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.
Cited by 2
Aurélien Grabsch et al., Pfaffian Formula for Fermion Parity Fluctuations in a Superconductor and Application to Majorana Fusion Detection
ANNALEN DER PHYSIK 531, 1900129 (2019) [Crossref]
Inanc Adagideli et al., Time-resolved electrical detection of chiral edge vortex braiding
SciPost Phys. 8, 013 (2020) [Crossref]