  We study the quantum dynamics of massive impurities embedded in a strongly
interacting two-dimensional atomic gas driven into the fractional quantum Hall
(FQH) regime under the effect of a synthetic magnetic field. For suitable
values of the atom-impurity interaction strength, each impurity can capture one
or more quasi-hole excitations of the FQH liquid, forming a bound molecular
state with novel physical properties. An effective Hamiltonian for such anyonic
molecules is derived within the Born-Oppenheimer approximation, which provides
renormalized values for their effective mass, charge and statistics by
combining the finite mass of the impurity with the fractional charge and
statistics of the quasi-holes. The renormalized mass and charge of a single
molecule can be extracted from the cyclotron orbit that it describes as a free
particle in a magnetic field. The anyonic statistics introduces a statistical
phase between the direct and exchange scattering channels of a pair of
indistinguishable colliding molecules, and can be measured from the angular
position of the interference fringes in the differential scattering cross
section. Implementations of such schemes beyond cold atomic gases are
highlighted, in particular in photonic systems.
