  Despite the striking progress in the field of quantum gases, one of their
much anticipated application -- the simulation of quantum Hall states --
remains elusive: all experimental approaches so far failed in reaching a
sufficiently small ratio between atom and vortex densities. In this paper we
consider rotating Rydberg--dressed atoms in magnetic traps: these gases offer
strong and tunable non-local repulsive interactions and very low densities;
hence they provide an exceptional platform to reach the quantum Hall regime.
Based on the Lindemann criterion and the analysis of the interplay of the
length scales of the system, we show that there exists an optimal value of the
dressing parameters that minimizes the ratio between the filling factor of the
system and its critical value to enter the Hall regime, thus making it possible
to reach this strongly--correlated phase for more than 1000 atoms under
realistic conditions.
