  In this article, we present a systematic study of quantum statistics and
dynamics of a pair of anyons in the lowerst Landau level (LLL), of direct
relevance to quasiparticle excitations in the quantum Hall bulk. We develop the
formalism for such a two-dimensional setting of two charged particles subject
to a transverse field, including fractional angular momentum states and the
related algebra stemming from the anyonic boundary condition, coherent state
descriptions of localized anyons, and bunching features associated with such
anyons. We analyze the dynamic motion of the anyons in a harmonic trap,
emphasizing phase factors emerging from exchange statistics. We then describe
non-equilibrium dynamics upon the application of a saddle potential,
elaborating on its role as a squeezing operator acting on LLL coherent states,
and its action as a beam splitter for anyons. Employing these potential
landscapes as building blocks, we analyze anyon dynamics in a quantum Hall bulk
interferometer. We discuss parallels between the presented LLL setting and
other realms, extensively in the context of quantum optics, whose formalism we
heavily borrow from, and briefly in that of black hole phenomena.
