Intensity interferometry with anyons

A pairwise correlation function in relative momentum space is discussed as a tool to characterize the properties of an incoherent source of noninteracting Abelian anyons. This is analogous to the Hanbury-Brown Twiss effect for particles with fractional statistics in two dimensions. In particular, using a flux tube model for anyons, the effects of source shape and quantum statistics on a two-particle correlation function are examined. Such a tool may prove useful in the context of quantum computing and other experimental applications where studying anyon sources are of interest.

Figure 1

$C_{2_{\alpha }}$ vs $q{r}_0$ from a normalized Gaussian source given by Eq. (13) in two dimensions. The curves represent different values of the anyon parameter $\alpha$. The top curve is the boson case $\left(\alpha =0\right)$ and the bottom curve is the fermion case $\left(\alpha =1\right)$. From top to bottom, $\alpha =0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9$, and 1. The source function, plotted in arbitrary units, is shown inset vs $r∕r_0$.

Figure 2

$C_{2_{\alpha }}$ from a normalized step function source given by Eq. (14). The anyon parameterization is the same as in Fig. 1. The source function, plotted in arbitrary units, is inset plotted vs $r∕r_0$.