a non-deterministic fusion rule:
When two vortices merge they may or they may not produce an unpaired fermion
with equal probability. Building on a recent proposal to inject edge vortices
in a chiral mode by means of a Josephson junction, we show how the fusion rule
manifests itself in an electrical measurement. A $2\pi$ phase shift at a pair
of Josephson junctions creates a topological qubit in a state of even-even
fermion parity, which is transformed by the chiral motion of the edge vortices
into an equal-weight superposition of even-even and odd-odd fermion parity.
Fusion of the edge vortices at a second pair of Josephson junctions results in
a correlated charge transfer of zero or one electron per cycle, such that the
current at each junction exhibits shot noise, but the difference of the
currents is nearly noiseless.