  The resonant dipole-dipole interaction between highly excited Rydberg levels
dominates the interaction of neutral atoms at short distances scaling as
$1/r^3$. Here we take advantage of the combined effects of strong dipole-dipole
interaction and multifrequency driving fields to propose one type of selective
Rydberg pumping mechanism. In the computational basis of two atoms
$\{|00\rangle, |01\rangle,|10\rangle,|11\rangle\}$, this mechanism allows
$|11\rangle$ to be resonantly pumped upwards to the single-excited Rydberg
states while the transitions of the other three states are suppressed. From the
perspective of mathematical form, we achieve an analogous F\"{o}ster resonance
for ground states of neutral atoms. The performance of this selective Rydberg
pumping is evaluated using the definition of fidelity for controlled-$Z$ gate,
which manifests a characteristic of robustness to deviation of interatomic
distance, fluctuation of F\"{o}ster resonance defect, and spontaneous emission
of double-excited Rydberg states. As applications of this mechanism, we discuss
in detail the preparation of the maximally entangled symmetric state for two
atoms via ground-state blockade, and the maximally entangled antisymmetric
state via engineered spontaneous emission, within the state-of-the-art
experiments, respectively.
