  We show that a linear term coupling the atoms of an ultracold binary mixture
provides a simple method to induce an effective and tunable population
imbalance between them. This term is easily realized by a Rabi coupling between
different hyperfine levels of the same atomic species. The resulting effective
imbalance holds for one-particle states dressed by the Rabi coupling and
obtained diagonalizing the mixing matrix of the Rabi term. This way of
controlling the chemical potentials applies for both bosonic and fermionic
atoms and it allows also for spatially and temporally dependent imbalances. As
a first application, we show that, in the case of two attractive fermionic
hyperfine levels with equal chemical potentials and coupled by the Rabi pulse,
the same superfluid properties of an imbalanced binary mixture are recovered.
We finally discuss the properties of m-species mixtures in the presence of
SU(m)-invariant interactions.
