  Non-Abelian excitations are an interesting feature of many fractional quantum
Hall phases, including those phases described by the Moore-Read (or Pfaffian)
wave function. However, the detection of the non-Abelian quasiparticles is
challenging. Here, we consider a system described by the Moore-Read wave
function, and assume that impurity particles bind to its quasiholes. Then, the
angular momentum of the impurities, reflected also by the impurity density,
provides a useful witness of the physics of the non-Abelian excitations. By
demanding that the impurities are constrained to the lowest Landau level, we
are able to write down the corresponding many-body wave function describing
both the Moore-Read liquid and the impurities. Through Monte Carlo sampling we
determine the impurity angular momentum, and we show that it suggests a
quantum-statistical parameter $\alpha = a\nu -b +P/2$ for the quasiholes, where
$\alpha$ ranges from $0$ for bosons to $1$ for fermions. A reasonable agreement
with the Monte Carlo results is obtained for $a=1/4$, $b=1/8$ and $P=0,1$
depending on the parity of the particle number in the Moore-Read liquid. This
parity-dependence of the angular momentum serves as an unambiguous
demonstration of the non-Abelian nature of the excitations. In addition to the
studies of excitations in the Moore-Read liquid, we also apply our scheme to
Laughlin liquids, for which we focus on interacting bosonic impurities. With
this, the impurities themselves form Laughlin states, which allows for a study
of hierarchical fractional quantum Hall states.
