Selective Rydberg pumping via strong dipole blockade

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.