Shot noise in an anyonic Mach-Zehnder interferometer

We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian from non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor (in units of the electron charge) is always lower than unity. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds 1.

Figure 1

Schematic picture of the anyonic Mach-Zehnder interferometer. Arrows indicate the edge mode propagation directions from source S1 to drain D1 and from source S2 to drain D2.

Figure 2

(a) States and transition probabilities in a Laughlin liquid with the filling factor $\nu$. (b) In the $\nu =5∕2$ QHE liquid, each state of the interferometer is labeled by the topological charge of edge 2 and the number of the previous tunneling events mod 4.

Figure 3

The diagram for the calculation of the statistical phase ${\varphi }_{ab}$. Note that the left diagram depends only on the combined topological charge $b$ of the excitations $a$ and $x$, which should be viewed as one composite object at the calculation of that diagram.

Figure 4

The diagram for the calculation of the fusion amplitudes.