Correlated parity measurements as a probe of non-Abelian statistics in one-dimensional superconducting wires

Abstract

We propose a method to detect a signature of non-abelian statistics in a 1D superconducting wire by tuning the effective coupling between a pair of Majorana particles. Our experiment requires a single wire with two segments in the topological superconducting phase, and a total of 4 Majorana particles. We show that an appropriately timed "pulse" in the coupling between the two middle Majoranas leads to a coherent rotation of the two q-bits associated with the pairs of Majoranas in the two TSC segments, in much the same way that an appropriate-length pulse of a transverse magnetic field can be used to rotate spins in NMR. This can be exploited both to probe the correlations of the Majoranas, and to manipulate the Majorana q-bits, in these 1D wires. We discuss the experimental requirements for such a coherent rotation to be observable when the wire system is coupled to a fermionic bath.