Correlations and beam splitters for quantum Hall anyons

We study the system of two localized anyons in the lowest Landau level and show how anyonic signatures extrapolating between antibunching tendencies of fermions and bunching tendencies of bosons become manifest in the two-particle correlations. Toward probing these correlations, we discuss the influence of a saddle potential on these anyons; we exploit analogies from quantum optics to analyze the time evolution of such a system. We show that the saddle potential can act as a beam-splitter akin to those in bosonic and fermionic systems, and can provide a means of measuring the derived anyonic signatures.

Figure 1

(Color online)The bunching parameter as a function of the dimensionless distance between particles $\left|z\right|$ for different values of anyonic phase $\alpha$. Curves from the topmost along the $y$ axis correspond to values $\alpha =1$, $\alpha =3/5$, $\alpha =1/3$, and $\alpha =0$. Inset: the value $z_0$ as a function of $\alpha$, where $\chi \left(\left|z_0\right|,\alpha \right)=0$ determines the crossover between antibunching and bunching behavior.