  A method is proposed to produce atomic ensembles with sub-Poissonian atom
number distributions. The method consists of removing the excess atoms using
the interatomic interactions induced by Rydberg dressing. The selective removal
of atoms occurs via spontaneous decay into untrapped states using an
electromagnetically induced transparency scheme. Ensembles with the desired
number of atoms can be produced almost deterministically. Numerical simulations
predict a strong reduction of the atom number fluctuations, with the variance
twenty times less than the Poisson noise level (the predicted Fano factor is F
= 0.05). Strikingly, the method is suitable for both fermions and bosons. It
solves the problem of the atom-number fluctuations in bosons, whose weak
interactions have usually been an obstacle to controlling the number of atoms.
