  We analyze the role of impurities in the fractional quantum Hall effect using
a highly controllable system of ultracold atoms. We investigate the mechanism
responsible for the formation of plateaux in the resistivity/conductivity as a
function of the applied magnetic field in the lowest Landau level regime. To
this aim, we consider an impurity immersed in a small cloud of an ultracold
quantum Bose gas subjected to an artificial magnetic field. We consider
scenarios corresponding to experimentally realistic systems with gauge fields
induced either by rotation or by appropriately designed laser fields. Systems
of this kind are adequate to simulate quantum Hall effects in ultracold atom
setups. We use exact diagonalization for few atoms and, to emulate transport
equations, we analyze the time evolution of the system under a periodic
perturbation. We provide a theoretical proposal to detect the up-to-now elusive
presence of strongly correlated states related to fractional filling factors in
the context of ultracold atoms. We analyze the conditions under which these
strongly correlated states are associated with the presence of the
resistivity/conductivity plateaux. Our main result is the presence of a plateau
in a region, where the transfer between localized and non-localized particles
takes place, as a necessary condition to maintain a constant value of the
resistivity/conductivity as the magnetic field increases.

Quantum Gases