Weak Measurement Protocols for Majorana Bound State Identification

We propose a continuous weak measurement protocol testing the nonlocality of Majorana bound states through current shot noise correlations. The experimental setup contains a topological superconductor island with three normal-conducting leads weakly coupled to different Majorana states. Putting one lead at finite voltage and measuring the shot noise correlations between the other two (grounded) leads, devices with true Majorana states are distinguished from those without by strong current correlations. The presence of true Majorana states manifests itself in unusually high noise levels or the near absence of noise, depending on the chosen device configuration. Monitoring the noise statistics amounts to a weak continuous measurement of the Majorana qubit and yields information similar to that of a full braiding protocol, but at much lower experimental effort. Our theory can be adapted to different platforms and should allow for the clear identification of Majorana states.

Figure 1

Setup for probing Majorana bound states in a system of topological quantum wires. (Left panel) Three of the Majorana states (dots) on a Majorana-Cooper box with three topological hybrid nanowires connected by a superconducting backbone [14, 15] are tunnel coupled to normal-conducting leads. The schematic on the left indicates that one of the leads ($\alpha =0$) is biased with a voltage $V$ and acts as a source of electrons into the grounded drain leads ($\alpha =1$, 2). Tunable tunnel couplings $t_0$ introduce a direct link between the source and drain leads. Andreev states are distinguished from genuine Majorana states as pairs of MBSs ${\gamma }_{\alpha }^i$ (with $i=1$, 2) centered close to the tunnel interface (see the faded dot, representing an $i=2$ state in the wire 0). The cross-correlation shot noise amplitude $S_{12}$ of the currents $I_1$ and $I_2$ [Eq. (1)] unambiguously distinguishes between the two types of states. (Right panels) The same experiment can be carried out on a wide range of possible device layouts. The two schematics on the right give examples for additional realistic geometries using only two nanowires.